ChemWiki - User contributions [en]

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T15:44:53Z

Mwb11: /* Further Study */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirable physical properties for synthetic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The inductive effect of the nitrogen atom via the sigma framework of the molecule also depends on the strength of the orbital overlap between the nitrogen an carbon atoms, as both atoms are in the same row of the periodic table we can expect that there will be good overlap between the orbitals. The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overall positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In [P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. This is also due to the fact there is a weaker orbital overlap between the second row carbon atom and third row phosphorous atom (due to mismatch of orbital sizes) and so there is a weaker lone pair donation onto the carbon atom, leading to the large positive charge on the phosphorous atom. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In [S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. This is also due to the fact that there is a weaker overlap between the second row carbon orbitals and the third row sulphur orbitals, leading to a weaker lone pair donation and so more of the positive charge is localised on the sulphur atom. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (anti-periplanar) hydrogen atoms have a less positive value whilst the equitorial (syn-periplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the anti-periplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the anti-periplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and hetero-atom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Second order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|150px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawal effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawal effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbital, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor and so will interact with an anion more strongly, leading to a higher thermal stability and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indicative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were initially investigated via computational methods and their physical properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

===Further Study===

Research into the effects of hydrogen bonding due to the hydroxy group in the [N(CH3)3(CH2OH)]+ molecule could be done in order to determine how much this phenomenon effects the shapes of the MOs and so the molecules HOMO-LUMO energy gap. The cations could also be modeled in gaussian coordinating with an anion to show how this also effects the HOMO-LUMO energy gap of the molecules and so their chemical and physical properties as ionic liquids.

==References==
<references/>

Rep:Mod:MWBINORAGNIC

2014-03-07T15:39:55Z

Mwb11: /* Frequency analysis for BH3 and GaBr3 */

==Optimisation of BH3==

BH3 was optimised using 3-21G basis set and then re-optimised with a higher level basis set of 6-31G(d,p) using B3LYP method. Before optimisations B-H bond lengths were set to 1.55 Å, 1.54 Å and 1.53 Å in Gaussview. After this the two basis sets used in each optimisation were compared in order to determine the success of each method.

===Optimisation with 3-21G basis set===

{| class="wikitable"
|+ BH3 Optimisation Summary
|-
! Property
! Output
|-
|File Name
|MWBBH3optimisation
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|3-21G
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -26.46226429 a.u.
|-
|RMS Gradient Norm
|0.00008851 a.u.
|-
|Dipole Moment
|0.0003 Debye
|-
|Point Group
|CS
|-
|Job cpu time
|16.0 seconds
|-
|}

<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>

The optimisation has converged therefore a stationary point has been found on the BH3 potential energy surface.

The optimisation file is linked [[Media:MWBBH3OPTIMISATION.LOG| here]]

[[File:BH3energy graph1part2.png|400px|thumb|center|Potential energy surface of BH3]]

[[File:BH3energy graph3.png|400px|thumb|center|Root mean square gradient of BH3]]

The RMS (root mean square) gradient of the second graph gives the energy of the BH3 molecule at each step of the optimisation performed. This corresponds to finding the sum of the energy gradient divided by the sum of the distance parameter gradient at each point and traversing the potential energy surface of the BH3 molecule to find the critical point at which the gradient is zero. This corresponds to a minima or maxima, through frequency analysis this can be determined and if a minimum is found this is due to the lowest energy optimised structure of BH3. The graphs show the result of solving the Schrodinger equation after each optimisation step, moving towards the lowest energy state of the molecule.

[[File:RMS gradient equation.png|200px|thumb|center|Root mean square gradient equation]]

[[File:BH3optimisationmovie.gif|400px|thumb|center|Optimisation steps of BH3]]

The movie above shows the optimisation steps of the BH3 molecule, it is important to note that the first structure has no visible bonds which highlights the fact that Gaussian visualises bonds based on distance dependent criteria. In fact the bond is present, albeit longer than the accepted pre-defined value.

===Optimisation with 6-31G(d,p) basis set===

{| class="wikitable"
|+ BH3 Optimisation Summary
|-
! Property
! Output
|-
|File Name
|MWBBH3OPTIMISATION631gdp
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|6-31G(d,p)
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -26.61532360 a.u.
|-
|RMS Gradient Norm
|0.00000707 a.u.
|-
|Dipole Moment
|0.00 Debye
|-
|Point Group
|CS
|-
|Job cpu time
|6.0 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069047D-09
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the BH3 potential energy surface.

The optimisation file is linked [[Media:MWBBH3OPTIMISATION631GDP5.LOG| here]]

{| class="wikitable"
|+ BH3 Summary
|-
! Property
! Value
|-
| Optimised average Bond length (Å)
| 1.19
|-
| Optimised average Bond angle (H-B-H,°)
| 120.0
|-
|}

The literature value of the B-H bond length was found to be 1.190 Å which matches well with the computed value, but could be improved further by use of a larger basis set.<ref>Kawaguchi Kentarou,''Fourier transform infrared spectroscopy of the BH3 ν3 band'', Journal of Chemical Physics, 1992, '''96''' (5),3411</ref>

Energies of molecules can only be compared if they have the same number of atoms and with exactly the same basis-set used on every atom. The energy difference the between the two optimisations using different basis sets was 0.15305931 a.u., which is about 402 kJ/mol. This is a large amount of energy and so comparisons between the basis sets are not valid and have no quantitative significance. However it can be seen that the the 6-31G(d,p) basis set gives a much better approximation than the 3-21G basis set as the 6-31G double-zeta basis set includes two polarisation functions which account for the distortion of orbitals from their ideal shapes and so gives an overall more accurate description.

===GaBr3 Optimisation===

GaBr3 was constrained to a D3h geometry and was optimised using a medium level LanL2DZ basis set and B3LYP method, which includes pseudo potentials applied to heavier non first row atoms due to the increase in electron density in gallium compared to boron. This can cause the system to exhibit relativistic effects which cannot be recovered by the standard Schrodinger equation and so pseudo potentials are used to account for this.

{| class="wikitable"
|+ GaBr3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|log_88461(1)
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|LANL2DZ
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -41.70082783 a.u.
|-
|RMS Gradient Norm
|0.00000016 a.u.
|-
|Dipole Moment
|0.00 Debye
|-
|Point Group
|D3H
|-
|Job cpu time
|27.8 seconds
|-
|}

<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=-1.282680D-12
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the GaBr3 potential energy surface.

The optimisation file is linked [[Media:Log 88461(1).log| here]]

{| class="wikitable"
|+ GaBr3 Summary
|-
! Property
! Value
|-
| Optimised average Bond length (Å)
| 2.35
|-
| Optimised average Bond angle (Br-Ga-Br,°)
| 120.0
|-
|}

The GaBr3 monomer has a literature bond length of 2.250 Å which is in good agreement with the computed value, however a more accurate value could be obtained by using a larger basis set in the optimisation.<ref> Balazs Reffy, Maria Kolonits and Magdolna Hargittai,''Gallium tribromide: molecular geometry of monomer and dimer from gas-phase electron diffraction'', Journal of Molecular Structure, 1998, '''445''', 139</ref>

===BBr3 Optimisation===

BBr3 molecule was optimised using the GEN basis set, a pseudo potential was also applied to the Br atoms by using the keyword "pseudo=read gfinput", the LanL2DZ basis set was used for the bromine atoms while the 6-31G(d,p) basis set was used for boron.

{| class="wikitable"
|+ BBr3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|BBr3optGEN
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|Gen
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -64.43644911 a.u.
|-
|RMS Gradient Norm
|0.00000968 a.u.
|-
|Dipole Moment
|0.00 Debye
|-
|Point Group
|CS
|-
|Job cpu time
|38.9 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000112 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.260115D-09
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the BBr3 potential energy surface.

The optimisation file is linked [[Media:BBr3optGEN.log| here]]

{| class="wikitable"
|+ BBr3 Summary
|-
! Property
! Value
|-
| Optimised average Bond length (Å)
| 1.93
|-
| Optimised average Bond angle (Br-B-Br,°)
| 120.0
|-
|}

The BBr3 monomer has a literature bond length of 1.904 Å which is in good agreement with the computed value, however a more accurate value could be obtained by using a larger basis set in the optimisation.<ref> Martinsen, Kjell-Gunnar; Vogt, Natalja; Volden, Hans Vidar; Lyutsarev, Vasilii S. and Vogt, Jurgen,''Molecular structure and force field of boron tribromide as determined from combined analysis of gas electron diffraction and spectroscopic data and supported by quantum-chemical density-functional calculations'', Journal of Molecular Structure, 1996, '''385''' (3), 159</ref>

===Bond Comparison===

{| class="wikitable"
|+ Bond comparison Summary
|-
! Molecule
! Bond length (Å)
|-
| BH3
| 1.19
|-
| BBr3
| 1.93
|-
| GaBr3
| 2.35
|-
|}

On changing the ligand from H to Br, in the case of boron as the central atom, had the effect of weakening and lengthing the bond. Both atoms act as X-type ligands, donating one electron to form a single bond between itself and the central atom. The larger B-Br bond is due to the fact that bromine is a heavier and more electronegative atom and so has more electrons and more diffuse orbitals which forms longer and more polarised bonds than the hydrogen atom. This leads to weaker orbital overlap between the bromine and boron orbitals and so to a weaker and longer bond.

B and Ga are both group 13 elements and so both form single bonds with a trigonal planer structure with bromine. On changing the central atom from B to a heavier Ga atom, the bond was seen to weaken and increase in length. This is due to the fact that Ga has larger more diffuse orbitals compared to boron and so the orbital overlap between the central atom and the Br ligands is weaker, which results in a larger bond length than the B-Br bond.

===Bond Discussion===

In optimisation calculations it is important to note that some structures have no visible bonds which highlights the fact that Gaussian visualises bonds based on distance dependent criteria. The bond is in fact present, albeit longer than the accepted pre-defined value.

A bond is the directional net attractive force between two atoms,which is a stabilising interaction, and so the total energy of the bond has a lower energy than the separated atoms. A bond is usually an electrostatic interaction between two atoms, as seen in ionic bonding, which results from the transfer of electrons from an electropositve atom to an electronegative atom causing the formation of an anion and cation pair which bond to each other through electrostatic attraction. In the case of covalent bonding, a bond is formed through the sharing of one or more pair of valence electrons between two atoms and the resulting electrostatic attraction between the atoms nuclei and the shared pair of electrons. Metallic bonding is described as the non-directional electrostatic attractions between the cationic metal centres and "sea of electrons" donated from the valence metal orbitals.

Another type of bonding can be described which are much weaker than conventional bonds, these are so called non-covalent interactions. An example of this is a hydrogen bond which is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X-H where X is more electronegative than H and so an electrostatic force is seen via a dipole-dipole interaction.

==Frequency analysis for BH3 and GaBr3==

Frequency analysis was performed on BH3 and GaBr3 in order to compare the vibrational modes of the two molecules.

