== EX3 section ==

=== BH3 optimisation ===

Initially, to get accustomed with the software, I ran a simple optimisation on a BH3 molecule. The bong lengths were set to; 1.55 Å, 1.53 Å and 1.54 Å. The method was set to B3LYP and the basis set was 3-21G. Using solutions to the Schrodinger equation, the SCF part of the calculation finds the energy of the electronic density. Then, by periodically moving the nuclei in the OPT part of the calculation and recalculating the SCF for each position the optimised geometry with the lowest energy can be obtained.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_BH3_summary.PNG]] || [[File:JLS_BH3_optimisation.PNG]] || <jmol><jmolApplet>
<title>Optimisied BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_bh3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

[[File:JLS_optimisation_graph.PNG|right]] The two graphs calculated by Gaussview show information about the energy of optimisation. The first shows the total energy curve, showing the changes in energy over the optimisation steps, following the curve down until it is at the optimised geometries with the minimum energy. This is the stable state equilibrium position. The graph moves along the potential energy surface for the molecule until reaching the lowest energy geometry.

The second graph is the Root Mean Square gradient of the total energy. The gradient represents the force from nuclear-nuclear repulsion or nuclear-electron attraction which changes the positions of the nuclei. When at the energy minima the gradient will reach zero as no geometry change will lower the energy so there will be no force on the molecule. The graph reaches zero when at the least optimisation step showing the energy minima is reached.

The log file can be found [[Media:JLS BH3 OPT.LOG| here]]

=== Basis set: 6-31G(d,p) ===

Basis sets are determinants of how precise the optimisation is, with basis sets with a higher number of functions allowing higher precision but calculations take a longer amount of time.

For the previous calculation a relatively small basis set, 3-21G, was use to optimise BH3. However, now a higher level basis set, 6-31G(d,p), will be used to get a more accurate calculation.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_BH3_summary_631g.PNG]] || [[File:JLS_BH3_OPT_631g_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BH3_OPT_631G.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_BH3_OPT_631G.LOG| here]]

=== Pseudo Potentials ===

Pseudo potentials are used for molecules containing heavier atoms when the calculations become to lengthy due to the large number of electrons. This means an simpler approximation is used for core electrons than the valence electrons as these are those most involved in bonding.

==== GaBr3 ====

The symmetry was set at D3h and a medium basis set was used, LanL2DZ. This uses a separate basis set for the first row atoms and heavier elements.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:GaBr3_optimisation_summary.PNG]] || [[File:GaBr3_optimisation_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied GaBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log_GaBr3_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>

|}
The optimsation log file can be found here {{DOI|10042/143675}}

==== BBr3 ====

For BBr3 a mixture of pseudo-potentials and basis sets was used. For the lighter boron atom a basis set 6-31G(d,p) was used and for the heavier bromine atoms a pseudo-potential LanL2DZ is used. This is achieved by using basis set GEN in GaussView which allows the assigning of basis sets manually. The results are given below:

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:BBr3_OPT_summary.PNG]] || [[File:BBr3_OPT_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BBr3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The symmetry should be C3v. The optimsation log file can be found here {{DOI|10042/143682}}

=== Structural Comparison [BH3, GaBr3, BBr3 ] ===

From the above three optimisations, the following data was found regarding bond length and bond angle:

{| class="wikitable" border="1"
|+ Geometry Data
! !! BH3 !! GaBr3 !! BBr3
|-
| r(E-X) [Å] || 1.19 || 2.35 || 2.02 ||
|-
| θ(X-E-X) || 120.0 || 120.0 || 120.0 ||
|}

'''Ligands''': From the values comparing BH3 and BBr3 it can be seen that changing the ligand does not effect the bond angle but does affect the bond length. Bromine and hydrogen are similar in that they both monovalent and so bonding to boron completes the outer orbital of electrons.
It was found that the B-H bond is relatively much smaller than the B-Br bond, indicating that it is a much stronger bond. This is likely due to the difference in energies between the orbitals. Boron and Hydrogen are both small atoms, so compared to the larger bromine, the hydrogens core orbital can get much closer to the boron. Also, the valence electron on hydrogen sits in a 1s orbital means it is denser and so forms a stronger bond compared to the valence electrons in bromine which sit in more diffuse p orbitals. Also, hydrogen 1s orbitals will sit much closer in energy to bromine valence p orbitals leading to stronger bonding.

'''Central Element''': Again, changing the central atom has no observed effect on the bond angles but does affect the bong length. Gallium and boron are both in group 13 so have 3 electrons in their valence p orbital. This leads to them both forming trigonal planar complexes. Gallium, as further down the group has a larger atomic radius and so has larger more diffuse outer orbitals, as there is also a set of d orbitals between the valence and the nucleus. This leads to the gallium having longer and therefore weaker bonds.

'''Bonding''': A classical view of a covalent bond is that a pair of electrons is shared between two atoms due to an electrostatic attraction between electrons and protons. Double and triple bonds are the sharing of a two or three electron pairs respectively. Ionic bonds are held together by electrostatic forces as opposing charges are formed from exchange of electrons to complete electron 'shells'. However, this is a very simple outlook on bonding and there is actually a wide continuum of bonding, which can be examined more with molecular orbital theory. This enables the bond order of the molecule to be worked out, which is a parameter which assess the two atoms molecular orbitals and how many bonds are formed between. <ref name="BondOrder" /> Many bonds are not simply ionic or covalent and can be on the spectrum between the two. Also, there are weaker, partial bonds such as hydrogen bonds and van der waals forces. These are due to the polarisation of electron density and consequential small attractive interactions between the slight charges caused by the difference in electron density.
A strong bond is formed from good overlap of interacting orbitals. Also, a large difference in electronegativity can form strong ionic bonds, especially those at the top of the periodic table where the nucleus has greater effect on the electrons as there is less shielding.

An example of a strong, covalent bond is that between N2, this has high bond order as it is a triple bond and because it is a homonuclear bond, energy levels are the same increasing orbital overlap of orbitals that are dense so form a very strong bond at 948.1 kcal/mol. <ref name="N2" /> This is comparison to the comparitvely very weak homonuclear bond between the large diffuse orbitals of Cs2 which is 43.5 kJ/mol <ref name="N2" /> which is a weak bond. A medium bond is the C-H bond in methane which is 432.9 kJ/mol <ref name="CH" />

For some structures in gaussview there are no bonds joining molecules where we would expect them, for example with the intial calculations on BH3. This is due to the bond distance being longer than the one gaussview has assigned for those atoms and so does not necessarily mean there is no bonding. There could still be bonding character where orbitals are overlapping.
<jmol><jmolApplet>
<title>BH3 with no apparent bonds</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BH3_OPT_no_bond.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===

'''BH3'''

Deriving the second derivative of the potential energy allows energy minima to be determined as if it is a positive value for a stationary point it indicates that this is a minimum as it gives the curvature of the potential energy curve. This frequency analysis allows the stationary points to be resolved into minimum, if all positive, stationary point and if one is negative then it is a stationary point. It also allows computation of the different vibrational modes of the molecule, 3N-6 if non-linear, which as well as being visualised can also be compared with the IR spectrum of experiment.

This analysis was performed on the 6-31G(d,p) optimised BH3 molecule but with symmetry set at D3h.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_BH3_FREQUENCY_OPT_summary.PNG]] || [[File:JLS_bh3_frequency_opt_lowfrequencies.PNG]]

|}

The log file can be found [[Media:JLS_BH3_FREQUENCY_OPT_.LOG| here]]

[[File:JLS_bh3_frequency_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 1163 || 93 || Yes || bend
|-
| 1213 || 14 || Slight || bend
|-
| 1213 || 14 || Slight || bend
|-
| 2583 || 0 || No || Stretch
|-
| 2716 || 126 || Yes || Stretch
|-
| 2716 || 126 || Yes || Stretch

|}

The predicted IR spectrum shows fewer peaks, 3, to number of vibrations found, 6. This is due to degeneracy of the peaks meaning they overlay on the spectrum and also for one of the vibrations there is no change in dipole therefore will not be IR active.
The spectrum shows clearly 2 large peaks which corresponds to the strong active vibrations 1163 and 2716 cm-1. Then also there is a weaker signal at 1213cm-1 to the degenerate peak which has relatively small intensity, due to a smaller change in dipole.

'''GaBr3'''

Frequency analysis was also run on GaBr3 with basis set LANL2DZ and B3LYP method used. The frequency data is shown below:

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_GaBr3_FREQUENCY_summary.PNG]] || [[File:JLS_GaBr3_frequency_lowfrequencies.PNG]]

|}

The frequency log file can be found here {{DOI|10042/149182}}

[[File:JLS_GaBr3_frequency_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 76 || 3 || Slight || bend
|-
| 76 || 3 || Slight || bend
|-
| 100 || 9 || Slight || bend
|-
| 197 || 0 || No || Stretch
|-
| 316 || 57 || Yes || Stretch
|-
| 316 || 57 || Yes || Stretch

|}

'''Vibrational comparison between GaBr3 and BH3'''
[[File:Bh3_BEND.PNG|thumb|right|BH3 A2" umbrella motion]]
[[File:GaBR3_BEND.PNG|thumb|right|GaBr3 A2" umbrella motion]]
Vibrational frequency is dependent on the mass and force constant, which reflects the strength of the bond.
ν = (1/2π)(k/μ)1/2
where k is the force constant and μ is the reduced mass. This shows that the heavier the atoms the lower the frequency as the frequency is inversely proportional to the square of the reduced mass. Also, the stronger the bond, the the larger the force constant, which frequency is proportional to the square of.