===BH3 Frequency Calculation===

It was found that when the frequency analysis was performed on the symmetry broken BH3 molecule, which was used in previous calculations, the energy did not converge well to the minimum as the low frequency values were greater than +/- 15cm-1. This indicated a large deviation of the centre of mass translational and rotational frequencies from the accepted values and showed a minimum in the potential energy surface was not found. Therefore BH3 with D3h symmetry was optimised using DFT 6-31G(d,p) basis set and the frequency calculation was run on this.

{| class="wikitable"
|+ BH3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|MWBBH3OPTIMISATION631GDPFREQ5
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|6-31G(d,p)
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -26.61532364 a.u.
|-
|RMS Gradient Norm
|0.00000215 a.u.
|-
|Dipole Moment
|0.00 Debye
|-
|Point Group
|D3H
|-
|Job cpu time
|7.0 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069047D-09
Optimization completed.
-- Stationary point found.
</pre>

The optimisation file is liked to [[Media:MWBBH3OPTIMISATION631GDP.LOG| here]]

The optimisation has converged therefore a stationary point has been found on the BH3 potential energy surface.

<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>

The frequency calculation file is liked to [[Media:MWBBH3OPTIMISATION631GDPFREQ5.LOG| here]]

Here we can see that the low frequencies are not negative and so a minimum energy structure has been found, with the second derivative of the potential energy surface for BH3 being positive, therefore avoiding finding a possible transition state structure.

{| class="wikitable" style="text-align:center"
|+ Vibrational modes of BH3
|-
! No. !! Form of the vibration !! Frequency !! Intensity !! Symmetry D3h point group
|-
| 1 || [[File:MWBBIDWELL Bh3 freq vibrations 1.gif|300px|thumb|center|The hydrogen atoms are moving in a concerted motion out of the plane of the BH3 molecule, with the boron atom moving slightly in the opposite direction]] || 1163 || 93 || A2"
|-
| 2 || [[File:Bh3_freq_vibrations_2.gif|300px|thumb|center|All three of the hydrogen atoms are moving left to right in the plane of the molecule, creating two scissoring motions, with the boron atom remaining stationary]] || 1213 || 14 || E'
|-
| 3 || [[File:Bh3_freq_vibrations_3.gif|300px|thumb|center|Two hydrogens are moving in a scissoring motion with the other hydrogen moving slightly up and down with the central atom]] || 1213 || 14 || E'
|-
| 4 || [[File:Bh3_freq_vibrations_4.gif|300px|thumb|center|The three hydrogens are symmetrically stretching in a concerted motion in the plane of the molecule with the boron atom remaining stationary]] || 2583 || 0 || A1'
|-
| 5 || [[File:Bh3_freq_vibrations_5.gif|300px|thumb|center|Two hydrogens are asymmetrically stretching in the plane of the molecule with the boron atom and the remaining hydrogen moving from left to right with the stretches]] || 2716 || 126 || E'
|-
| 6 || [[File:Bh3_freq_vibrations_6.gif|300px|thumb|center|Two of the hydrogens are stretching in a symmetric fashion while the other hydrogen is asymmetrically stretching with respect to them. The boron atom also moves up and down slightly]] || 2716 || 126 || E'
|}

[[File:MWB IR spectrum BH3.svg|500px|thumb|center|IR spectrum of BH3]]

There are only three peaks in the IR spectrum of BH3 as two sets of two of the vibrations are degenerate with the same vibrational frequencies and intensities they overlap and correspond to one peak each(this is seen for the two E' symmetry labelled peaks at 1213 and 2716 cm-1). The symmetrical stretching vibrational mode has no dipole moment and so is IR inactive, therefore doesn't show a peak in the IR spectrum. The remaining peak corresponds to the A2" symmetry labelled bending mode at 1163 cm-1 . Therefore we can see why six vibrations in the BH3 molecule only produce three peaks in the IR spectrum.

===GaBr3 Frequency calculation===

Frequency analysis was performed on the previously optimised GaBr3 so that the vibrational modes of the molecule could be inspected, low frequency values were shown to be less than +/- 15cm-1, therefore it can be said with some confidence that the minimum energy structure was found.

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

The frequency calculation file is liked to [[Media:GABR3FREQTHISTIMEWORK.LOG| here]]

Here we can see that the low frequencies are not negative and so a minimum energy structure has been found, with the second derivative of the potential energy surface for GaBr3 being positive.

{| class="wikitable" style="text-align:center"
|+ Vibrational modes of GaBr3
|-
! No. !! Form of the vibration !! Frequency !! Intensity !! Symmetry D3h point group
|-
| 1 || [[File:Mwb11GaBr2_movie_1.gif|300px|thumb|center|All three of the bromine atoms are moving left to right in the plane of the molecule, creating two scissoring motions, with the gallium atom remaining stationary]] || 76 || 3 || E'
|-
| 2 || [[File:Mwb11GaBr2_movie_2.gif|300px|thumb|center|Two bromines are moving in a scissoring motion with the other bromine moving slightly up and down with the central atom]] || 76 || 3 || E'
|-
| 3 || [[File:Mwb11GaBr2_movie_3.gif|300px|thumb|center|The bromine atoms are moving in a concerted motion out of the plane of the GaBr3 molecule, with the gallium atom moving slightly in the opposite direction]] || 100 || 9 || A2"
|-
| 4 || [[File:Mwb11GaBr2_movie_4.gif|300px|thumb|center|The three bromines are symmetrically stretching in a concerted motion in the plane of the molecule with the gallium atom remaining stationary]] || 197 || 0 || A1'
|-
| 5 || [[File:Mwb11GaBr2_movie_5.gif|300px|thumb|center|Two bromines are asymmetrically stretching in the plane of the molecule with the gallium atom and the remaining bromine atom moving from left to right with the stretches]] || 316 || 57 || E'
|-
| 6 || [[File:Mwb11GaBr2_movie_6.gif|300px|thumb|center|Two of the bromines are stretching in a symmetric fashion while the other bromine atom is asymmetrically stretching with respect to them. The gallium atom also moves up and down with the strecthes.]]|| 316 || 57 || E'
|}

[[File:IR spectrum GaBr3.svg|400px|thumb|center|IR Spectrum of GaBr3]]

There are three peaks in the IR spectrum of GaBr3 as the two sets of the two E' symmetry labelled vibrations are degenerate with the same vibrational frequencies and intensities. They overlap and correspond to one peak each at 76 and 316 cm-1 wave-numbers respectively. The symmetrical stretching vibrational mode with A1' symmetry has no dipole moment and so is IR inactive, therefore doesn't show a peak in the IR spectrum. The remaining peak corresponds to the A2" symmetry labelled bending mode at 100 cm-1 . Therefore just as with BH3 we can see why six vibrational modes in the GaBr3 molecule only produce three peaks in the IR spectrum.

The lowest real normal vibrational mode is due to the peak at 76 cm-1 with the E' symmetry element.

===Vibrational comparison===

{| class="wikitable"
|+ Vibrational mode Summary
|-
! No.
! BH3 Vibrational frequencies (cm-1)
! GaBr3 Vibrational frequencies (cm-1)
|-
|1
|1163
|76
|-
|2
|1213
|76
|-
|3
|1213
|100
|-
|4
|2583
|197
|-
|5
|2716
|316
|-
|6
|2716
|316
|-
|}

The large difference in frequency values between BH3 and GaBr3 indicates that the GaBr3 molecule has weaker bonds, which is due to the poorer orbital overlap of the Ga sp2 orbital with Br and a larger difference in electronegativty compared with B and H leading to a more polarised and weaker bond. The difference in frequency values also stems from the fact that the Ga-Br bond has a much higher reduced mass than the B-H bond due to the fact the atoms are much heavier, this relationship can be seen in the equation below.

[[File:MWB frequency equation.png|300px|thumb|center|Vibrational frequency equation]]

It can be seen from the comparison of the vibrational modes of both molecules that a reordering of modes has occured, the A2" mode in GaBr3 is higher in energy than the degenerate E' mode, which is the opposite way around in the BH3 molecule. This is due to the fact that in the GaBr3 molecule the Br ligands are heavier than the central Ga atom and so remain much more stationary relative to the Ga atom vibrating up and down. This is reversed in the case of BH3 as the H atoms are much lighter than the B atom and so they vibrate more than the relatively stationary central atom in the A2" mode. This differnce leads to the relative shift and reordering of energies in the E' and A2" vibrational modes. However the two spectra are similar as they both have three peaks due to the fact that both molecules have D3h symmetry and four atoms, leading to both spectra having 3N-6 (N=4) vibrational modes. It can also be seen that in both spectra the A2" and E' modes at low energy, and also the A1' and E' modes at higher energy, lie close together. This is due to the fact that the lower energy vibrations are both bending vibrational modes and the higher energy vibrations are both stretching modes.

The same method and basis set must be used for both optimisation and frequency analysis to ensure that the frequency calculations can be performed on the same potential energy surface that the molecule was optimised one so that the values obtained are meaningful. The purpose of carrying out a frequency analysis is to ensure a minimum in the potential energy surface for the molecule has been found, and also that the computationally obtained results can be compared to experimental findings to check the accuracy of the computational methods employed. Low frequencies represent the centre of mass motion of the molecule through the three translational and three rotational eigenvalues reported, and theoretically should equal zero, however in this case they are within an accepted range of +/-15cm-1 which corresponds to a well optimised molecule at an energy minimum.

===Molecular Orbitals of BH3===

A population analysis was done using the previously optimised BH3 molecule with 6-31G(d,p)basis and B3LYP method with keywords pop=full, opt=tight, int=ultrafine, scf=conver=9.

The population analysis file is liked to [[Media:BH3OPTENERGYMOB3LYP6-31G.LOG| here]]

[[File:MWB2 BH3 MO diagram.jpg|400px|thumb|center|MO diagram of BH3]]

The real MOs computed by Gaussian match up well with the LCAO MOs predicted by MO theory. This shows us that for small molecules like BH3 qualitative MO theory is accurate, however for larger molecules deviations would be expected due to larger basis sets needed to model the molecule accurately.

===NBO Analysis for NH3===

NH3 was optimised using the 6-31G(d,p) basis set and B3LYP method using keywords opt=tight, int=ultrafine, scf=conver=9. As the molecule is small a higher level basis set can be used straight away to model it.

{| class="wikitable"
|+ NH3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|NH3optmisation631gdpFREQ
|-
|File Type
|.log
|-
|Calculation Type
|FREQ
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|6-31G(d,p)
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -56.55776872 a.u.
|-
|RMS Gradient Norm
|0.00000322 a.u.
|-
|Dipole Moment
|1.85 Debye
|-
|Point Group
|C3
|-
|Job cpu time
|9.0 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000015 YES
RMS Force 0.000004 0.000010 YES
Maximum Displacement 0.000012 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-9.845967D-11
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the NH3 potential energy surface.

The optimisation calculation file is liked to [[Media:NH3OPTMISATION631GDP.LOG| here]]

<pre>
Low frequencies --- -0.0137 -0.0025 0.0014 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

Here we can see that the low frequencies are not negative and so a minimum energy structure has been found, with the second derivative of the potential energy surface for NH3 being positive.

The frequency calculation file is liked to [[Media:NH3OPTMISATION631GDPFREQ.LOG| here]]

[[File:MWB NH3 Charge distribution.png|400px|thumb|center|Charge Distribution of NH3]]

Charge range is from -1.125 to +1.125, it can be seen that the nitrogen atom has a highly negative charge as expected, as it has a much larger electronegativity value than the hydrogen atoms.

[[File:MWB NH3 Charge distribution numbers.png|400px|thumb|center|Charge Distribution values of NH3]]

Above the charge distribution values for the individual atoms are shown (-1.125 for N, and +0.375 for the H atoms). The sum of the charges add up to zero which confirms the fact that NH3 is a neutral molecule.

The population analysis file is liked to [[Media:NH3OPTMISATION631GDPENERGYMO.LOG| here]]

===Summary of Natural Population Analysis===

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
N 1 -1.12514 1.99982 6.11104 0.01429 8.12514
H 2 0.37505 0.00000 0.62250 0.00246 0.62495
H 3 0.37505 0.00000 0.62250 0.00246 0.62495
H 4 0.37505 0.00000 0.62250 0.00246 0.62495
=======================================================================
* Total * 0.00000 1.99982 7.97852 0.02166 10.00000
</pre>

The charge distribution for the atoms are shown as above, the majority of the electron density is seen to be located on the central nitrogen atom, which acts as a Lewis base, donating electron density into the hydrogen orbitals.

===(Occupancy) Bond orbital/ Coefficients/ Hybrids===

<pre>
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0014
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0014
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0014
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310<
</pre>

The information in the table above shows that the electron density in the two centre two electron bonds are primary from the nitrogen atom orbitals which makes up 69% of the bond and have a hybridisation of 25%s+75%p, whilst 31% of the electron density of the bond comes from the H orbital which is 100%s.

===Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis===

<pre>
Threshold for printing: 0.50 kcal/mol
</pre>

This table summarises interactions from bonding NBOs into non-bonding or antibonding orbitals. However it is not of interest as the value is below 20 kcal/mol.

===Natural Bond Orbitals (Summary)===

<pre>
Principal Delocalizations
NBO Occupancy Energy (geminal,vicinal,remote)
====================================================================================
Molecular unit 1 (H3N)
1. BD ( 1) N 1 - H 2 1.99909 -0.60417
2. BD ( 1) N 1 - H 3 1.99909 -0.60417
3. BD ( 1) N 1 - H 4 1.99909 -0.60417
4. CR ( 1) N 1 1.99982 -14.16768
5. LP ( 1) N 1 1.99721 -0.31757 16(v),20(v),24(v),17(v)
</pre>

The table above summarises the energy and occupation of the N-H bonds, and the nitrogen lone pair. All the N-H bonds are at the same energy of -0.6 a.u., whereas the core nitrogen orbital is higher in energy with an energy of -14.2 a.u. This is why we leave the core orbitals off an MO diagram, as they are very deep in energy compared to the valence orbitals and so are low-lying enough to be irrelevant in terms of the valence bonding scheme.

===Association energies: Ammonia-Borane===

In the molecule the nitrogen atom formally donates two electrons to the boron atom. However in reality the electrons are shared between the boron and nitrogen, this was shown in the NBO analysis above.

NH3BH3 was optimised using the 6-31G(d,p) basis set and B3LYP method with the keywords opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ NH3BH3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|NH3BH3optimisation631Gdp
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|6-31G(d,p)
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -83.22468908 a.u.
|-
|RMS Gradient Norm
|0.00000138 a.u.
|-
|Dipole Moment
|5.56 Debye
|-
|Point Group
|C1
|-
|Job cpu time
|1 minutes 30.0 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-1.180805D-10
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the NH3BH3 potential energy surface.

The optimisation calculation file is liked to [[Media:NH3BH3OPTIMISATION631GDP.LOG| here]]

<pre>
Low frequencies --- -2.9451 -0.0014 -0.0011 -0.0010 1.7800 3.7236
Low frequencies --- 263.3834 632.9581 638.4631
</pre>

Here we can see that the low frequencies are not negative and so a minimum energy structure has been found, with the second derivative of the potential energy surface for NH3BH3 being positive.

The frequency calculation file is liked to [[Media:NH3BH3OPTIMISATION631GDPFREQ.LOG| here]]

===Association energy calaculations===

An analysis of the bond association energy of the combination of NH3 and BH3 to form NH3BH3 is provided below.

{| class="wikitable"
|+ Association energies
|-
! Molecule
! Energy (a.u.)
|-
| NH3
| -56.55776872
|-
| BH3
| -26.61532364
|-
| NH3BH3
| -83.22468908
|-
|}

The association energy of NH3 and BH3 can be calculated by using the following equation:

ΔE = E(NH3BH3) − [(E(BH3) + E(NH3)]

ΔE = -83.22468908(a.u.) - [( -26.61532364(a.u.)) + ( -56.55776872(a.u.)]

ΔE = − 0.05159672(a.u.)

The energy value was then converted from Hartrees to kJ/mol by multiplying by a conversion factor of 2625.50 producing a value of ΔE = -135.46719868 kJ/mol. Conversely we can see that the value of NH3BH3 dissociation bond energy is +135.46719868 kJ/mol.

This value of the bond association energy is a reasonable value as it is within the usual range of bond energies being hundreds of kJ/mol, roughly 100-600 kJ/mol for common molecules.

==References==

<references/>

Rep:Mod:MWBINORAGNIC

2014-03-07T15:38:24Z

Mwb11: /* Optimisation of BH3 */

==Optimisation of BH3==

BH3 was optimised using 3-21G basis set and then re-optimised with a higher level basis set of 6-31G(d,p) using B3LYP method. Before optimisations B-H bond lengths were set to 1.55 Å, 1.54 Å and 1.53 Å in Gaussview. After this the two basis sets used in each optimisation were compared in order to determine the success of each method.

===Optimisation with 3-21G basis set===

{| class="wikitable"
|+ BH3 Optimisation Summary
|-
! Property
! Output
|-
|File Name
|MWBBH3optimisation
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|3-21G
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -26.46226429 a.u.
|-
|RMS Gradient Norm
|0.00008851 a.u.
|-
|Dipole Moment
|0.0003 Debye
|-
|Point Group
|CS
|-
|Job cpu time
|16.0 seconds
|-
|}

<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>

The optimisation has converged therefore a stationary point has been found on the BH3 potential energy surface.

The optimisation file is linked [[Media:MWBBH3OPTIMISATION.LOG| here]]

[[File:BH3energy graph1part2.png|400px|thumb|center|Potential energy surface of BH3]]

[[File:BH3energy graph3.png|400px|thumb|center|Root mean square gradient of BH3]]

The RMS (root mean square) gradient of the second graph gives the energy of the BH3 molecule at each step of the optimisation performed. This corresponds to finding the sum of the energy gradient divided by the sum of the distance parameter gradient at each point and traversing the potential energy surface of the BH3 molecule to find the critical point at which the gradient is zero. This corresponds to a minima or maxima, through frequency analysis this can be determined and if a minimum is found this is due to the lowest energy optimised structure of BH3. The graphs show the result of solving the Schrodinger equation after each optimisation step, moving towards the lowest energy state of the molecule.

[[File:RMS gradient equation.png|200px|thumb|center|Root mean square gradient equation]]

[[File:BH3optimisationmovie.gif|400px|thumb|center|Optimisation steps of BH3]]

The movie above shows the optimisation steps of the BH3 molecule, it is important to note that the first structure has no visible bonds which highlights the fact that Gaussian visualises bonds based on distance dependent criteria. In fact the bond is present, albeit longer than the accepted pre-defined value.

===Optimisation with 6-31G(d,p) basis set===

{| class="wikitable"
|+ BH3 Optimisation Summary
|-
! Property
! Output
|-
|File Name
|MWBBH3OPTIMISATION631gdp
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|6-31G(d,p)
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -26.61532360 a.u.
|-
|RMS Gradient Norm
|0.00000707 a.u.
|-
|Dipole Moment
|0.00 Debye
|-
|Point Group
|CS
|-
|Job cpu time
|6.0 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069047D-09
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the BH3 potential energy surface.

The optimisation file is linked [[Media:MWBBH3OPTIMISATION631GDP5.LOG| here]]

{| class="wikitable"
|+ BH3 Summary
|-
! Property
! Value
|-
| Optimised average Bond length (Å)
| 1.19
|-
| Optimised average Bond angle (H-B-H,°)
| 120.0
|-
|}

The literature value of the B-H bond length was found to be 1.190 Å which matches well with the computed value, but could be improved further by use of a larger basis set.<ref>Kawaguchi Kentarou,''Fourier transform infrared spectroscopy of the BH3 ν3 band'', Journal of Chemical Physics, 1992, '''96''' (5),3411</ref>

Energies of molecules can only be compared if they have the same number of atoms and with exactly the same basis-set used on every atom. The energy difference the between the two optimisations using different basis sets was 0.15305931 a.u., which is about 402 kJ/mol. This is a large amount of energy and so comparisons between the basis sets are not valid and have no quantitative significance. However it can be seen that the the 6-31G(d,p) basis set gives a much better approximation than the 3-21G basis set as the 6-31G double-zeta basis set includes two polarisation functions which account for the distortion of orbitals from their ideal shapes and so gives an overall more accurate description.

===GaBr3 Optimisation===

GaBr3 was constrained to a D3h geometry and was optimised using a medium level LanL2DZ basis set and B3LYP method, which includes pseudo potentials applied to heavier non first row atoms due to the increase in electron density in gallium compared to boron. This can cause the system to exhibit relativistic effects which cannot be recovered by the standard Schrodinger equation and so pseudo potentials are used to account for this.

{| class="wikitable"
|+ GaBr3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|log_88461(1)
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|LANL2DZ
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -41.70082783 a.u.
|-
|RMS Gradient Norm
|0.00000016 a.u.
|-
|Dipole Moment
|0.00 Debye
|-
|Point Group
|D3H
|-
|Job cpu time
|27.8 seconds
|-
|}

<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=-1.282680D-12
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the GaBr3 potential energy surface.