Both GaBr3 and BH3 have six vibrational modes due to equation 3N-6 where N is 4. The infrared spectrum of GaBr3 is in the range of lower frequencies than BH3 due to heavier mass of the atoms and so a larger reduced mass. This consequently means lower vibrational frequency.
For GaBr3 the energy of the vibrational modes is reordered. For example, the A2" umbrella motion. For BH3 is the lowest frequency and for GaBr3 it is the highest bending frequency, this difference is due to the difference in the mass of the atoms in the different molecules. As can be seen on the images, the displacement vectors are smaller than the for GaBr3 bromine atoms than for BH3 hydrogen atoms. This is due to the difference in mass, as bromine is heavier than the central atom, so the motion is more in the central gallium atom than in bromine whereas for BH3, the hyrdogens are much lighter and so move more easily than the boron. This difference in the nature of the vibration can be seen on the gaussview animation. Then considerable difference to hydrogen in mass for the gallium is why it is a higher in the vibration order as more energy is needed for it to move.

'''Review of Frequency Analysis'''

The same method for optimisation and frequency must be used as because the optimised structure is highly dependent on the type of basis set and method used so will not be same structure the frequency is being calculated for as previous optimisation.
The purpose of the frequency analysis is too confirm the optimised structure found is at the energy minimum as the structure is just optimised to a stationary point. By using the second derivative of this energy profile the vibrational analysis confirms that this stationary point is in fact a minima.
The 'low frequencies' correspond to the motions of the center of mass of the molecule being observed. Ideally they should be zero, and get smaller with the better method used as the center of mass is moving less.

=== Calculating Molecular Orbitals ===

Using the 6-31G(d,p) optimised BH3 molecule the molecule orbitals were calculated and can be found here: {{DOI|10042/146859}}

[[File:JLS_BH3_MO.png]]

Comparing the predicted orbitals in the molecular orbital diagram with that calculated there is reasonable agreement. The small constricted nature of the 1s orbital can be seen in both, the more diffuse nature of the higher energy orbitals is only really seen in the calculated orbitals opposed those from the MO diagram. Also, some of the contributions from specific orbitals to certain molecular orbitals are not in agreement, for example in 3a1' the computed contribution of the 2s orbital is smaller than that predicted. However, for a qualitative method the MO diagram is reasonably accurate and therefore useful to predict orbitals in smaller simpler molecules without computational methods.

==== NH3 ====

'''Optimisation'''
Using basis set 6-31G(d,p), NH3 was optimised. The bond angle between the N-H bonds was found to be 106° and the bond length was found to be 1.02 Å.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NH3_opt_summary.PNG]] || [[File:JLS_NH3_opt_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:NH3_OPT.LOG| here]]

'''Frequency analysis'''
Using the optimised molecule and setting the point group to C3v a frequency analysis was run as before, with basis set 6-31G(d,p) and the B3LYP method, to confirm the energy minima.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NH3_freq_summary.PNG]] || [[File:JLS_NH3_freq_lowfrequencies.PNG]]

|}

It can be seen that the the frequencies are low and that there is no negative frequencies showing the energy minima has been found.

[[File:JLS_NH3_freq_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 1089 || 145 || Yes || bend
|-
| 1694 || 14 || Yes || bend
|-
| 1694 || 14 || Yes || bend
|-
| 3461 || 1 || Slight || Stretch
|-
| 3590 || 0 || No || Stretch
|-
| 3590 || 0 || No || Stretch

|}

The log file can be found [[Media:JLS_NH3_FREQ.LOG| here]]

'''MO and NBO'''
[[File:JLS_NH3_charge_distribution.PNG|thumb|right|Charge distribution on an optimised NH3 molecule with red indicating negative charge and green positive charge ]]
The molecular orbitals were computed again using 6-31G(d,p) basis set and the B3LYP method with set C3v symmetry. The log file can be found here: {{DOI|10042/147006}}.

The charge distribution is shown, with nitrogen possessing a negative charge of -1.125 and the hydrogen's with 0.375 each.

=== Association Energies ===

==== Ammonia-Borane ====

Ammonia-borane is a Lewis acid-base complex where by definition the nitrogen is donating a pair of electrons to the boron however the nature of this bond is not so straight forward and can be investigated by examining association energies.
The energies of the reactants and products are needed to calculate reaction energy which will give the energy for the dative bond between nitrogen and hydrogen. NH3 and BH3 have already been calculated and so NH3BH3 was optimisation was run.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NH3BH3_OPT_summary.PNG]] || [[File:JLS_NH3BH3_OPT_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_NH3BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_NH3BH3_OPT.LOG| here]]

Frequency analysis was then also performed on NH3BH3

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NH3BH3_FREQ_summary.PNG]] || [[File:JLS_NH3BH3_FREQ_lowfrequencies.PNG]]

|}

The log file for the frequency analysis can be found [[Media:JLS_NH3BH3_FREQ.LOG| here]]

The energies calculated for the reagents and products were found to be:

{| class="wikitable" border="1"
|+ Energies
! !! NH3 !! BH3 !! NH3BH3
|-
| Energies (a.u) || -56.5577687 || -26.6153235 || -83.2246889

|}

The dissociation energy is given by ΔE=E(NH3BH3)-[E(NH3)+E(BH3)].
So ΔE= -0.0515967 a.u
ΔE= -135.44 KJ/mol
This is a relatively weak bond as in much smaller than the medium bond of C-H of 432.9 kJ/mol <ref name="CH" />, this is likely due to the nature of the dative covalent bond not being as strong as a fully covalent bond. However it is not a weak as that between Cs2 which is 43.5 kJ/mol <ref name="N2" />.

== Ionic Liquids: Designer Solvents ==

Green chemistry is a large growing field in chemistry and has led to the development of replacements for traditional solvents which are flammable and volatile leading to unwanted wastage. Ionic liquids have good solvating properties and are recyclable and non-volatile/non-flammable so are good potential replacements for usual solvents. <ref name="IL1" />

Their composition is that of room temperature liquid ions which is achievable through bulky groups so the ions cannot pack together well generating the property of low melting points. This property can be fine tuned by the use of smaller anions and increasing the bulkiness and unsymmetrical nature of the cation, leading to a decrease in melting point. <ref name="IL1" />

This shows that the chemical composition and nature of these ions affect the properties of these solvents and therefore their use in synthesis thus using computational techniques different ionic liquids cations will be investigated at the molecular level. The difference in central atom will be explored and also considered is the affect of additional functional groups, compareing electron withdrawing groups with electron donating.

=== Onium Cations ===

==== [N(CH3)4]+ ====

The cation was optimised using 6-31G(d,p) basis set and the B3LYP method. The symmetry was not constrained as this would increase computing time and may lend it to error.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NCH34_OPT_summary1.PNG]] || [[File:JLS_NCH34_OPT_file1.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_NCH34_OPT1.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_NCH34_OPT1.LOG| here]]

It was found that the optimised bond lengths were: N-C [1.51 Å], C-H [1.09 Å] and the bond angles around nitrogen was 109.5 ° but for the carbon there was less perfect sp3 hybridization as the angles between the hydrogens, 110.1 °, were larger than between the nitrogen and hydrogens, 108.9 °. This could be due to the high electronegativity of the nitrogen central atom meaning a larger build up of electron density in the centre so hydrogens repulsed more away the nitrogen centre.

Frequency analysis was also ran with 6-31G(d,p) basis set and the B3LYP method to confirm the minimum energy point found. The low frequencies are checked at +/-15 cm-1.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NCH34_FREQ_summary1.PNG]] || [[File:JLS_NCH34_FREQ_low1.PNG]]

|}

The log file can be found [[Media:JLS_NCH34_FREQ1.LOG| here]]

Molecular orbital analysis was also run and the log file for the molecular optimisation calculations can be found [[Media:JLS_NCH34_MO1.LOG| here]]. The molecular orbitals are analysed more below as well as the charge distribution in the molecule.

==== [P(CH3)4]+ ====

[P(CH3)4]+ was optimised using 6-31G(d,p) basis set and the B3LYP method.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_PCH34_OPT_summary1.PNG]] || [[File:JLS_PCH34_OPT_file1.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_PCH34_OPT1.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_PCH34_OPT.LOG| here]]

Analysis of the bond angles shows that the around the carbon, the angle between hydrogen and nitrogen is 109.9 ° compared to angle between the hydrogens at 109.0 °. The angle around the nitrogen is 109.5 °. The P-C bond is 1.82 Å and the C-H bond is 1.09 Å. This data shows that the molecule is nearly perfectly sp3 hybridised as all angles are very close to 109 °. The lack of slight distortion found in [N(CH3)4]+ is likely due to the difference in elctronegativities in the two central atoms.

Again vibrational analysis was run on the cation with 6-31G(d,p) basis set and the B3LYP method to confirm minima.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_PCH34_FREQ_summary1.PNG]] || [[File:JLS_PCH34_FREQ_low1.PNG]]

|}

The log file can be found [[Media:JLS_PCH34_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_PCH34_MO.LOG| here]] and the charge distributions are discussed and compared below aswell as the nbo population for the C-P being analysed.

==== [S(CH3)3]+ ====

[S(CH3)3]+ was optimised using 6-31G(d,p) basis set and the B3LYP method.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_SCH33_OPT_summary.PNG]] || [[File:JLS_SCH33_OPT_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_SCH33_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_SCH33_OPT.LOG| here]]

[[File:JLS_SCH33_angles.png|thumb|right|[S(CH3)3]+ showing different bond angles]]

The structure of the molecule is not planar, due to the lone pair situated on the sulphur. This means the angle between the carbons is 102.8 °. The angle between the hydrogen and sulphur is 107.3 ° for the hydrogens pointing 'up' and 110.6 for those pointing 'down'. This difference in angles is due to the different environments the hydrogens are in due to the unsymmetrical nature of the molecule. However, the both C-H bond lengths are 1.09 Å and the S-C length is 1.82 Å.

Frequency analysis was run on the molecule with a B-31G(d,p) basis set and the B3LYP method to confirm the energy minimum.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_SCH33_FREQ_summary.PNG]] || [[File:JLS_SCH33_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_SCH33_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_SCH33_MO.LOG| here]] and the charge distribution and nbo population in analysed below.