The optimisation file is linked [[Media:Log 88461(1).log| here]]

{| class="wikitable"
|+ GaBr3 Summary
|-
! Property
! Value
|-
| Optimised average Bond length (Å)
| 2.35
|-
| Optimised average Bond angle (Br-Ga-Br,°)
| 120.0
|-
|}

The GaBr3 monomer has a literature bond length of 2.250 Å which is in good agreement with the computed value, however a more accurate value could be obtained by using a larger basis set in the optimisation.<ref> Balazs Reffy, Maria Kolonits and Magdolna Hargittai,''Gallium tribromide: molecular geometry of monomer and dimer from gas-phase electron diffraction'', Journal of Molecular Structure, 1998, '''445''', 139</ref>

===BBr3 Optimisation===

BBr3 molecule was optimised using the GEN basis set, a pseudo potential was also applied to the Br atoms by using the keyword "pseudo=read gfinput", the LanL2DZ basis set was used for the bromine atoms while the 6-31G(d,p) basis set was used for boron.

{| class="wikitable"
|+ BBr3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|BBr3optGEN
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|Gen
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -64.43644911 a.u.
|-
|RMS Gradient Norm
|0.00000968 a.u.
|-
|Dipole Moment
|0.00 Debye
|-
|Point Group
|CS
|-
|Job cpu time
|38.9 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000112 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.260115D-09
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the BBr3 potential energy surface.

The optimisation file is linked [[Media:BBr3optGEN.log| here]]

{| class="wikitable"
|+ BBr3 Summary
|-
! Property
! Value
|-
| Optimised average Bond length (Å)
| 1.93
|-
| Optimised average Bond angle (Br-B-Br,°)
| 120.0
|-
|}

The BBr3 monomer has a literature bond length of 1.904 Å which is in good agreement with the computed value, however a more accurate value could be obtained by using a larger basis set in the optimisation.<ref> Martinsen, Kjell-Gunnar; Vogt, Natalja; Volden, Hans Vidar; Lyutsarev, Vasilii S. and Vogt, Jurgen,''Molecular structure and force field of boron tribromide as determined from combined analysis of gas electron diffraction and spectroscopic data and supported by quantum-chemical density-functional calculations'', Journal of Molecular Structure, 1996, '''385''' (3), 159</ref>

===Bond Comparison===

{| class="wikitable"
|+ Bond comparison Summary
|-
! Molecule
! Bond length (Å)
|-
| BH3
| 1.19
|-
| BBr3
| 1.93
|-
| GaBr3
| 2.35
|-
|}

On changing the ligand from H to Br, in the case of boron as the central atom, had the effect of weakening and lengthing the bond. Both atoms act as X-type ligands, donating one electron to form a single bond between itself and the central atom. The larger B-Br bond is due to the fact that bromine is a heavier and more electronegative atom and so has more electrons and more diffuse orbitals which forms longer and more polarised bonds than the hydrogen atom. This leads to weaker orbital overlap between the bromine and boron orbitals and so to a weaker and longer bond.

B and Ga are both group 13 elements and so both form single bonds with a trigonal planer structure with bromine. On changing the central atom from B to a heavier Ga atom, the bond was seen to weaken and increase in length. This is due to the fact that Ga has larger more diffuse orbitals compared to boron and so the orbital overlap between the central atom and the Br ligands is weaker, which results in a larger bond length than the B-Br bond.

===Bond Discussion===

In optimisation calculations it is important to note that some structures have no visible bonds which highlights the fact that Gaussian visualises bonds based on distance dependent criteria. The bond is in fact present, albeit longer than the accepted pre-defined value.

A bond is the directional net attractive force between two atoms,which is a stabilising interaction, and so the total energy of the bond has a lower energy than the separated atoms. A bond is usually an electrostatic interaction between two atoms, as seen in ionic bonding, which results from the transfer of electrons from an electropositve atom to an electronegative atom causing the formation of an anion and cation pair which bond to each other through electrostatic attraction. In the case of covalent bonding, a bond is formed through the sharing of one or more pair of valence electrons between two atoms and the resulting electrostatic attraction between the atoms nuclei and the shared pair of electrons. Metallic bonding is described as the non-directional electrostatic attractions between the cationic metal centres and "sea of electrons" donated from the valence metal orbitals.

Another type of bonding can be described which are much weaker than conventional bonds, these are so called non-covalent interactions. An example of this is a hydrogen bond which is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X-H where X is more electronegative than H and so an electrostatic force is seen via a dipole-dipole interaction.

==Frequency analysis for BH3 and GaBr3==

Frequency analysis was performed on BH3 and GaBr3 in order to compare the vibrational modes of the two molecules.

===BH3 Frequency Calculation===

It was found that when the frequency analysis was performed on the symmetry broken BH3 molecule, which was used in previous calculations, the energy did not converge well to the minimum as the low frequency values were greater than +/- 15cm-1. This indicated a large deviation of the centre of mass translational and rotational frequencies from the accepted values and showed a minimum in the potential energy surface was not found. Therefore BH3 with D3h symmetry was optimised using DFT 6-31G(d,p) basis set and the frequency calculation was run on this.

{| class="wikitable"
|+ BH3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|MWBBH3OPTIMISATION631GDPFREQ5
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|6-31G(d,p)
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -26.61532364 a.u.
|-
|RMS Gradient Norm
|0.00000215 a.u.
|-
|Dipole Moment
|0.00 Debye
|-
|Point Group
|D3H
|-
|Job cpu time
|7.0 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069047D-09
Optimization completed.
-- Stationary point found.
</pre>

The optimisation file is liked to [[Media:MWBBH3OPTIMISATION631GDP.LOG| here]]

The optimisation has converged therefore a stationary point has been found on the BH3 potential energy surface.

<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>

The frequency calculation file is liked to [[Media:MWBBH3OPTIMISATION631GDPFREQ5.LOG| here]]

Here we can see that the low frequencies are not negative and so a minimum energy structure has been found, with the second derivative of the potential energy surface for BH3 being positive, therefore avoiding finding a possible transition state structure.

{| class="wikitable" style="text-align:center"
|+ Vibrational modes of BH3
|-
! No. !! Form of the vibration !! Frequency !! Intensity !! Symmetry D3h point group
|-
| 1 || [[File:MWBBIDWELL Bh3 freq vibrations 1.gif|300px|thumb|center|The hydrogen atoms are moving in a concerted motion out of the plane of the BH3 molecule, with the boron atom moving slightly in the opposite direction]] || 1163 || 93 || A2"
|-
| 2 || [[File:Bh3_freq_vibrations_2.gif|300px|thumb|center|All three of the hydrogen atoms are moving left to right in the plane of the molecule, creating two scissoring motions, with the boron atom remaining stationary]] || 1213 || 14 || E'
|-
| 3 || [[File:Bh3_freq_vibrations_3.gif|300px|thumb|center|Two hydrogens are moving in a scissoring motion with the other hydrogen moving slightly up and down with the central atom]] || 1213 || 14 || E'
|-
| 4 || [[File:Bh3_freq_vibrations_4.gif|300px|thumb|center|The three hydrogens are symmetrically stretching in a concerted motion in the plane of the molecule with the boron atom remaining stationary]] || 2583 || 0 || A1'
|-
| 5 || [[File:Bh3_freq_vibrations_5.gif|300px|thumb|center|Two hydrogens are asymmetrically stretching in the plane of the molecule with the boron atom and the remaining hydrogen moving from left to right with the stretches]] || 2716 || 126 || E'
|-
| 6 || [[File:Bh3_freq_vibrations_6.gif|300px|thumb|center|Two of the hydrogens are stretching in a symmetric fashion while the other hydrogen is asymmetrically stretching with respect to them. The boron atom also moves up and down slightly]] || 2716 || 126 || E'
|}

[[File:MWB IR spectrum BH3.svg|500px|thumb|center|IR spectrum of BH3]]

There are only three peaks in the IR spectrum of BH3 as two sets of two of the vibrations are degenerate with the same vibrational frequencies and intensities they overlap and correspond to one peak each(this is seen for the two E' symmetry labelled peaks at 1213 and 2716 cm-1). The symmetrical stretching vibrational mode has no dipole moment and so is IR inactive, therefore doesn't show a peak in the IR spectrum. The remaining peak corresponds to the A2" symmetry labelled bending mode at 1163 cm-1 . Therefore we can see why six vibrations in the BH3 molecule only produce three peaks in the IR spectrum.

===GaBr3 Frequency calculation===

Frequency analysis was performed on the previously optimised GaBr3 so that the vibrational modes of the molecule could be inspected, low frequency values were shown to be less than +/- 15cm-1, therefore it can be said with some confidence that the minimum energy structure was found.

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

The frequency calculation file is liked to [[Media:GABR3FREQTHISTIMEWORK.LOG| here]]

Here we can see that the low frequencies are not negative and so a minimum energy structure has been found, with the second derivative of the potential energy surface for GaBr3 being positive.

{| class="wikitable" style="text-align:center"
|+ Vibrational modes of GaBr3
|-
! No. !! Form of the vibration !! Frequency !! Intensity !! Symmetry D3h point group
|-
| 1 || [[File:Mwb11GaBr2_movie_1.gif|300px|thumb|center|All three of the bromine atoms are moving left to right in the plane of the molecule, creating two scissoring motions, with the gallium atom remaining stationary]] || 76 || 3 || E'
|-
| 2 || [[File:Mwb11GaBr2_movie_2.gif|300px|thumb|center|Two bromines are moving in a scissoring motion with the other bromine moving slightly up and down with the central atom]] || 76 || 3 || E'
|-
| 3 || [[File:Mwb11GaBr2_movie_3.gif|300px|thumb|center|The bromine atoms are moving in a concerted motion out of the plane of the GaBr3 molecule, with the gallium atom moving slightly in the opposite direction]] || 100 || 9 || A2"
|-
| 4 || [[File:Mwb11GaBr2_movie_4.gif|300px|thumb|center|The three bromines are symmetrically stretching in a concerted motion in the plane of the molecule with the gallium atom remaining stationary]] || 197 || 0 || A1'
|-
| 5 || [[File:Mwb11GaBr2_movie_5.gif|300px|thumb|center|Two bromines are asymmetrically stretching in the plane of the molecule with the gallium atom and the remaining bromine atom moving from left to right with the stretches]] || 316 || 57 || E'
|-
| 6 || [[File:Mwb11GaBr2_movie_6.gif|300px|thumb|center|Two of the bromines are stretching in a symmetric fashion while the other bromine atom is asymmetrically stretching with respect to them. The gallium atom also moves up and down with the strecthes.]]|| 316 || 57 || E'
|}

[[File:IR spectrum GaBr3.svg|400px|thumb|center|IR Spectrum of GaBr3]]

There are three peaks in the IR spectrum of GaBr3 as the two sets of the two E' symmetry labelled vibrations are degenerate with the same vibrational frequencies and intensities. They overlap and correspond to one peak each at 76 and 316 cm-1 wavenumbers respectively. The symmetrical stretching vibrational mode with A1' symmetry has no dipole moment and so is IR inactive, therefore doesn't show a peak in the IR spectrum. The remaining peak corresponds to the A2" symmetry labelled bending mode at 100 cm-1 . Therefore just as with BH3 we can see why six vibrational modes in the GaBr3 molecule only produce three peaks in the IR spectrum.

The lowest real normal vibrational mode is due to the peak at 76 cm-1 with the E' symmetry element.

===Vibrational comparison===

{| class="wikitable"
|+ Vibrational mode Summary
|-
! No.
! BH3 Vibrational frequencies (cm-1)
! GaBr3 Vibrational frequencies (cm-1)
|-
|1
|1163
|76
|-
|2
|1213
|76
|-
|3
|1213
|100
|-
|4
|2583
|197
|-
|5
|2716
|316
|-
|6
|2716
|316
|-
|}

The large difference in frequency values between BH3 and GaBr3 indicates that the GaBr3 molecule has weaker bonds, which is due to the poorer orbital overlap of the Ga sp2 orbital with Br and a larger difference in electronegativty compared with B and H leading to a more polarised and weaker bond. The difference in frequency values also stems from the fact that the Ga-Br bond has a much higher reduced mass than the B-H bond due to the fact the atoms are much heavier, this relationship can be seen in the equation below.

[[File:MWB frequency equation.png|300px|thumb|center|Vibrational frequency equation]]

It can be seen from the comparison of the vibrational modes of both molecules that a reordering of modes has occured, the A2" mode in GaBr3 is higher in energy than the degenerate E' mode, which is the opposite way around in the BH3 molecule. This is due to the fact that in the GaBr3 molecule the Br ligands are heavier than the central Ga atom and so remain much more stationary relative to the Ga atom vibrating up and down. This is reversed in the case of BH3 as the H atoms are much lighter than the B atom and so they vibrate more than the relatively stationary central atom in the A2" mode. This differnce leads to the relative shift and reordering of energies in the E' and A2" vibrational modes. However the two spectra are similar as they both have three peaks due to the fact that both molecules have D3h symmetry and four atoms, leading to both spectra having 3N-6 (N=4) vibrational modes. It can also be seen that in both spectra the A2" and E' modes at low energy, and also the A1' and E' modes at higher energy, lie close together. This is due to the fact that the lower energy vibrations are both bending vibrational modes and the higher energy vibrations are both stretching modes.

The same method and basis set must be used for both optimisation and frequency analysis to ensure that the frequency calculations can be performed on the same potential energy surface that the molecule was optimised one so that the values obtained are meaningful. The purpose of carrying out a frequency analysis is to ensure a minimum in the potential energy surface for the molecule has been found, and also that the computationaly obtained results can be compared to experimental findings to check the accuracy of the computational methods employed. Low frequencies represent the centre of mass motion of the molecule through the three translational and three rotational eigenvalues reported, and theoretically should equal zero, however in this case they are within an accepted range of +/-15cm-1 which corresponds to a well optimised molecule at an energy minimum.

===Molecular Orbitals of BH3===

A population analysis was done using the previously optimised BH3 molecule with 6-31G(d,p)basis and B3LYP method with keywords pop=full, opt=tight, int=ultrafine, scf=conver=9.

The population analysis file is liked to [[Media:BH3OPTENERGYMOB3LYP6-31G.LOG| here]]

[[File:MWB2 BH3 MO diagram.jpg|400px|thumb|center|MO diagram of BH3]]

The real MOs computed by Gaussian match up well with the LCAO MOs predicted by MO theory. This shows us that for small molecules like BH3 qualitative MO theory is accurate, however for larger molecules deviations would be expected due to larger basis sets needed to model the molecule accurately.

===NBO Analysis for NH3===

NH3 was optimised using the 6-31G(d,p) basis set and B3LYP method using keywords opt=tight, int=ultrafine, scf=conver=9. As the molecule is small a higher level basis set can be used straight away to model it.

{| class="wikitable"
|+ NH3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|NH3optmisation631gdpFREQ
|-
|File Type
|.log
|-
|Calculation Type
|FREQ
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|6-31G(d,p)
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -56.55776872 a.u.
|-
|RMS Gradient Norm
|0.00000322 a.u.
|-
|Dipole Moment
|1.85 Debye
|-
|Point Group
|C3
|-
|Job cpu time
|9.0 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000015 YES
RMS Force 0.000004 0.000010 YES
Maximum Displacement 0.000012 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-9.845967D-11
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the NH3 potential energy surface.

The optimisation calculation file is liked to [[Media:NH3OPTMISATION631GDP.LOG| here]]

<pre>
Low frequencies --- -0.0137 -0.0025 0.0014 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

Here we can see that the low frequencies are not negative and so a minimum energy structure has been found, with the second derivative of the potential energy surface for NH3 being positive.

The frequency calculation file is liked to [[Media:NH3OPTMISATION631GDPFREQ.LOG| here]]

[[File:MWB NH3 Charge distribution.png|400px|thumb|center|Charge Distribution of NH3]]

Charge range is from -1.125 to +1.125, it can be seen that the nitrogen atom has a highly negative charge as expected, as it has a much larger electronegativity value than the hydrogen atoms.

[[File:MWB NH3 Charge distribution numbers.png|400px|thumb|center|Charge Distribution values of NH3]]

Above the charge distribution values for the individual atoms are shown (-1.125 for N, and +0.375 for the H atoms). The sum of the charges add up to zero which confirms the fact that NH3 is a neutral molecule.

The population analysis file is liked to [[Media:NH3OPTMISATION631GDPENERGYMO.LOG| here]]

===Summary of Natural Population Analysis===

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
N 1 -1.12514 1.99982 6.11104 0.01429 8.12514
H 2 0.37505 0.00000 0.62250 0.00246 0.62495
H 3 0.37505 0.00000 0.62250 0.00246 0.62495
H 4 0.37505 0.00000 0.62250 0.00246 0.62495
=======================================================================
* Total * 0.00000 1.99982 7.97852 0.02166 10.00000
</pre>

The charge distribution for the atoms are shown as above, the majority of the electron density is seen to be located on the central nitrogen atom, which acts as a lewis base, donating electron density into the hydrogen orbitals.

===(Occupancy) Bond orbital/ Coefficients/ Hybrids===

<pre>
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0014
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0014
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0014
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310<
</pre>

The information in the table above shows that the electron density in the two centre two electron bonds are primary from the nitrogen atom orbitals which makes up 69% of the bond and have a hybridisation of 25%s+75%p, whilst 31% of the electron density of the bond comes from the H orbital which is 100%s.

===Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis===

<pre>
Threshold for printing: 0.50 kcal/mol
</pre>

This table summarises interactions from bonding NBOs into non-bonding or antibonding orbitals. However it is not of interest as the value is below 20 kcal/mol.

===Natural Bond Orbitals (Summary)===

<pre>
Principal Delocalizations
NBO Occupancy Energy (geminal,vicinal,remote)
====================================================================================
Molecular unit 1 (H3N)
1. BD ( 1) N 1 - H 2 1.99909 -0.60417
2. BD ( 1) N 1 - H 3 1.99909 -0.60417
3. BD ( 1) N 1 - H 4 1.99909 -0.60417
4. CR ( 1) N 1 1.99982 -14.16768
5. LP ( 1) N 1 1.99721 -0.31757 16(v),20(v),24(v),17(v)
</pre>

The table above summarises the energy and occupation of the N-H bonds, and the nitrogen lone pair. All the N-H bonds are at the same energy of -0.6 a.u., whereas the core nitrogen orbital is higher in energy with an energy of -14.2 a.u. This is why we leave the core orbitals off an MO diagram, as they are very deep in energy compared to the valence orbitals and so are low-lying enough to be irrelevant in terms of the valence bonding scheme.

===Association energies: Ammonia-Borane===

In the molecule the nitrogen atom formally donates two electrons to the boron atom. However in reality the electrons are shared between the boron and nitrogen, this was shown in the NBO analysis above.

NH3BH3 was optimised using the 6-31G(d,p) basis set and B3LYP method with the keywords opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ NH3BH3 optimisation Summary
|-
! Property
! Output
|-
|File Name
|NH3BH3optimisation631Gdp
|-
|File Type
|.log
|-
|Calculation Type
|FOPT
|-
|Calculation Method
|RB3LYP
|-
|Basis Set
|6-31G(d,p)
|-
|Charge
|0
|-
|Spin
|Singlet
|-
|E(RB3LYP)
| -83.22468908 a.u.
|-
|RMS Gradient Norm
|0.00000138 a.u.
|-
|Dipole Moment
|5.56 Debye
|-
|Point Group
|C1
|-
|Job cpu time
|1 minutes 30.0 seconds
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-1.180805D-10
Optimization completed.
-- Stationary point found.
</pre>

The optimisation has converged therefore a stationary point has been found on the NH3BH3 potential energy surface.

The optimisation calculation file is liked to [[Media:NH3BH3OPTIMISATION631GDP.LOG| here]]

<pre>
Low frequencies --- -2.9451 -0.0014 -0.0011 -0.0010 1.7800 3.7236
Low frequencies --- 263.3834 632.9581 638.4631
</pre>

Here we can see that the low frequencies are not negative and so a minimum energy structure has been found, with the second derivative of the potential energy surface for NH3BH3 being positive.

The frequency calculation file is liked to [[Media:NH3BH3OPTIMISATION631GDPFREQ.LOG| here]]

===Association energy calaculations===

An analysis of the bond association energy of the combination of NH3 and BH3 to form NH3BH3 is provided below.

{| class="wikitable"
|+ Association energies
|-
! Molecule
! Energy (a.u.)
|-
| NH3
| -56.55776872
|-
| BH3
| -26.61532364
|-
| NH3BH3
| -83.22468908
|-
|}

The association energy of NH3 and BH3 can be calculated by using the following equation:

ΔE = E(NH3BH3) − [(E(BH3) + E(NH3)]

ΔE = -83.22468908(a.u.) - [( -26.61532364(a.u.)) + ( -56.55776872(a.u.)]

ΔE = − 0.05159672(a.u.)

The energy value was then converted from Hartrees to kJ/mol by multiplying by a conversion factor of 2625.50 producing a value of ΔE = -135.46719868 kJ/mol. Conversely we can see that the value of NH3BH3 dissociation bond energy is +135.46719868 kJ/mol.

This value of the bond association energy is a reasonable value as it is within the usual range of bond energies being hundreds of kJ/mol, roughly 100-600 kJ/mol for common molecules.