==== Geometries comparison ====

The bond lengths and the bond angles of the above cations were taken from their optimised structure and compared in the table below.

{| class="wikitable" border="1"
|+ Geometries
! Molecule !! X-C length (Å) !! C-H length (Å) !! C-X-C angle (°) !! X-C-H angle (°) !! H-C-H angle (°)
|-
| [N(CH3)4]+ || 1.51 || 1.09 || 109.5 || 108.9 || 110.1
|-
| [P(CH3)4]+ || 1.82 || 1.09 || 109.5 || 109.9 || 109.0
|-
| [S(CH3)3]+ || 1.82 || 1.09 || 102.8 || 110.6/107.3 ||111.1/109.4

|}

It can be seen that the bond length between N-C is significantly smaller than the P-C or S-C showing that is a stronger bond. This is due to the higher electronegativity of nitrogen and lower outer p orbitals that are at similar energy to carbon so have very good overlap leading to stronger interaction. Phosphorus and sulphur are of similar energy in comparison so form similarly strong bonds with the carbon. It can be seen that changing the central atom does not affect the length of the C-H bonds as they are the same in all three molecules.
Both the nitrogen and sulphur molecules have the same angles of the methyl groups round the central atom, showing perfect sp3 hybridisation

==== MO and NBO analysis of [N(CH3)4]+ ====

Using five different molecular orbitals found from calculations on the electronic structure of [N(CH3)4]+ to get a better picture of the different levels of bonding. Core electrons are not considered as they are so low in energy they are not involved in bonding. Bonding interaction are produced from in-phase overlap and anti-bonding from out-of-phase overlap. Boundaries between phase changes are defined as nodes and indicate anti-bonding character. Due to the smaller directionality and more diffuse nature pi interactions are weaker than sigma type.

{| class="wikitable" border="1"
|+ MO of [N(CH3)4]+
|-
|The first non-core molecular orbital is highly bonding. This is likely due to bonding through the s-orbital interaction, leading to a highly bonding molecular orbital with no anti-bonding contribution.There are no nodes and all interactions are σ, this dense nature of the orbital creates the strong bonding and therefore stabilisation of the electrons in this orbital. The MO is very tight on the orbitals. ||[[File:JLS_6.PNG|thumb|First core orbital, energy level 6]]
|-
| This molecular orbital still shows large lobes of bonding in-phase interactions, probably between s-orbitals on the hydrogens and the carbon of predominately two of the methyl groups. There is also strong through bond interaction between the central nitrogen through hybridised sp3 and the corresponding phase s-orbital. However, there is also now some anti-bonding character in the molecule seen by the nodal plane which splits the molecular orbital. This means there will be some weak through space anti-bonding interactions which will slightly destabilise the orbital. || [[File:JLS_9.png|thumb|MO 8]]
|-
| Again, this molecular orbital shows strong bonding interactions through bonds between the hydrogen and the carbon. Most likely between the s orbital of the hydrogen and the sp3 hybridised carbon orbital which would be pointing in the direction of the bond. This could then forms another bonding interaction with the s-orbital of the nitrogen. There is a spherical nodal plane around the central atom. There is also though-space anti-bonding interactions which are relatively close in space so will be relatively destabilising for through-space interactions. The atomic orbitals in the molecules are now getting more diffuse as the MOs are getting higher energy. || [[File:JLS_10.png|thumb| Level 10 MO]]
|-
|The MO at energy level 14 orbitals shows the lobes are spreading further across the molecule as they get more diffuse.There are two nodal planes, criss-crossing the central nitrogen atom. The atomic orbitals proposed to be involved are the sp3 of the carbon and s orbitals of the hydrogen. This lends to strong through bond bonding interactions, but then there is also weak through space anti-bonding interaction between the the opposite phase s orbitals of the methyl hydrogens. However, this has a minimal destabilising effect compared to the stabilising affect of the through bond bonding. There is also more even weaker through space anti-bonding interactions between the different methyl groups of opposite phase, but also stabilising through space bonding interactions that elongate the phases across the molecule. ||
[[File:JLS_14_2.png|thumb|Level 14 MO]]
|-
| The 18th molecular orbital a relatively high energy bonding orbital which can be explained by its increased anti-bonding nature in comparison to the MOs above. It has three nodal planes and features the interaction of mainly 3 of the CH3, with most of the electron density spread over two of the hyrdogens on these groups. The interacting orbitals are quite diffuse, espcially compared to level 6 meaning both bonding and antibonding interactions are weaker than in above orbitals. The bonding, stabilising effect comes from the interaction between the sp3 orbitals on the carbon with the s atomic orbitals on the hydrogens. This leads to quite strong through bonding interactions which outweighs the weaker through space anti-bonding interactions across nodes and so therefore overall the molecular orbital is still stabilising. || [[File:JLS_18.png|thumb|Level 18 MO]]
|}

==== Charge Distribution Comparison ====

From the natural bond orbital analysis of the cations the distribution of charge across the molecules could be calculated over the molecule. The differing central atom can be seen, by the tables below, to greatly effect the way that charge is disbursed across the molecule.

{| class="wikitable" border="1"
|+ Charge Distribution
! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| [[File:JLS_NCH34_MO_charge.PNG]] || [[File:JLS_PCH34_MO_charge.PNG]] || [[File:JLS_SCH33_MO_charge.PNG]]

|}

{| class="wikitable" border="1"
|+ Charges
! Atom !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Central[N/P/S] || -0.295 || 1.667 || 0.917
|-
| C || -0.483 || -1.060 || -0.846
|-
| H || 0.269 || 0.298 || 0.297/0.279

|}

All three molecules hold a positive charge which is usually placed at the central atom. However, the central atoms differs in charge from -0.342 on the nitrogen to 1.667 on the phosphorus.
This difference is due to the difference in electronegativity of the central atom. . Nitrogen has a the highest electronegativity at 3.04<ref name="BondOrder" /> this is compared to carbon which has a Pauling electronegativity of 2.55<ref name="BondOrder" />.
This means that in comparison to phosphorus and sulphur the nitrogen has lower energy atomic orbitals, closer in energy to the carbons allowing efficient overlap for the positive charge to be distributed farthest away from the electronegative nitrogen and which can be seen as all positive charge is situated on the hydrogens. Also carbons are significantly smaller negative charge than the other two cations due to the spreading of the positive charge and the electronegative pull of the nitrogen drawing electron density towards it in the bond.

In comparison, the phosphorus is a row down from nitrogen so is less electronegative, 2.19<ref name="BondOrder" />, and has larger, more diffuse orbitals. This leads to poorer orbital overlap with the carbon so does not show the spread of charge that can be seen in [N(CH3)4]+. This means that the central atom now holds onto the positive charge. Also, due to carbon being more electronegative and the lack of overlap and more electrons in the system means that the carbon is much more negatively charged than on the other two molecules.
Sulphur is more electronegative, 2.58<ref name="BondOrder" />, than phosphorus so atomic orbitals will be lower in energy than and will be able to overlap more than phosphorus hence the positive charge on the central atom is smaller as the charge is able to distribute more, hence making the charge on the carbon less negative.
Also, the sulphur has one less substituent which means that the charge on the hydrogens is not evenly distributed as those hydrogens facing 'up' are more positive than those facing towards other hydrogens, this could be due to a build up of electron density between the hydrogens.

==== [NR4]+ ====

In the traditional characterisation of [NR4]<suop>+ cations the charge is placed on the central nitrogen. This formal assignment is made as the nitrogen is the atom with the higher number of substituents and in basic valence bond theory would be the atom lacking one electron so would be positively charged. However, as can be seen from the charge distribution this is clearly not the case and the positive charge is actually distributed across the hydrogens. This shows that the formal description is not valid for the [N(CH3)4]<suop>+ molecule. However, it is more true for the the phosphorus and sulphur cations as these have more of a positive charge on the central atom.

==== Relative contributions of C-X ====

In comparison between the C-X bonds of the molecule the NBO analysis can be evaluated from the MO calculations run on the three different molecules. The nitrogen contributes 66% to the bond whereas phosphorus contributes 40% and sulphur contributes 51%. This correlates to the different electronegativities of the 3 atoms which are stated above. The higher the electronegativity the more the larger the pull on electrons in the bond and so the higher the contribution.
These relative contributions can also be seen in the charge distributions discussed above as it is seen that nitrogen has the highest percentage contribution and so has a higher amount of electron density on its centre and therefore has the more negative charge. And phosphorus which has the lowest contribution also has the most positive charge situated on it.

The NBO analysis also confirms that the central atom is sp3 hybridised as there is about a 25% contribution from s orbital and 75% from p orbital. This is in the 1:3 ratio as expected in sp3 hybridised orbitals. However, as discussed in the geometry analysis the sulphur molecule is not perfect sp3 hybridised and this is reflected in the s and p contributions as the s contribution is 20% and p is 80%, meaning that there is less s character to the bond than would be expected.

=== Influence of functional groups ===

'''[N(CH3)3(CH2OH)]+'''

[N(CH3)3(CH2OH)]+ was optimised using the B3LYP method and using the basis set 6-31G(d,p).

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_N(CH3)3(CH2OH)_OTP_summary.PNG]] || [[File:JLS_N(CH3)3(CH2OH)_OTP_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_N(CH3)3(CH2OH)_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2OH)_OPT.LOG| here]]

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_N(CH3)3(CH2OH)_FREQ_summary.PNG]] || [[File:JLS_N(CH3)3(CH2OH)_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2OH)_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_N(CH3)3(CH2OH)_MO.LOG| here]]

'''[N(CH3)3(CH2CN)]+'''

[N(CH3)3(CH2OH)]+ was optimised using the B3LYP method and using the basis set 6-31G(d,p).