==References==

<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T15:29:20Z

Mwb11: /* NBO Analysis */

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T15:18:49Z

Mwb11: /* Conclusion */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirable physical properties for synthetic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The inductive effect of the nitrogen atom via the sigma framework of the molecule also depends on the strength of the orbital overlap between the nitrogen an carbon atoms, as both atoms are in the same row of the periodic table we can expect that there will be good overlap between the orbitals. The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overall positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In [P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. This is also due to the fact there is a weaker orbital overlap between the second row carbon atom and third row phosphorous atom (due to mismatch of orbital sizes) and so there is a weaker lone pair donation onto the carbon atom, leading to the large positive charge on the phosphorous atom. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In [S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (anti-periplanar) hydrogen atoms have a less positive value whilst the equitorial (syn-periplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the anti-periplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the anti-periplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and hetero-atom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Second order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|150px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawal effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawal effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbital, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor and so will interact with an anion more strongly, leading to a higher thermal stability and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indicative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were initially investigated via computational methods and their physical properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

===Further Study===

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T15:12:58Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirable physical properties for synthetic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The inductive effect of the nitrogen atom via the sigma framework of the molecule also depends on the strength of the orbital overlap between the nitrogen an carbon atoms, as both atoms are in the same row of the periodic table we can expect that there will be good overlap between the orbitals. The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overall positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In [P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. This is also due to the fact there is a weaker orbital overlap between the second row carbon atom and third row phosphorous atom (due to mismatch of orbital sizes) and so there is a weaker lone pair donation onto the carbon atom, leading to the large positive charge on the phosphorous atom. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In [S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (anti-periplanar) hydrogen atoms have a less positive value whilst the equitorial (syn-periplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the anti-periplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the anti-periplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and hetero-atom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Second order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|150px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawal effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawal effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbital, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor and so will interact with an anion more strongly, leading to a higher thermal stability and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indicative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were initially investigated via computational methods and their physical properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T14:29:55Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirable physical properties for synthetic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The la The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overall positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (anti-periplanar) hydrogen atoms have a less positive value whilst the equitorial (syn-periplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the anti-periplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the anti-periplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and hetero-atom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Second order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|150px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawal effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawal effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbital, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor and so will interact with an anion more strongly, leading to a higher thermal stability and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indicative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were initially investigated via computational methods and their physical properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T14:14:12Z

Mwb11: /* Part 2 Influence of Functional Groups */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirable physical properties for synthetic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overall positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (anti-periplanar) hydrogen atoms have a less positive value whilst the equitorial (syn-periplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the anti-periplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the anti-periplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and hetero-atom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Second order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|150px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawal effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawal effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbital, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor and so will interact with an anion more strongly, leading to a higher thermal stability and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indicative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were initially investigated via computational methods and their physical properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T14:11:12Z

Mwb11: /* Week 2 - Ionic Liquids Mini-Project */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirable physical properties for synthetic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary frequencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overall positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (anti-periplanar) hydrogen atoms have a less positive value whilst the equitorial (syn-periplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the anti-periplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the anti-periplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and hetero-atom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|150px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T14:09:50Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overall positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (anti-periplanar) hydrogen atoms have a less positive value whilst the equitorial (syn-periplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the anti-periplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the anti-periplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|150px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T13:06:07Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|150px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T13:05:43Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO3 NCH33CN+ new.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

File:MWB MO LUMO3 NCH33CN+ new.png

2014-03-07T13:05:19Z

Mwb11:

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T13:04:20Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO2 NCH33CN+.png|100px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T13:04:01Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MWB MO LUMO2 NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

File:MWB MO LUMO2 NCH33CN+.png

2014-03-07T13:03:35Z

Mwb11:

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T12:59:04Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.) || HOMO-LUMO Energy Gap (kJ/mol)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632|| style="text-align: center;"|1171.8
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303|| style="text-align: center;"|953.1
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865|| style="text-align: center;"|836.6
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T12:53:53Z

Mwb11: /* Part 2 Influence of Functional Groups */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

=Part 2 Influence of Functional Groups=

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T04:56:02Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation. This is due to the decreased antibonding interactions of the p orbitals of the methyl groups with the diffuse electron density at the centre of the molecule via the reduction of the orbital size by the inductive withdrawl effect of the nitrile group. Even though antibonding interactions occur between the pi bond of the nitrile group and the adjacent CH2 orbtal, overall the interactions are more stabilising and so the LUMO is lower in energy with respect to the LUMO of the tetramethylammonium cation. Therefore we can expect that the cation will act as a better acceptor ando so will interact with an anion more strongly, leading to a higher thermal stabilty and melting point.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T04:38:01Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that in the HOMO of [N(CH3)3(CH2OH)]+ molecule there is no longer a bonding interaction between the methyl hydrogens of the three carbon atoms, the introduction of the hydroxy group has reduced the delocalisation of the MO due to the the electronegative withdrawl effects of the oxygen atom. Antibonding interactions are also seen between the lone pair of the oxygen and the adjacent CH2 group which increases the overall antibonding character of the MO and so it has a higher energy compared to the [N(CH3)4]+ HOMO.

In the LUMO of the [N(CH3)4]+ molecule there is a large amount of delocalisation of charge, however when the OH group is introduced the sigma bonding framework of the molecule is disrupted via electron donation of the oxygen atom lone pair into the N-C-O fragment of the molecule as seen in the NBO charge analysis above. This reduction in symmetry causes the LUMO to have a higher antibonding character and energy than in the tetramethylammonium cation. This destabilisation of the molecule therefore infers that it will be a weaker acceptor and so will not interact with the ion pair anion as strongly, leading to a lower thermal stability and melting point. However the effect of hydrogen bonding due to the hydroxy group may need to be taken into account.

We can see in the HOMO of [N(CH3)3(CH2CN)]+ that a large proportion of the electron density has been pulled away from the central nitrogen atom and methyl group fragments and almost no interactions are present here. However most of the electron density is situated on the nitrile group due to its electron withdrawing effects via pi bonding framework, and antibonding interactions can be seen between the nitrile group and the methyl hydrogen atoms which raise the energy of the HOMO and its antibonding character with respect to the tetramethylammonium cation.

Considering the LUMO of [N(CH3)3(CH2CN)]+ we can see it lies deeper in energy than the corresponding [N(CH3)4]+ cation.

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T00:44:51Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

It can be seen that the introduction of the OH and CN ligands have drastically changed the shapes of the molecular orbitals. One of the main differences is that the HOMO of [N(CH3)3(CH2OH)]+

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T00:26:02Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO HOMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-07T00:18:55Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

It can be seen that there is a reduction in the HOMO-LUMO gap of the functionalised cations compared to [N(CH3)4]+. The HOMO-LUMO gap is indictative of the stability of the cations, and a smaller energy gap shows that both of the functionalised cations will lead to more stable ion-pairs, as the addition of electron density to the cation is less energetically demanding, and so will be more suitable ionic liquids.

===Conclusion===

The three onoium cations [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were intially investigated via computational methods and their phsycial properties and charge distributions were rationalised via NBO population analysis and second order perturbation theory. Subsequently different functional groups were placed on the [N(CH3)4]+ cation and they were analysed through the same methods previously described in order to compare and contrast the affect of different ligands on the shapes and energies of the resulting molecular orbitals and so on the properties of the ionic liquids, showing the potential applications of the designer solvents.

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T23:24:22Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T23:23:23Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]] Energy of MO: -0.57934 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]]Energy of MO: -0.48763 a.u.||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.0.50047 a.u.
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]] Energy of MO: -0.13302 a.u.||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]] Energy of MO: -0.12460 a.u.||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]] Energy of MO: -0.18182 a.u.
|-
|}

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T23:13:56Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|[[File:MO HOMO NCH34+.png|200px|thumb|center| HOMO of [N(CH3)4]+]]||[[File:MO LUMO NCH3OH.png|200px|thumb|center| HOMO of [N(CH3)3(CH2OH)]+]]||[[File:MO HOMO NCH33CN+.png|200px|thumb|center| HOMO of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|[[File:MO LUMO NCH34+.png|200px|thumb|center| LUMO of [N(CH3)4]+]]||[[File:MO LUMO NCH3OH.png|200px|thumb|center| LUMO of [N(CH3)3(CH2OH)]+]]||[[File:MO LUMO NCH33CN+.png|200px|thumb|center| LUMO of [N(CH3)3(CH2CN)]+]]
|-
|}

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T23:02:35Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"| Molecular orbitals of[N(CH3)4]+
| Molecular orbitals of [N(CH3)3(CH2OH)]+
| Molecular orbitals of [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
|}

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T23:00:34Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|[N(CH3)4
| [N(CH3)3(CH2OH)]+
| [N(CH3)3(CH2CN)]+
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
|}

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap (a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T22:55:55Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
|}

{|class="wikitable"
|-
!Cation || HOMO-LUMO Energy Gap(a.u.)
|-
|[N(CH3)4]+|| style="text-align: center;"|0.44632
|-
|[N(CH3)3(CH2OH]+|| style="text-align: center;"|0.36303
|-
|[N(CH3)3(CH2CN]+|| style="text-align: center;"|0.31865
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T19:57:40Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T19:56:42Z

Mwb11: /* HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T19:51:20Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

The CN ligand is an electron withdrawing ligand, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The central nitrogen atom has a similar value of negative charge with respect to the nitrogen atom in the [N(CH3)4]+, however the carbon atom adjacent to the central nitrogen (carbon atom 6) has significantly less electron density than the other methyl carbon atoms due to the electron withdrawing pi orbital inductive effects of the nitrile ligand, which is less significant than the hydroxy groups inductive effect as this propagates via sigma orbitals.

The nitrile group carbon atom has a positive charge due to the inductive withdrawal effects of the neighbouring nitrogen atom which has a greater value of electronegativity causing electron density to pulled towards the nitrogen atom.

The hydrogen atoms 11 and 12 also have a larger positive charge than the other methyl hydrogen due to the electron withdrawing effects of the nitrile group.

===HOMO and LUMO comparison of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T19:11:28Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8. Seconf order perturbation analysis was also done on the donation of the oxygen lone pair on to the central nitrogen atom which has a value of 18.96 kcal/mol which is quite large and indicates a significant degree of delocalisation of the oxygen lone pair via the N-C-O fragment as mentioned above.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T19:06:59Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
25. LP ( 2) O 17 /140. BD*( 1) C 5 - N 16 18.96 0.51 0.088
</pre>

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:59:50Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
24. LP ( 1) O 17 /138. BD*( 1) C 5 - H 8 1.21 1.04 0.032
24. LP ( 1) O 17 /139. BD*( 1) C 5 - H 9 3.97 1.02 0.057
25. LP ( 2) O 17 /138. BD*( 1) C 5 - H 8 2.97 0.77 0.043
25. LP ( 2) O 17 /139. BD*( 1) C 5 - H 9 0.83 0.75 0.023
</pre>

It can be seen that the oxygen atom donates a larger amount of electron density from its lone pair onto hydrogen atom 9 therefore as we expect it has a lower positive charge than hydrogen atom 8.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:47:36Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:45:32Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through the Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:44:00Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|200px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdrawal effects of the oxygen atom on the carbon atom due to differences in electronegativity.

Lastly we can see that hydrogen atoms 8 and 9 which are adjacent to the hydroxy group have a slightly less positive charge than the other methyl hydrogens in the molecule. This is due to electron density from the oxygen lone pair being donated onto the two hydrogen atoms, which can be seen through

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:39:04Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with the [N(CH3)4]+ molecule. The first thing to note is that the there is now a more negative charge on the central nitrogen atom than in [N(CH3)4]+ due to the delocalisation of electron density between the N-C-O fragment, allowing the hydroxy oxygen atom to donate electron density onto the nitrogen atom, which can be seen through the molecular orbital diagram below.

[[File:MO NCO fragment MWB.png|300px|thumb|center| MO diagram showing the delocalisation of the N-C-O fragment]]

The second point to note is that all of the carbon atoms have a similar values of negative charge on them compared to the [N(CH3)4]+ molecule except for the carbon atom adjacent to the hydroxy group which bears a slightly positive charge of +0.088. This is due to the inductive withdraw effects of the oxygen atom on the carbon atom due to differences in electronegativity.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

File:MO NCO fragment MWB.png

2014-03-06T18:38:33Z

Mwb11:

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:20:34Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with [N(CH3)4]+.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge picture NCH33CN colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge picture NCH33CN numbers.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:19:21Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with [N(CH3)4]+.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2CN)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.485
|-
|2||H||0.271
|-
|3||H||0.277
|-
|4||H||0.271
|-
|5||C||-0.489
|-
|6||C||-0.358
|-
|7||C||-0.489
|-
|8||H||0.274
|-
|9||H||0.269
|-
|10||H||0.282
|-
|11||H||0.309
|-
|12||H||0.309
|-
|13||H||0.282
|-
|14||H||0.269
|-
|15||H||0.274
|-
|16||N||-0.289
|-
|17||C||0.209
|-
|18||N||-0.186
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:13:25Z

Mwb11: /* Population Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with [N(CH3)4]+.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:12:37Z

Mwb11: /* NBO Analysis */

=Week 2 - Ionic Liquids Mini-Project=

==Introduction==

Ionic Liquids are solutions composed entirely of ions which melt below 100ºC, unlike simple inorganic salts such as NaCl which are termed as molten salts as they only melt at high temperatures (such as over 800ºC in this case). A large number of potential anion and cation groups allow for the tuning of unique and desirible physical properties for syntheic applications.<ref> Hermann Weingartner, ''Understanding Ionic Liquids at the Molecular Level:Facts, Problems, and Controversies'', Angewandte Chemie,2008, '''47''' (4),654 </ref> Commonly ionic liquids are composed of a bulky organic cations and inorganic anions, due to their low volatility they are a green alternative to traditional organic solvents and have high thermal stabilities due to very stable ion pairs.

==Optimisation==

[N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method. The nosymm keyword was used to optimise the cations so that they did not have a fixed geometry and so the global minimum on the potential energy surface could be found if the methyl groups were to rotate. Keywords opt=tight int=ultrafine scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptmisedNCH34.png|200px|thumb|center|Optimised structure of [N(CH3)4]+]]
| [[File:OptimisedPCH3structure.png|200px|thumb|center|Optimised structure of [P(CH3)4]+]]
| [[File:Optimised SCH33 structure.png|200px|thumb|center|Optimised structure of [S(CH3)3]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||log_88856optnosym||log_88852||log_88853
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-214.18127322||-500.82701172||-517.68327440
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000044||0.00000074||0.00000112
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||6.70||19.01||5.91
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|C-X bond length (Å)||1.51||1.82||1.82
|-
| align="center" style="background:#f0f0f0;"|C-X-C bond angle (°)||109.5||109.5||102.7
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||15 minutes 5.9 seconds||20 minutes 40.0 seconds|| 8 minutes 4.2 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:Log 88856optnosym.log| here]]||[[Media:OptimisationPLog 88852.log| here]]||[[Media:OpyimisationSLog 88853.log| here]]
|}

It was calculated that the [N(CH3)4]+ C-N bond length is 1.51 Å which matches well with the literature value of 1.49 Å.<ref>E. A. Trush, O. V. Shishkin, V. A. Trush, I. S. Konovalovab and T. Y. Sliva, ''Tetramethylammonium dimethyl (phenylsulfonylamido)phosphate(1−)'', Acta Crystallographica, 2012, '''68'''(2), 273 </ref> To get a more exact value matching to literature a larger basis set such as MP2 could be used. The C-N-C bond angle was calculated to be 109.5° which validates the expected sp3 tetrahedral structure of the molecule.

It was calculated that the [P(CH3)4]+ P-N bond length is 1.82 Å which matches well with the literature value of 1.83 Å.<ref> Andreas Kornath, F. Neumann and H. Oberhammer, ''Tetramethylphosphonium Fluoride:“Naked” Fluoride and Phosphorane'', Inorganic Chemistry, 2003 '''42''' (9), 2894 </ref> The C-P-C angle was also determined to be 109.5° which confirms the molecules tetrahedral structure.

It was calculated that the [S(CH3)3]+ C-S bond length is 1.82 Å which is very close to the literature bond length of 1.81 Å.<ref> Pradip Ghosh and Animesh Chakravorty, ''On alkyl sulfonium salts of triiodomercury(II) and structure of the trimethyl salt'', Indian Journal of Chemistry, 2013, '''52A''', 1247</ref> The C-S-C bond angle was calculated to be 102.7°, this differs quite a lot from the assumed pyramidal bond angle of 107.5° (in NH3). This is due to the contribution of two factors, firstly the sulphur lone-pair in the 3sp3 causing a large repulsion between the the three 2 centre 2 electron sigma bonds, causing the bond to compress, secondly due to the weak overlap of the diffuse 3sp3 orbitals of sulphur with the 2sp3 hybridised on carbon. As sulphur is not as electronegative as nitrogen, it doesn't hold as much as the electron density near itself and as a result the methyl groups are pushed closer together, therefore reducing the bond angle.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-2.610693D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[P(CH3)4]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000013 0.000040 YES
Predicted change in Energy=-9.323328D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[S(CH3)3]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000055 0.000060 YES
RMS Displacement 0.000019 0.000040 YES
Predicted change in Energy=-1.568213D-10
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)4]+
|<pre>
Low frequencies --- -5.4183 -2.1310 -0.0010 -0.0008 -0.0008 4.0442
Low frequencies --- 183.7687 288.4039 288.9032
</pre>
|[[File:IR spectrum.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:Log 88857FREQ.log| here]]
|-
|[P(CH3)4]+
|<pre>
Low frequencies --- -2.5571 -0.0012 -0.0010 0.0009 5.1789 7.5929
Low frequencies --- 156.4456 192.0342 192.2771
</pre>
|[[File:PCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:Log 88855FREQ.log| here]]
|-
|[S(CH3)3]+
|<pre>
Low frequencies --- -7.2509 -6.2783 0.0023 0.0025 0.0044 9.6364
Low frequencies --- 162.1102 199.4681 200.0905
</pre>
|[[File:SCH33 IR spectrum.svg|300px|thumb|center|IR spectrum of [S(CH3)3]+]]
|[[Media:Log 88854FREQ.log| here]]
|-
|}

The low frequency values for the three cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis was carried out on the previously optimised structures of the three cations with 6-31G basis set, B3LYP method and keywords: pop=full, opt=tight, int=ultrafine and scf=conver=9. Below are 5 MOs of the non-core orbitals of [N(CH3)4]+ showing highly bonding and antibonding orbital interactions.

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Log file
|-
|[N(CH3)4]+
|[[Media:Log 88858SCH33MOandNBO.log| here]]
|-
|[P(CH3)4]+
|[[Media:Log 88859PCH33MOandNBO.log| here]]
|-
|[S(CH3)3]+
|[[Media:Log 88860NCH33MOandNBO.log| here]]
|-
|}

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|MO no.
| align="center" style="background:#f0f0f0;"|MO depiction
| align="center" style="background:#f0f0f0;"|MO description
|-
| align="center" style="background:#f0f0f0;"|6||[[File:MO_6_NCH34+annotated3.jpg|100px|thumb|center|Highly bonding MO of [N(CH3)4]+]]|| Strong bonding interactions are seen through the non-core atomic orbitals due to possible bonding overlap of S atomic orbitals. There are also weakly bonding through space interactions which contribute to the overall bonding character of the MO which has no nodes. The MO is very delocalised with charge being smeared across all of the atoms.
|-
| align="center" style="background:#f0f0f0;"|10||[[File:MO_10_NCH34+annotated3.jpg|100px|thumb|center| Bonding MO of [N(CH3)4]+]]|| There are strong bonding interactions between the methyl groups AOs, but also an antibonding interaction at the central nitrogen atom with the four adjacent carbon atoms which leads to four nodal planes. There are also bonding through space interactions present between the methyl groups which leads to an overall bonding partly delocalised MO.
|-
| align="center" style="background:#f0f0f0;"|13||[[File:MO_13_NCH34+annotated3.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There is a bonding interaction between the central nitrogen atom and two of the adjacent carbon atoms possibly due to the overlap of their Pz orbitals, there is also a bonding interaction between the methyl carbons and their attached hydrogens which lead to the formation of two nodal planes. There are several weak through space antibonding interactions as well which leads to a weakly bonding MO which isn't very delocalised.
|-
| align="center" style="background:#f0f0f0;"|16||[[File:MO_16_NCH34+annotated3.jpg|100px|thumb|center|Antibonding MO of [N(CH3)4]+]]|| This MO features four nodal planes, there are some overlapping bonding interactions between the methyl carbon p orbitals and the hydrogen atom s orbitals but this is a weak interaction with a small overlap and there are many through space antibonding interactions which contribute to make this a not very delocalised antibonding MO.
|-
| align="center" style="background:#f0f0f0;"|21||[[File:MO_21_NCH34+annotated2.jpg|100px|thumb|center|Weakly bonding MO of [N(CH3)4]+]]|| There are three nodes in the MO which all lie on atoms, rather than in between bonds. There are bonding through space interactions between the axial H3 fragment and adjacent methyl groups as well overall bonding interactions between the carbon atoms and their respective hydrogens. It can be seen a reasonable amount of mixing occurs between the axial hydrogens and less for the equitorial hydrogen atoms. Overall the MO is moderately delocalised and weakly bonding.
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [N(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture NCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|N || style="text-align: center;" |-0.295
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.483
|-
| style="text-align: center;"|H || style="text-align: center;"|0.269
|}

In the NBO charge distribution picture above it can be seen that the carbon atoms bear most of the negative charge, whereas the hydrogen atoms bear all of the positive charge. This is contrasted with the traditional view of the cation with most of the positive charge on the nitrogen atom, even though the nitrogen atom has donated its lone pair to form an extra N-C bond it still retains some of its electron density due to its high electronegativity leading to a tightly bound lone pair and a negative charge (66% still on the N atom as seen by NBO analysis). The carbon atoms are negatively charged due to inductive withdrawing effects with the attached hydrogen atoms as the carbon atoms are more electronegative leading to overal positively charge hydrogen atoms. As we can see a more appropriate representation of the cation would be with the positive charge smeared out overall the whole molecule as in [N(CH3)4]+ rather than solely on the central nitrogen atom. As expected the total charge of the molecule adds up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [P(CH3)4]+]
|-
| colspan="2"|[[File:NBO charge picture of PCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|P || style="text-align: center;" |1.667
|-
| style="text-align: center;"|C || style="text-align: center;"|-1.06
|-
| style="text-align: center;"|H || style="text-align: center;"|0.298
|}

In P(CH3)4]+ the central P atom is less electronegative than N in the previous molecule, and so holds onto its lone pair less tightly and is able to donate it more freely. The Carbon atoms are more electronegative than the the phosphorous atom and so this leads to a positively charged P atom with negatively charged C atoms surrounding it. In the NBO analysis we can see that 60% of the electron density is pulled towards the sp3 hybridised carbon atom in the P-C bond. The hydrogen atoms bear a positive charge again due to the inductive withdrawing effects of the carbon atoms, and the carbon atoms bear a more negative charge than in N(CH3)4]+ molecule due to these effects. Overall as expected the charges add up to one.