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_N(CH3)3(CH2CN)_OTP_summary.PNG]] || [[File:JLS_N(CH3)3(CH2CN)_OTP_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_N(CH3)3(CH2CN)_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2CN)_OPT.LOG| here]]

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_N(CH3)3(CH2CN)_FREQ_summary.PNG]] || [[File:JLS_N(CH3)3(CH2CN)_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2CN)_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_N(CH3)3(CH2CN)_MO.LOG| here]]

==== Charge distribution analysis ====

Using the molecular orbital calculation the charge distributions of the two optimised cations could be analysed. The table below shows the distribution of charge in both molecules;

{| class="wikitable" border="1"
|+ Charge Distributions
! [[File:JLS_N(CH3)3(CH2OH)_charge.PNG]] !! [[File:JLS_N(CH3)3(CH2CN)_charge.PNG]]

|}

The difference between in charge distribution can be explained by the nature of the attached functional group. The lone pairs on the oxygen in the OH group can be donated, this would explain why the central nitrogen has a more negative charge than in N(CH3)3(CH2CN)+. The attached carbon however is more positive which is due to oxygen being much higher in electronegativity than carbon so polarising the bond. The cyanide group however is electron withdrawing hence the carbon it attached to being less negatively charged than the other methyl groups. Also, it can be seen that more of the negative charge sits on the nitrogen in the functional group. Also, the nitrogen is slightly less negative than in N(CH3)4+ but not significantly so.

==== HOMO LUMO comparison ====

Also from the molecular orbital calculations the highest occupied orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) can be analysed. Below is a table of the three different cations

{| class="wikitable" border="1"
! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
! colspan="3" | HOMO
|-
| [[File:JLS_NCH34_HOMO.PNG|thumb]] || [[File:JLS_N(CH3)3(CH2OH)_HOMO.PNG|thumb]] || [[File:JLS_N(CH3)3(CH2CN)_HOMO.PNG|thumb]]
|-
! colspan="3" | LUMO
|-
! [[File:JLS_NCH34_LUMO.PNG|thumb]] !! [[File:JLS_N(CH3)3(CH2OH)_LUMO.PNG|thumb]] !![[File:JLS_N(CH3)3(CH2CN)_LUMO.PNG|thumb]]

|}

It can be seen that the shape of the HOMO and LUMO orbitals has changed across the three different molecules, most dramatically between the HOMO orbitals. It can be seen that for the molecules with functional groups the HOMO orbitals are centred around these groups, this can be especially seen in [N(CH3)3(CH2CN)]+ whereas for N(CH3)4+ it is spread across the molecule and is more diffuse.
The shape of the LUMO between N(CH3)4+ and [N(CH3)3(CH2OH)]+ changes less, but with more spreading along the OH bond. Again for N(CH3)4+ the LUMO is now more focused on the functional group but still is spread over the entire molecule.

Comparison of energies is important in discerning the chemical impact of the differences in the HOMO/LUMOs.

{| class="wikitable" border="1"
! colspan="3" | HOMO Energies (a.u)
|-
! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| -0.57932 || -0.48762 || -0.50048
|-
! colspan="3" | LUMO Energies (a.u)
|-
| -0.13304 || -0.12460 ||-0.18181
|-
! colspan="3" | HOMO-LUMO gap (kJ/mol)
|-
| 1171 || 953 || 836.51

|}

Compared to N(CH3)4+ the energy of the HOMO has increased for both functional group molecules and for [N(CH3)3(CH2OH)]+ the LUMO has also increased as the addition of an electron donating group has added more electron density to the molecule therefore destabilising it. In contrast, the electron withdrawing group CN decreases the energy of the molecule showing the stabilising effect. This means that it can now more readily accept electrons so would be better oxidant or lewis acid.

The HOMO-LUMO energy gap in N(CH3)4+ is the largest and so means this is likely the most stable and less likely to donate electrons. The addition of the two functional groups decreases the gap meaning they are more likely to promote an electron from the HOMO to the LUMO creating an excited state molecule.

== References ==
<references>

<ref name="BondOrder"> C. Housecroft, A. Sharpe, Inorganic Chemistry,2012, Pearson, 4 ed, 50 & 30. </ref>

<ref name="N2"> T. Ghanty and S. Ghosh, J. Phys. Chem., 1991, 6512–6514.</ref>

<ref name="CH"> G. K. Jarvis, K.-M. Weitzel, M. Malow, T. Baer, Y. Song and C. Y. Ng, Phys. Chem. Chem. Phys., 1999, 1, 5259–5262. </ref>
</references>

<ref name="IL1"> S. Keskin, D. Kayrak-Talay, U. Akman and Ö. Hortaçsu, J. Supercrit. Fluids, 2007, 43, 150–180.</ref>

Rep:Mod:JennySamphire

2014-12-19T10:09:22Z

Jls12: /* Onium Cations */

== EX3 section ==

=== BH3 optimisation ===

Initially, to get accustomed with the software, I ran a simple optimisation on a BH3 molecule. The bong lengths were set to; 1.55 Å, 1.53 Å and 1.54 Å. The method was set to B3LYP and the basis set was 3-21G. Using solutions to the Schrodinger equation, the SCF part of the calculation finds the energy of the electronic density. Then, by periodically moving the nuclei in the OPT part of the calculation and recalculating the SCF for each position the optimised geometry with the lowest energy can be obtained.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_BH3_summary.PNG]] || [[File:JLS_BH3_optimisation.PNG]] || <jmol><jmolApplet>
<title>Optimisied BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_bh3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

[[File:JLS_optimisation_graph.PNG|right]] The two graphs calculated by Gaussview show information about the energy of optimisation. The first shows the total energy curve, showing the changes in energy over the optimisation steps, following the curve down until it is at the optimised geometries with the minimum energy. This is the stable state equilibrium position. The graph moves along the potential energy surface for the molecule until reaching the lowest energy geometry.

The second graph is the Root Mean Square gradient of the total energy. The gradient represents the force from nuclear-nuclear repulsion or nuclear-electron attraction which changes the positions of the nuclei. When at the energy minima the gradient will reach zero as no geometry change will lower the energy so there will be no force on the molecule. The graph reaches zero when at the least optimisation step showing the energy minima is reached.

The log file can be found [[Media:JLS BH3 OPT.LOG| here]]

=== Basis set: 6-31G(d,p) ===

Basis sets are determinants of how precise the optimisation is, with basis sets with a higher number of functions allowing higher precision but calculations take a longer amount of time.

For the previous calculation a relatively small basis set, 3-21G, was use to optimise BH3. However, now a higher level basis set, 6-31G(d,p), will be used to get a more accurate calculation.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_BH3_summary_631g.PNG]] || [[File:JLS_BH3_OPT_631g_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BH3_OPT_631G.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_BH3_OPT_631G.LOG| here]]

=== Pseudo Potentials ===

Pseudo potentials are used for molecules containing heavier atoms when the calculations become to lengthy due to the large number of electrons. This means an simpler approximation is used for core electrons than the valence electrons as these are those most involved in bonding.

==== GaBr3 ====

The symmetry was set at D3h and a medium basis set was used, LanL2DZ. This uses a separate basis set for the first row atoms and heavier elements.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:GaBr3_optimisation_summary.PNG]] || [[File:GaBr3_optimisation_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied GaBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log_GaBr3_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>

|}
The optimsation log file can be found here {{DOI|10042/143675}}

==== BBr3 ====

For BBr3 a mixture of pseudo-potentials and basis sets was used. For the lighter boron atom a basis set 6-31G(d,p) was used and for the heavier bromine atoms a pseudo-potential LanL2DZ is used. This is achieved by using basis set GEN in GaussView which allows the assigning of basis sets manually. The results are given below:

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:BBr3_OPT_summary.PNG]] || [[File:BBr3_OPT_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BBr3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The symmetry should be C3v. The optimsation log file can be found here {{DOI|10042/143682}}

=== Structural Comparison [BH3, GaBr3, BBr3 ] ===

From the above three optimisations, the following data was found regarding bond length and bond angle:

{| class="wikitable" border="1"
|+ Geometry Data
! !! BH3 !! GaBr3 !! BBr3
|-
| r(E-X) [Å] || 1.19 || 2.35 || 2.02 ||
|-
| θ(X-E-X) || 120.0 || 120.0 || 120.0 ||
|}

'''Ligands''': From the values comparing BH3 and BBr3 it can be seen that changing the ligand does not effect the bond angle but does affect the bond length. Bromine and hydrogen are similar in that they both monovalent and so bonding to boron completes the outer orbital of electrons.
It was found that the B-H bond is relatively much smaller than the B-Br bond, indicating that it is a much stronger bond. This is likely due to the difference in energies between the orbitals. Boron and Hydrogen are both small atoms, so compared to the larger bromine, the hydrogens core orbital can get much closer to the boron. Also, the valence electron on hydrogen sits in a 1s orbital means it is denser and so forms a stronger bond compared to the valence electrons in bromine which sit in more diffuse p orbitals. Also, hydrogen 1s orbitals will sit much closer in energy to bromine valence p orbitals leading to stronger bonding.

'''Central Element''': Again, changing the central atom has no observed effect on the bond angles but does affect the bong length. Gallium and boron are both in group 13 so have 3 electrons in their valence p orbital. This leads to them both forming trigonal planar complexes. Gallium, as further down the group has a larger atomic radius and so has larger more diffuse outer orbitals, as there is also a set of d orbitals between the valence and the nucleus. This leads to the gallium having longer and therefore weaker bonds.

'''Bonding''': A classical view of a covalent bond is that a pair of electrons is shared between two atoms due to an electrostatic attraction between electrons and protons. Double and triple bonds are the sharing of a two or three electron pairs respectively. Ionic bonds are held together by electrostatic forces as opposing charges are formed from exchange of electrons to complete electron 'shells'. However, this is a very simple outlook on bonding and there is actually a wide continuum of bonding, which can be examined more with molecular orbital theory. This enables the bond order of the molecule to be worked out, which is a parameter which assess the two atoms molecular orbitals and how many bonds are formed between. <ref name="BondOrder" /> Many bonds are not simply ionic or covalent and can be on the spectrum between the two. Also, there are weaker, partial bonds such as hydrogen bonds and van der waals forces. These are due to the polarisation of electron density and consequential small attractive interactions between the slight charges caused by the difference in electron density.
A strong bond is formed from good overlap of interacting orbitals. Also, a large difference in electronegativity can form strong ionic bonds, especially those at the top of the periodic table where the nucleus has greater effect on the electrons as there is less shielding.

An example of a strong, covalent bond is that between N2, this has high bond order as it is a triple bond and because it is a homonuclear bond, energy levels are the same increasing orbital overlap of orbitals that are dense so form a very strong bond at 948.1 kcal/mol. <ref name="N2" /> This is comparison to the comparitvely very weak homonuclear bond between the large diffuse orbitals of Cs2 which is 43.5 kJ/mol <ref name="N2" /> which is a weak bond. A medium bond is the C-H bond in methane which is 432.9 kJ/mol <ref name="CH" />

For some structures in gaussview there are no bonds joining molecules where we would expect them, for example with the intial calculations on BH3. This is due to the bond distance being longer than the one gaussview has assigned for those atoms and so does not necessarily mean there is no bonding. There could still be bonding character where orbitals are overlapping.
<jmol><jmolApplet>
<title>BH3 with no apparent bonds</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BH3_OPT_no_bond.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===

'''BH3'''

Deriving the second derivative of the potential energy allows energy minima to be determined as if it is a positive value for a stationary point it indicates that this is a minimum as it gives the curvature of the potential energy curve. This frequency analysis allows the stationary points to be resolved into minimum, if all positive, stationary point and if one is negative then it is a stationary point. It also allows computation of the different vibrational modes of the molecule, 3N-6 if non-linear, which as well as being visualised can also be compared with the IR spectrum of experiment.

This analysis was performed on the 6-31G(d,p) optimised BH3 molecule but with symmetry set at D3h.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_BH3_FREQUENCY_OPT_summary.PNG]] || [[File:JLS_bh3_frequency_opt_lowfrequencies.PNG]]

|}

The log file can be found [[Media:JLS_BH3_FREQUENCY_OPT_.LOG| here]]

[[File:JLS_bh3_frequency_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 1163 || 93 || Yes || bend
|-
| 1213 || 14 || Slight || bend
|-
| 1213 || 14 || Slight || bend
|-
| 2583 || 0 || No || Stretch
|-
| 2716 || 126 || Yes || Stretch
|-
| 2716 || 126 || Yes || Stretch

|}

The predicted IR spectrum shows fewer peaks, 3, to number of vibrations found, 6. This is due to degeneracy of the peaks meaning they overlay on the spectrum and also for one of the vibrations there is no change in dipole therefore will not be IR active.
The spectrum shows clearly 2 large peaks which corresponds to the strong active vibrations 1163 and 2716 cm-1. Then also there is a weaker signal at 1213cm-1 to the degenerate peak which has relatively small intensity, due to a smaller change in dipole.

'''GaBr3'''

Frequency analysis was also run on GaBr3 with basis set LANL2DZ and B3LYP method used. The frequency data is shown below:

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_GaBr3_FREQUENCY_summary.PNG]] || [[File:JLS_GaBr3_frequency_lowfrequencies.PNG]]

|}

The frequency log file can be found here {{DOI|10042/149182}}

[[File:JLS_GaBr3_frequency_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 76 || 3 || Slight || bend
|-
| 76 || 3 || Slight || bend
|-
| 100 || 9 || Slight || bend
|-
| 197 || 0 || No || Stretch
|-
| 316 || 57 || Yes || Stretch
|-
| 316 || 57 || Yes || Stretch

|}

'''Vibrational comparison between GaBr3 and BH3'''
[[File:Bh3_BEND.PNG|thumb|right|BH3 A2" umbrella motion]]
[[File:GaBR3_BEND.PNG|thumb|right|GaBr3 A2" umbrella motion]]
Vibrational frequency is dependent on the mass and force constant, which reflects the strength of the bond.
ν = (1/2π)(k/μ)1/2
where k is the force constant and μ is the reduced mass. This shows that the heavier the atoms the lower the frequency as the frequency is inversely proportional to the square of the reduced mass. Also, the stronger the bond, the the larger the force constant, which frequency is proportional to the square of.

Both GaBr3 and BH3 have six vibrational modes due to equation 3N-6 where N is 4. The infrared spectrum of GaBr3 is in the range of lower frequencies than BH3 due to heavier mass of the atoms and so a larger reduced mass. This consequently means lower vibrational frequency.
For GaBr3 the energy of the vibrational modes is reordered. For example, the A2" umbrella motion. For BH3 is the lowest frequency and for GaBr3 it is the highest bending frequency, this difference is due to the difference in the mass of the atoms in the different molecules. As can be seen on the images, the displacement vectors are smaller than the for GaBr3 bromine atoms than for BH3 hydrogen atoms. This is due to the difference in mass, as bromine is heavier than the central atom, so the motion is more in the central gallium atom than in bromine whereas for BH3, the hyrdogens are much lighter and so move more easily than the boron. This difference in the nature of the vibration can be seen on the gaussview animation. Then considerable difference to hydrogen in mass for the gallium is why it is a higher in the vibration order as more energy is needed for it to move.

'''Review of Frequency Analysis'''

The same method for optimisation and frequency must be used as because the optimised structure is highly dependent on the type of basis set and method used so will not be same structure the frequency is being calculated for as previous optimisation.
The purpose of the frequency analysis is too confirm the optimised structure found is at the energy minimum as the structure is just optimised to a stationary point. By using the second derivative of this energy profile the vibrational analysis confirms that this stationary point is in fact a minima.
The 'low frequencies' correspond to the motions of the center of mass of the molecule being observed. Ideally they should be zero, and get smaller with the better method used as the center of mass is moving less.

=== Calculating Molecular Orbitals ===

Using the 6-31G(d,p) optimised BH3 molecule the molecule orbitals were calculated and can be found here: {{DOI|10042/146859}}

[[File:JLS_BH3_MO.png]]

Comparing the predicted orbitals in the molecular orbital diagram with that calculated there is reasonable agreement. The small constricted nature of the 1s orbital can be seen in both, the more diffuse nature of the higher energy orbitals is only really seen in the calculated orbitals opposed those from the MO diagram. Also, some of the contributions from specific orbitals to certain molecular orbitals are not in agreement, for example in 3a1' the computed contribution of the 2s orbital is smaller than that predicted. However, for a qualitative method the MO diagram is reasonably accurate and therefore useful to predict orbitals in smaller simpler molecules without computational methods.

==== NH3 ====

'''Optimisation'''
Using basis set 6-31G(d,p), NH3 was optimised. The bond angle between the N-H bonds was found to be 106° and the bond length was found to be 1.02 Å.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NH3_opt_summary.PNG]] || [[File:JLS_NH3_opt_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:NH3_OPT.LOG| here]]

'''Frequency analysis'''
Using the optimised molecule and setting the point group to C3v a frequency analysis was run as before, with basis set 6-31G(d,p) and the B3LYP method, to confirm the energy minima.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NH3_freq_summary.PNG]] || [[File:JLS_NH3_freq_lowfrequencies.PNG]]

|}

It can be seen that the the frequencies are low and that there is no negative frequencies showing the energy minima has been found.

[[File:JLS_NH3_freq_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 1089 || 145 || Yes || bend
|-
| 1694 || 14 || Yes || bend
|-
| 1694 || 14 || Yes || bend
|-
| 3461 || 1 || Slight || Stretch
|-
| 3590 || 0 || No || Stretch
|-
| 3590 || 0 || No || Stretch

|}

The log file can be found [[Media:JLS_NH3_FREQ.LOG| here]]

'''MO and NBO'''
[[File:JLS_NH3_charge_distribution.PNG|thumb|right|Charge distribution on an optimised NH3 molecule with red indicating negative charge and green positive charge ]]
The molecular orbitals were computed again using 6-31G(d,p) basis set and the B3LYP method with set C3v symmetry. The log file can be found here: {{DOI|10042/147006}}.

The charge distribution is shown, with nitrogen possessing a negative charge of -1.125 and the hydrogen's with 0.375 each.

=== Association Energies ===

==== Ammonia-Borane ====

Ammonia-borane is a Lewis acid-base complex where by definition the nitrogen is donating a pair of electrons to the boron however the nature of this bond is not so straight forward and can be investigated by examining association energies.
The energies of the reactants and products are needed to calculate reaction energy which will give the energy for the dative bond between nitrogen and hydrogen. NH3 and BH3 have already been calculated and so NH3BH3 was optimisation was run.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NH3BH3_OPT_summary.PNG]] || [[File:JLS_NH3BH3_OPT_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_NH3BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_NH3BH3_OPT.LOG| here]]

Frequency analysis was then also performed on NH3BH3

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NH3BH3_FREQ_summary.PNG]] || [[File:JLS_NH3BH3_FREQ_lowfrequencies.PNG]]

|}

The log file for the frequency analysis can be found [[Media:JLS_NH3BH3_FREQ.LOG| here]]

The energies calculated for the reagents and products were found to be:

{| class="wikitable" border="1"
|+ Energies
! !! NH3 !! BH3 !! NH3BH3
|-
| Energies (a.u) || -56.5577687 || -26.6153235 || -83.2246889

|}

The dissociation energy is given by ΔE=E(NH3BH3)-[E(NH3)+E(BH3)].
So ΔE= -0.0515967 a.u
ΔE= -135.44 KJ/mol
This is a relatively weak bond as in much smaller than the medium bond of C-H of 432.9 kJ/mol <ref name="CH" />, this is likely due to the nature of the dative covalent bond not being as strong as a fully covalent bond. However it is not a weak as that between Cs2 which is 43.5 kJ/mol <ref name="N2" />.