{|- class="wikitable"
|-
! colspan="2" style="center"|Charge Distribution of [S(CH3)3]+]
|-
| colspan="2"|[[File:NBO charge picture SCH33.png|300px|]]
|-
! Atom || Charge (e)
|-
| style="text-align: center;"|S || style="text-align: center;" |0.917
|-
| style="text-align: center;"|C || style="text-align: center;"|-0.846
|-
| style="text-align: center;"|H equitorial || style="text-align: center;"|0.297
|-
| style="text-align: center;"|H axial || style="text-align: center;"|0.279
|}

In S(CH3)3]+ the carbon atoms bear all of the negative charge due to the inductive withdrawing effects on the adjacent hydrogen atoms due to the greater electronegativity of carbon compared to hydrogen. Sulphur has a lower electronegatvity than nitrogen and so is better at donating its lone pair, but has a similar value to carbon, therefore most of the positive charge is localised on it. However it can be seen that there are two different positive values for the charge distribution on the hydrogen atoms, the axial (antiperiplanar) hydrogen atoms have a less positive value whilst the equitorial (synperiplanar) hydrogens have a more positive value. This is due to secondary orbital interactions because of the overlap of the filled σ bond of the sulphur lone pair and σ* orbital of the antiperiplanar C-H bond. Thus donation of electron density into the C-H orbital reduces the positive charge at the H atom and so we can observe the difference in charges at the H atoms as seen above.

The Second Order Perturbation Theory Analysis of Fock Matrix in a NBO Basis below shows the interaction of the sulphur lone pair with the antiperiplanar hydrogens, which yields a value of 2.32 kcal/mol which could be responsible for the difference in charges seen on the hydrogens.

<pre>
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
======================================================================================
21. LP ( 1) S 13 /100. BD*( 1) C 1 - H 4 2.32 1.02 0.043
21. LP ( 1) S 13 /103. BD*( 1) C 5 - H 8 2.32 1.02 0.043
21. LP ( 1) S 13 /106. BD*( 1) C 6 - H 10 2.32 1.02 0.043
</pre>

===Orbital contributions to C-X bond===

NBO population analysis was done in order to compare and contrast the relative contributions of the C and heteroatom orbitals to the C-X bond of the three cations.

{| class="wikitable floatleft" border="1"
|+ Orbital contributions of the C-X bond
! Molecule !! Orbital contribution outcome
|-
| [N(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98452) BD ( 1) C 1 - N 17
( 33.65%) 0.5801* C 1 s( 20.78%)p 3.81( 79.06%)d 0.01( 0.16%)
-0.0003 -0.4552 0.0237 -0.0026 -0.8884
-0.0377 0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0352 0.0203
( 66.35%) 0.8146* N 17 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 -0.5000 0.0007 0.0000 0.8658
-0.0001 -0.0001 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -0.0154 0.0089
</pre>
|-
| [P(CH3)4]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98030) BD ( 1) C 1 - P 17
( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.8640
-0.0158 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0251 -0.0145
( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.8611 0.0012 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0800 -0.0462
</pre>
|-
|[S(CH3)3]+||
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
0.0003 0.4437 0.0140 -0.0033 0.8909
-0.0030 0.0436 0.0056 -0.0762 -0.0098
0.0032 -0.0055 0.0001 0.0316 -0.0183
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 0.0001 0.4117 -0.0075 0.0012
0.0000 -0.8977 0.0258 0.0000 -0.0637
-0.0179 0.0000 0.1112 0.0311 0.0161
-0.0281 -0.0040 0.0639 -0.0342
</pre>
|}

We can see from the table above that the nitrogen atom in the N(CH3)4]+ molecule holds 66.35% of the electron density in the C-N bond. The NBO analysis calculations model the electron density of the entire molecule via its constituent atomic orbitals , which is then used to make two centre two electron bonds. Traditionally the nitrogen atom bears the formal positive charge, however we can see that the electrons in the covalent C-N bond are not shared equally as electronegativty comes into play, therefor the nitrogen atom does not bear +1 charge but actually has a negative charge due to its high electronegativity as discussed previously.

In the P(CH3)4]+ molecule only 40.43% of the electron density in the C-P bond is localised on the phosphorous atom, therefore providing a charge of greater than +1 (+1.667) which is due to the the carbon atoms greater electronegativty and inductive effects.

Considering S(CH3)3]+, due to the similar electronegativty of the sulphur and carbon atoms, the sulphur atom has 51.33% of the electron density localised on it in the C-S bond. This leads to an almost equal share of electrons in the covalent bond and a nearly a +1 charge on the sulphur atom (+0.917).

==Part 2 Influence of Functional Groups==

==Optimisation==

[N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the medium level theory 6-31G(d,p) basis set and B3LYP method as in the previous section. Keywords used: nosymm, opt=tight, int=ultrafine and scf=conver=9 were also used to ensure a tight convergence to the minimum.

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| [[File:OptimisedNCH3OH.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2OH)]+]]
| [[File:OptimisedNCH33CN.png|300px|thumb|center|Optimised structure of [N(CH3)3(CH2CN)]+]]
|-
| align="center" style="background:#f0f0f0;"|File name||OptimisationNCH33OH631Gdpnosymm1||OptinisationNCH33CN631Gdptightnosymm1
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||6-31G(d,p)||6-31G(d,p)
|-
| align="center" style="background:#f0f0f0;"|Charge||1||1
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-289.39470749||-306.39376169
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000063||0.00000052
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||5.28||9.31
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||33 minutes 21.5 seconds||28 minutes 30.0 seconds
|-
| align="center" style="background:#f0f0f0;"|Link to log file||[[Media:OptimisationNCH33OH631Gdpnosymm1.log| here]]||[[Media:OptinisationNCH33CN631Gdptightnosymm1.log| here]]
|}

{| class="wikitable"
|+ Optimisation Summary
|-
! Molecule
! Item table
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.768701D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000025 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-1.748765D-11
Optimization completed.
-- Stationary point found.
</pre>
|-
|}

It can be seen that all of the optimisations on the molecules have converged to a stationary point on their respective potential energy surfaces, therefore further frequency analysis will determine whether a minimum has been found.

===Frequency Analysis===

The frequency analysis was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: nosymm, opt=tight, int=ultrafine, scf=conver=9.

{| class="wikitable"
|+ Frequency Analysis Summary
|-
! Molecule
! Low frequencies
! IR spectrum
! Log file
|-
|[N(CH3)3(CH2OH)]+
|<pre>
Low frequencies --- -7.4589 -4.3208 0.0006 0.0007 0.0011 4.4674
Low frequencies --- 131.4307 214.2624 255.4547
</pre>
|[[File:IR_spectrum_of_NCH33OH.svg|300px|thumb|center|IR spectrum of [N(CH3)4]+]]
|[[Media:OptimisationNCH33OH631Gdpnosymm1FREQ.log| here]]
|-
|[N(CH3)3(CH2CN)]+
|<pre>
Low frequencies --- -4.3090 -3.5018 -0.0012 -0.0010 -0.0010 5.3613
Low frequencies --- 91.6075 153.8468 211.3408
</pre>
|[[File:IR_spectrum_NCH33CN.svg|300px|thumb|center|IR spectrum of [P(CH3)4]+]]
|[[Media:OptimisationNCH33CN631GdptightFREQ.log| here]]
|-
|}

The low frequency values for the two cations are within the +-20 cm-1 range, therefore indicating that the minimum energy structures have been found on the potential energy surface. There are no negative imaginary freqencies and so this can ensure a transition state structure has not been found.

===Population Analysis===

Population analysis calculations was carried out using the 6-31G(d,p) basis set and B3LYP method with keywords: pop=full, nosymm, opt=tight, int=ultrafine, scf=conver=9 on the previously optimised molecules.

{| class="wikitable"
|+ Population analysis calculations
|-
! Molecule
! Log file
|-
|[N(CH3)3(CH2OH]+
|[[Media:OptimisationNCH33OH631GdpnosymmMOandNBO.log| here]]
|-
|[N(CH3)3CN]+
|[[Media:OptimisationNCH33CN631GdptightMOandNBO2.log| here]]
|-
|}

===NBO Analysis===

The NBOs of the cations were generated through the .log files of the population analysis calculations, these were then tabulated below (charges range from -0.500 to 0.500).

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2OH)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

The OH ligand is an electron donating group, and so has had a marked change on the overall charge distribution of the molecule compared with [N(CH3)4]+.

{| class="wikitable"
|-
! Charge Distribution of [N(CH3)3(CH2CN)]+ || Labelled atoms of [N(CH3)3(CH2OH)]+ ||Atom number|| Atom || Charge (e)
|-
| rowspan="18"|[[File:NBO charge distribution NCH33OH colour.png|500px|thumb|center]] || rowspan="18"|[[File:NBO charge distribution NCH33OH numbered.png|500px|thumb|center]]||1 ||C||-0.491
|-
|2||H||0.266
|-
|3||H||0.282
|-
|4||H||0.266
|-
|5||C||0.088
|-
|6||C||-0.492
|-
|7||C||-0.494
|-
|8||H||0.249
|-
|9||H||0.237
|-
|10||H||0.274
|-
|11||H||0.266
|-
|12||H||0.269
|-
|13||H||0.262
|-
|14||H||0.272
|-
|15||H||0.271
|-
|16||N||-0.322
|-
|17||O||-0.725
|-
|18||H||0.521
|}

==References==
<references/>

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:11:05Z

Mwb11: /* Population Analysis */

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:10:19Z

Mwb11: /* NBO Analysis */

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:05:51Z

Mwb11: /* NBO Analysis */

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:04:17Z

Mwb11: /* NBO Analysis */

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:03:48Z

Mwb11: /* NBO Analysis */

Rep:Mod:MWBINORAGNICIONICLIQUIDS

2014-03-06T18:03:18Z

Mwb11: /* NBO Analysis */