== Ionic Liquids: Designer Solvents ==

Green chemistry is a large growing field in chemistry and has led to the development of replacements for traditional solvents which are flammable and volatile leading to unwanted wastage. Ionic liquids have good solvating properties and are recyclable and non-volatile/non-flammable so are good potential replacements for usual solvents. <ref name="IL1" />

Their composition is that of room temperature liquid ions which is achievable through bulky groups so the ions cannot pack together well generating the property of low melting points. This property can be fine tuned by the use of smaller anions and increasing the bulkiness and unsymmetrical nature of the cation, leading to a decrease in melting point. <ref name="IL1" />

This shows that the chemical composition and nature of these ions affect the properties of these solvents and therefore their use in synthesis thus using computational techniques different ionic liquids cations will be investigated at the molecular level. The difference in central atom will be explored and also considered is the affect of additional functional groups, compareing electron withdrawing groups with electron donating.

=== Onium Cations ===

==== [N(CH3)4]+ ====

The cation was optimised using 6-31G(d,p) basis set and the B3LYP method. The symmetry was not constrained as this would increase computing time and may lend it to error.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NCH34_OPT_summary1.PNG]] || [[File:JLS_NCH34_OPT_file1.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_NCH34_OPT1.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_NCH34_OPT1.LOG| here]]

It was found that the optimised bond lengths were: N-C [1.51 Å], C-H [1.09 Å] and the bond angles around nitrogen was 109.5 ° but for the carbon there was less perfect sp3 hybridization as the angles between the hydrogens, 110.1 °, were larger than between the nitrogen and hydrogens, 108.9 °. This could be due to the high electronegativity of the nitrogen central atom meaning a larger build up of electron density in the centre so hydrogens repulsed more away the nitrogen centre.

Frequency analysis was also ran with 6-31G(d,p) basis set and the B3LYP method to confirm the minimum energy point found. The low frequencies are checked at +/-15 cm-1.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NCH34_FREQ_summary1.PNG]] || [[File:JLS_NCH34_FREQ_low1.PNG]]

|}

The log file can be found [[Media:JLS_NCH34_FREQ1.LOG| here]]

Molecular orbital analysis was also run and the log file for the molecular optimisation calculations can be found [[Media:JLS_NCH34_MO1.LOG| here]]. The molecular orbitals are analysed more below as well as the charge distribution in the molecule.

==== [P(CH3)4]+ ====

[P(CH3)4]+ was optimised using 6-31G(d,p) basis set and the B3LYP method.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_PCH34_OPT_summary1.PNG]] || [[File:JLS_PCH34_OPT_file1.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_PCH34_OPT1.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_PCH34_OPT.LOG| here]]

Analysis of the bond angles shows that the around the carbon, the angle between hydrogen and nitrogen is 109.9 ° compared to angle between the hydrogens at 109.0 °. The angle around the nitrogen is 109.5 °. The P-C bond is 1.82 Å and the C-H bond is 1.09 Å. This data shows that the molecule is nearly perfectly sp3 hybridised as all angles are very close to 109 °. The lack of slight distortion found in [N(CH3)4]+ is likely due to the difference in elctronegativities in the two central atoms.

Again vibrational analysis was run on the cation with 6-31G(d,p) basis set and the B3LYP method to confirm minima.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_PCH34_FREQ_summary1.PNG]] || [[File:JLS_PCH34_FREQ_low1.PNG]]

|}

The log file can be found [[Media:JLS_PCH34_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_PCH34_MO.LOG| here]] and the charge distributions are discussed and compared below aswell as the nbo population for the C-P being analysed.

==== [S(CH3)3]+ ====

[S(CH3)3]+ was optimised using 6-31G(d,p) basis set and the B3LYP method.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_SCH33_OPT_summary.PNG]] || [[File:JLS_SCH33_OPT_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_SCH33_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_SCH33_OPT.LOG| here]]

[[File:JLS_SCH33_angles.PNG|thumb|right|[S(CH3)3]+ showing different bond angles]]

The structure of the molecule is not planar, due to the lone pair situated on the sulphur. This means the angle between the carbons is 102.8 °. The angle between the hydrogen and sulphur is 107.3 ° for the hydrogens pointing 'up' and 110.6 for those pointing 'down'. This difference in angles is due to the different environments the hydrogens are in due to the unsymmetrical nature of the molecule. However, the both C-H bond lengths are 1.09 Å and the S-C length is 1.82 Å.

Frequency analysis was run on the molecule with a B-31G(d,p) basis set and the B3LYP method to confirm the energy minimum.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_SCH33_FREQ_summary.PNG]] || [[File:JLS_SCH33_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_SCH33_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_SCH33_MO.LOG| here]] and the charge distribution and nbo population in analysed below.

==== Geometries comparison ====

The bond lengths and the bond angles of the above cations were taken from their optimised structure and compared in the table below.

{| class="wikitable" border="1"
|+ Geometries
! Molecule !! Central atom-C length (Å) !! C-H length (Å) !! Central atom-C-central atom angle (°) !! Central atom-C-H angle (°) !! H-C-H angle (°)
|-
| [N(CH3)4]+ || 1.51 || 1.09 || 109.5 || 108.9 || 110.1
|-
| [P(CH3)4]+ || 1.82 || 1.09 || 109.5 || 109.9 || 109.0
|-
| [S(CH3)3]+ || 1.82 || 1.09 || 102.8 || 110.6/107.3 ||111.1/109.4

|}

It can be seen that the bond length between N-C is significantly smaller than the P-C or S-C showing that is a stronger bond. This is due to the higher electronegativity of nitrogen and lower outer p orbitals that are at similar energy to carbon so have very good overlap leading to stronger interaction.

==== MO and NBO analysis of [N(CH3)4]+ ====

Using five different molecular orbitals found from calculations on the electronic structure of [N(CH3)4]+ to get a better picture of the different levels of bonding. Core electrons are not considered as they are so low in energy they are not involved in bonding. Bonding interaction are produced from in-phase overlap and anti-bonding from out-of-phase overlap. Boundaries between phase changes are defined as nodes and indicate anti-bonding character. Due to the smaller directionality and more diffuse nature pi interactions are weaker than sigma type.

{| class="wikitable" border="1"
|+ MO of [N(CH3)4]+
|-
|The first non-core molecular orbital is highly bonding. This is likely due to bonding through the s-orbital interaction, leading to a highly bonding molecular orbital with no anti-bonding contribution.There are no nodes and all interactions are σ, this dense nature of the orbital creates the strong bonding and therefore stabilisation of the electrons in this orbital. The MO is very tight on the orbitals. ||[[File:JLS_6.PNG|thumb|First core orbital, energy level 6]]
|-
| This molecular orbital still shows large lobes of bonding in-phase interactions, probably between s-orbitals on the hydrogens and the carbon of predominately two of the methyl groups. There is also strong through bond interaction between the central nitrogen through hybridised sp3 and the corresponding phase s-orbital. However, there is also now some anti-bonding character in the molecule seen by the nodal plane which splits the molecular orbital. This means there will be some weak through space anti-bonding interactions which will slightly destabilise the orbital. || [[File:JLS_9.png|thumb|MO 8]]
|-
| Again, this molecular orbital shows strong bonding interactions through bonds between the hydrogen and the carbon. Most likely between the s orbital of the hydrogen and the sp3 hybridised carbon orbital which would be pointing in the direction of the bond. This could then forms another bonding interaction with the s-orbital of the nitrogen. There is a spherical nodal plane around the central atom. There is also though-space anti-bonding interactions which are relatively close in space so will be relatively destabilising for through-space interactions. The atomic orbitals in the molecules are now getting more diffuse as the MOs are getting higher energy. || [[File:JLS_10.png|thumb| Level 10 MO]]
|-
|The MO at energy level 14 orbitals shows the lobes are spreading further across the molecule as they get more diffuse.There are two nodal planes, criss-crossing the central nitrogen atom. The atomic orbitals proposed to be involved are the sp3 of the carbon and s orbitals of the hydrogen. This lends to strong through bond bonding interactions, but then there is also weak through space anti-bonding interaction between the the opposite phase s orbitals of the methyl hydrogens. However, this has a minimal destabilising effect compared to the stabilising affect of the through bond bonding. There is also more even weaker through space anti-bonding interactions between the different methyl groups of opposite phase, but also stabilising through space bonding interactions that elongate the phases across the molecule. ||
[[File:JLS_14_2.png|thumb|Level 14 MO]]
|-
| The 18th molecular orbital a relatively high energy bonding orbital which can be explained by its increased anti-bonding nature in comparison to the MOs above. It has three nodal planes and features the interaction of mainly 3 of the CH3, with most of the electron density spread over two of the hyrdogens on these groups. The interacting orbitals are quite diffuse, espcially compared to level 6 meaning both bonding and antibonding interactions are weaker than in above orbitals. The bonding, stabilising effect comes from the interaction between the sp3 orbitals on the carbon with the s atomic orbitals on the hydrogens. This leads to quite strong through bonding interactions which outweighs the weaker through space anti-bonding interactions across nodes and so therefore overall the molecular orbital is still stabilising. || [[File:JLS_18.png|thumb|Level 18 MO]]
|}

==== Charge Distribution Comparison ====

From the natural bond orbital analysis of the cations the distribution of charge across the molecules could be calculated over the molecule. The differing central atom can be seen, by the tables below, to greatly effect the way that charge is disbursed across the molecule.

{| class="wikitable" border="1"
|+ Charge Distribution
! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| [[File:JLS_NCH34_MO_charge.PNG]] || [[File:JLS_PCH34_MO_charge.PNG]] || [[File:JLS_SCH33_MO_charge.PNG]]

|}

{| class="wikitable" border="1"
|+ Charges
! Atom !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Central[N/P/S] || -0.295 || 1.667 || 0.917
|-
| C || -0.483 || -1.060 || -0.846
|-
| H || 0.269 || 0.298 || 0.297/0.279

|}

All three molecules hold a positive charge which is usually placed at the central atom. However, the central atoms differs in charge from -0.342 on the nitrogen to 1.667 on the phosphorus.
This difference is due to the difference in electronegativity of the central atom. . Nitrogen has a the highest electronegativity at 3.04<ref name="BondOrder" /> this is compared to carbon which has a Pauling electronegativity of 2.55<ref name="BondOrder" />.
This means that in comparison to phosphorus and sulphur the nitrogen has lower energy atomic orbitals, closer in energy to the carbons allowing efficient overlap for the positive charge to be distributed farthest away from the electronegative nitrogen and which can be seen as all positive charge is situated on the hydrogens. Also carbons are significantly smaller negative charge than the other two cations due to the spreading of the positive charge and the electronegative pull of the nitrogen drawing electron density towards it in the bond.

In comparison, the phosphorus is a row down from nitrogen so is less electronegative, 2.19<ref name="BondOrder" />, and has larger, more diffuse orbitals. This leads to poorer orbital overlap with the carbon so does not show the spread of charge that can be seen in [N(CH3)4]+. This means that the central atom now holds onto the positive charge. Also, due to carbon being more electronegative and the lack of overlap and more electrons in the system means that the carbon is much more negatively charged than on the other two molecules.
Sulphur is more electronegative, 2.58<ref name="BondOrder" />, than phosphorus so atomic orbitals will be lower in energy than and will be able to overlap more than phosphorus hence the positive charge on the central atom is smaller as the charge is able to distribute more, hence making the charge on the carbon less negative.
Also, the sulphur has one less substituent which means that the charge on the hydrogens is not evenly distributed as those hydrogens facing 'up' are more positive than those facing towards other hydrogens, this could be due to a build up of electron density between the hydrogens.

==== [NR4]+ ====

In the traditional characterisation of [NR4]<suop>+ cations the charge is placed on the central nitrogen. This formal assignment is made as the nitrogen is the atom with the higher number of substituents and in basic valence bond theory would be the atom lacking one electron so would be positively charged. However, as can be seen from the charge distribution this is clearly not the case and the positive charge is actually distributed across the hydrogens. This shows that the formal description is not valid for the [N(CH3)4]<suop>+ molecule. However, it is more true for the the phosphorus and sulphur cations as these have more of a positive charge on the central atom.

==== Relative contributions of C-X ====

In comparison between the C-X bonds of the molecule the NBO analysis can be evaluated from the MO calculations run on the three different molecules. The nitrogen contributes 66% to the bond whereas phosphorus contributes 40% and sulphur contributes 51%. This correlates to the different electronegativities of the 3 atoms which are stated above. The higher the electronegativity the more the larger the pull on electrons in the bond and so the higher the contribution.
These relative contributions can also be seen in the charge distributions discussed above as it is seen that nitrogen has the highest percentage contribution and so has a higher amount of electron density on its centre and therefore has the more negative charge. And phosphorus which has the lowest contribution also has the most positive charge situated on it.

The NBO analysis also confirms that the central atom is sp3 hybridised as there is about a 25% contribution from s orbital and 75% from p orbital. This is in the 1:3 ratio as expected in sp3 hybridised orbitals. However, as discussed in the geometry analysis the sulphur molecule is not perfect sp3 hybridised and this is reflected in the s and p contributions as the s contribution is 20% and p is 80%, meaning that there is less s character to the bond than would be expected.

=== Influence of functional groups ===

'''[N(CH3)3(CH2OH)]+'''

[N(CH3)3(CH2OH)]+ was optimised using the B3LYP method and using the basis set 6-31G(d,p).

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_N(CH3)3(CH2OH)_OTP_summary.PNG]] || [[File:JLS_N(CH3)3(CH2OH)_OTP_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_N(CH3)3(CH2OH)_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2OH)_OPT.LOG| here]]

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_N(CH3)3(CH2OH)_FREQ_summary.PNG]] || [[File:JLS_N(CH3)3(CH2OH)_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2OH)_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_N(CH3)3(CH2OH)_MO.LOG| here]]

'''[N(CH3)3(CH2CN)]+'''

[N(CH3)3(CH2OH)]+ was optimised using the B3LYP method and using the basis set 6-31G(d,p).

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_N(CH3)3(CH2CN)_OTP_summary.PNG]] || [[File:JLS_N(CH3)3(CH2CN)_OTP_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_N(CH3)3(CH2CN)_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2CN)_OPT.LOG| here]]

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_N(CH3)3(CH2CN)_FREQ_summary.PNG]] || [[File:JLS_N(CH3)3(CH2CN)_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2CN)_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_N(CH3)3(CH2CN)_MO.LOG| here]]

==== Charge distribution analysis ====

Using the molecular orbital calculation the charge distributions of the two optimised cations could be analysed. The table below shows the distribution of charge in both molecules;

{| class="wikitable" border="1"
|+ Charge Distributions
! [[File:JLS_N(CH3)3(CH2OH)_charge.PNG]] !! [[File:JLS_N(CH3)3(CH2CN)_charge.PNG]]

|}

The difference between in charge distribution can be explained by the nature of the attached functional group. The lone pairs on the oxygen in the OH group can be donated, this would explain why the central nitrogen has a more negative charge than in N(CH3)3(CH2CN)+. The attached carbon however is more positive which is due to oxygen being much higher in electronegativity than carbon so polarising the bond. The cyanide group however is electron withdrawing hence the carbon it attached to being less negatively charged than the other methyl groups. Also, it can be seen that more of the negative charge sits on the nitrogen in the functional group. Also, the nitrogen is slightly less negative than in N(CH3)4+ but not significantly so.

==== HOMO LUMO comparison ====

Also from the molecular orbital calculations the highest occupied orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) can be analysed. Below is a table of the three different cations

{| class="wikitable" border="1"
! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
! colspan="3" | HOMO
|-
| [[File:JLS_NCH34_HOMO.PNG|thumb]] || [[File:JLS_N(CH3)3(CH2OH)_HOMO.PNG|thumb]] || [[File:JLS_N(CH3)3(CH2CN)_HOMO.PNG|thumb]]
|-
! colspan="3" | LUMO
|-
! [[File:JLS_NCH34_LUMO.PNG|thumb]] !! [[File:JLS_N(CH3)3(CH2OH)_LUMO.PNG|thumb]] !![[File:JLS_N(CH3)3(CH2CN)_LUMO.PNG|thumb]]

|}

It can be seen that the shape of the HOMO and LUMO orbitals has changed across the three different molecules, most dramatically between the HOMO orbitals. It can be seen that for the molecules with functional groups the HOMO orbitals are centred around these groups, this can be especially seen in [N(CH3)3(CH2CN)]+ whereas for N(CH3)4+ it is spread across the molecule and is more diffuse.
The shape of the LUMO between N(CH3)4+ and [N(CH3)3(CH2OH)]+ changes less, but with more spreading along the OH bond. Again for N(CH3)4+ the LUMO is now more focused on the functional group but still is spread over the entire molecule.

Comparison of energies is important in discerning the chemical impact of the differences in the HOMO/LUMOs.

{| class="wikitable" border="1"
! colspan="3" | HOMO Energies (a.u)
|-
! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| -0.57932 || -0.48762 || -0.50048
|-
! colspan="3" | LUMO Energies (a.u)
|-
| -0.13304 || -0.12460 ||-0.18181
|-
! colspan="3" | HOMO-LUMO gap (kJ/mol)
|-
| 1171 || 953 || 836.51

|}

Compared to N(CH3)4+ the energy of the HOMO has increased for both functional group molecules and for [N(CH3)3(CH2OH)]+ the LUMO has also increased as the addition of an electron donating group has added more electron density to the molecule therefore destabilising it. In contrast, the electron withdrawing group CN decreases the energy of the molecule showing the stabilising effect. This means that it can now more readily accept electrons so would be better oxidant or lewis acid.

The HOMO-LUMO energy gap in N(CH3)4+ is the largest and so means this is likely the most stable and less likely to donate electrons. The addition of the two functional groups decreases the gap meaning they are more likely to promote an electron from the HOMO to the LUMO creating an excited state molecule.

== References ==
<references>

<ref name="BondOrder"> C. Housecroft, A. Sharpe, Inorganic Chemistry,2012, Pearson, 4 ed, 50 & 30. </ref>

<ref name="N2"> T. Ghanty and S. Ghosh, J. Phys. Chem., 1991, 6512–6514.</ref>

<ref name="CH"> G. K. Jarvis, K.-M. Weitzel, M. Malow, T. Baer, Y. Song and C. Y. Ng, Phys. Chem. Chem. Phys., 1999, 1, 5259–5262. </ref>
</references>

<ref name="IL1"> S. Keskin, D. Kayrak-Talay, U. Akman and Ö. Hortaçsu, J. Supercrit. Fluids, 2007, 43, 150–180.</ref>

2014-12-18T14:43:24Z

Jls12: /* Charge Distribution Comparison */

== EX3 section ==

=== BH3 optimisation ===

Initially, to get accustomed with the software, I ran a simple optimisation on a BH3 molecule. The bong lengths were set to; 1.55 Å, 1.53 Å and 1.54 Å. The method was set to B3LYP and the basis set was 3-21G. Using solutions to the Schrodinger equation, the SCF part of the calculation finds the energy of the electronic density. Then, by periodically moving the nuclei in the OPT part of the calculation and recalculating the SCF for each position the optimised geometry with the lowest energy can be obtained.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_BH3_summary.PNG]] || [[File:JLS_BH3_optimisation.PNG]] || <jmol><jmolApplet>
<title>Optimisied BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_bh3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

[[File:JLS_optimisation_graph.PNG|right]] The two graphs calculated by Gaussview show information about the energy of optimisation. The first shows the total energy curve, showing the changes in energy over the optimisation steps, following the curve down until it is at the optimised geometries with the minimum energy. This is the stable state equilibrium position. The graph moves along the potential energy surface for the molecule until reaching the lowest energy geometry.

The second graph is the Root Mean Square gradient of the total energy. The gradient represents the force from nuclear-nuclear repulsion or nuclear-electron attraction which changes the positions of the nuclei. When at the energy minima the gradient will reach zero as no geometry change will lower the energy so there will be no force on the molecule. The graph reaches zero when at the least optimisation step showing the energy minima is reached.

The log file can be found [[Media:JLS BH3 OPT.LOG| here]]

=== Basis set: 6-31G(d,p) ===

Basis sets are determinants of how precise the optimisation is, with basis sets with a higher number of functions allowing higher precision but calculations take a longer amount of time.

For the previous calculation a relatively small basis set, 3-21G, was use to optimise BH3. However, now a higher level basis set, 6-31G(d,p), will be used to get a more accurate calculation.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_BH3_summary_631g.PNG]] || [[File:JLS_BH3_OPT_631g_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BH3_OPT_631G.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_BH3_OPT_631G.LOG| here]]

=== Pseudo Potentials ===

Pseudo potentials are used for molecules containing heavier atoms when the calculations become to lengthy due to the large number of electrons. This means an simpler approximation is used for core electrons than the valence electrons as these are those most involved in bonding.

==== GaBr3 ====

The symmetry was set at D3h and a medium basis set was used, LanL2DZ. This uses a separate basis set for the first row atoms and heavier elements.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:GaBr3_optimisation_summary.PNG]] || [[File:GaBr3_optimisation_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied GaBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log_GaBr3_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>

|}
The optimsation log file can be found here {{DOI|10042/143675}}

==== BBr3 ====

For BBr3 a mixture of pseudo-potentials and basis sets was used. For the lighter boron atom a basis set 6-31G(d,p) was used and for the heavier bromine atoms a pseudo-potential LanL2DZ is used. This is achieved by using basis set GEN in GaussView which allows the assigning of basis sets manually. The results are given below:

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:BBr3_OPT_summary.PNG]] || [[File:BBr3_OPT_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BBr3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The symmetry should be C3v. The optimsation log file can be found here {{DOI|10042/143682}}

=== Structural Comparison [BH3, GaBr3, BBr3 ] ===

From the above three optimisations, the following data was found regarding bond length and bond angle:

{| class="wikitable" border="1"
|+ Geometry Data
! !! BH3 !! GaBr3 !! BBr3
|-
| r(E-X) [Å] || 1.19 || 2.35 || 2.02 ||
|-
| θ(X-E-X) || 120.0 || 120.0 || 120.0 ||
|}

'''Ligands''': From the values comparing BH3 and BBr3 it can be seen that changing the ligand does not effect the bond angle but does affect the bond length. Bromine and hydrogen are similar in that they both monovalent and so bonding to boron completes the outer orbital of electrons.
It was found that the B-H bond is relatively much smaller than the B-Br bond, indicating that it is a much stronger bond. This is likely due to the difference in energies between the orbitals. Boron and Hydrogen are both small atoms, so compared to the larger bromine, the hydrogens core orbital can get much closer to the boron. Also, the valence electron on hydrogen sits in a 1s orbital means it is denser and so forms a stronger bond compared to the valence electrons in bromine which sit in more diffuse p orbitals. Also, hydrogen 1s orbitals will sit much closer in energy to bromine valence p orbitals leading to stronger bonding.

'''Central Element''': Again, changing the central atom has no observed effect on the bond angles but does affect the bong length. Gallium and boron are both in group 13 so have 3 electrons in their valence p orbital. This leads to them both forming trigonal planar complexes. Gallium, as further down the group has a larger atomic radius and so has larger more diffuse outer orbitals, as there is also a set of d orbitals between the valence and the nucleus. This leads to the gallium having longer and therefore weaker bonds.

'''Bonding''': A classical view of a covalent bond is that a pair of electrons is shared between two atoms due to an electrostatic attraction between electrons and protons. Double and triple bonds are the sharing of a two or three electron pairs respectively. Ionic bonds are held together by electrostatic forces as opposing charges are formed from exchange of electrons to complete electron 'shells'. However, this is a very simple outlook on bonding and there is actually a wide continuum of bonding, which can be examined more with molecular orbital theory. This enables the bond order of the molecule to be worked out, which is a parameter which assess the two atoms molecular orbitals and how many bonds are formed between. <ref name="BondOrder" /> Many bonds are not simply ionic or covalent and can be on the spectrum between the two. Also, there are weaker, partial bonds such as hydrogen bonds and van der waals forces. These are due to the polarisation of electron density and consequential small attractive interactions between the slight charges caused by the difference in electron density.
A strong bond is formed from good overlap of interacting orbitals. Also, a large difference in electronegativity can form strong ionic bonds, especially those at the top of the periodic table where the nucleus has greater effect on the electrons as there is less shielding.

An example of a strong, covalent bond is that between N2, this has high bond order as it is a triple bond and because it is a homonuclear bond, energy levels are the same increasing orbital overlap of orbitals that are dense so form a very strong bond at 948.1 kcal/mol. <ref name="N2" /> This is comparison to the comparitvely very weak homonuclear bond between the large diffuse orbitals of Cs2 which is 43.5 kJ/mol <ref name="N2" /> which is a weak bond. A medium bond is the C-H bond in methane which is 432.9 kJ/mol <ref name="CH" />

For some structures in gaussview there are no bonds joining molecules where we would expect them, for example with the intial calculations on BH3. This is due to the bond distance being longer than the one gaussview has assigned for those atoms and so does not necessarily mean there is no bonding. There could still be bonding character where orbitals are overlapping.
<jmol><jmolApplet>
<title>BH3 with no apparent bonds</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_BH3_OPT_no_bond.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===

'''BH3'''

Deriving the second derivative of the potential energy allows energy minima to be determined as if it is a positive value for a stationary point it indicates that this is a minimum as it gives the curvature of the potential energy curve. This frequency analysis allows the stationary points to be resolved into minimum, if all positive, stationary point and if one is negative then it is a stationary point. It also allows computation of the different vibrational modes of the molecule, 3N-6 if non-linear, which as well as being visualised can also be compared with the IR spectrum of experiment.

This analysis was performed on the 6-31G(d,p) optimised BH3 molecule but with symmetry set at D3h.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_BH3_FREQUENCY_OPT_summary.PNG]] || [[File:JLS_bh3_frequency_opt_lowfrequencies.PNG]]

|}

The log file can be found [[Media:JLS_BH3_FREQUENCY_OPT_.LOG| here]]

[[File:JLS_bh3_frequency_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 1163 || 93 || Yes || bend
|-
| 1213 || 14 || Slight || bend
|-
| 1213 || 14 || Slight || bend
|-
| 2583 || 0 || No || Stretch
|-
| 2716 || 126 || Yes || Stretch
|-
| 2716 || 126 || Yes || Stretch

|}

The predicted IR spectrum shows fewer peaks, 3, to number of vibrations found, 6. This is due to degeneracy of the peaks meaning they overlay on the spectrum and also for one of the vibrations there is no change in dipole therefore will not be IR active.
The spectrum shows clearly 2 large peaks which corresponds to the strong active vibrations 1163 and 2716 cm-1. Then also there is a weaker signal at 1213cm-1 to the degenerate peak which has relatively small intensity, due to a smaller change in dipole.

'''GaBr3'''

Frequency analysis was also run on GaBr3 with basis set LANL2DZ and B3LYP method used. The frequency data is shown below:

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_GaBr3_FREQUENCY_summary.PNG]] || [[File:JLS_GaBr3_frequency_lowfrequencies.PNG]]

|}

The frequency log file can be found here {{DOI|10042/149182}}

[[File:JLS_GaBr3_frequency_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 76 || 3 || Slight || bend
|-
| 76 || 3 || Slight || bend
|-
| 100 || 9 || Slight || bend
|-
| 197 || 0 || No || Stretch
|-
| 316 || 57 || Yes || Stretch
|-
| 316 || 57 || Yes || Stretch

|}

'''Vibrational comparison between GaBr3 and BH3'''
[[File:Bh3_BEND.PNG|thumb|right|BH3 A2" umbrella motion]]
[[File:GaBR3_BEND.PNG|thumb|right|GaBr3 A2" umbrella motion]]
Vibrational frequency is dependent on the mass and force constant, which reflects the strength of the bond.
ν = (1/2π)(k/μ)1/2
where k is the force constant and μ is the reduced mass. This shows that the heavier the atoms the lower the frequency as the frequency is inversely proportional to the square of the reduced mass. Also, the stronger the bond, the the larger the force constant, which frequency is proportional to the square of.

Both GaBr3 and BH3 have six vibrational modes due to equation 3N-6 where N is 4. The infrared spectrum of GaBr3 is in the range of lower frequencies than BH3 due to heavier mass of the atoms and so a larger reduced mass. This consequently means lower vibrational frequency.
For GaBr3 the energy of the vibrational modes is reordered. For example, the A2" umbrella motion. For BH3 is the lowest frequency and for GaBr3 it is the highest bending frequency, this difference is due to the difference in the mass of the atoms in the different molecules. As can be seen on the images, the displacement vectors are smaller than the for GaBr3 bromine atoms than for BH3 hydrogen atoms. This is due to the difference in mass, as bromine is heavier than the central atom, so the motion is more in the central gallium atom than in bromine whereas for BH3, the hyrdogens are much lighter and so move more easily than the boron. This difference in the nature of the vibration can be seen on the gaussview animation. Then considerable difference to hydrogen in mass for the gallium is why it is a higher in the vibration order as more energy is needed for it to move.

'''Review of Frequency Analysis'''

The same method for optimisation and frequency must be used as because the optimised structure is highly dependent on the type of basis set and method used so will not be same structure the frequency is being calculated for as previous optimisation.
The purpose of the frequency analysis is too confirm the optimised structure found is at the energy minimum as the structure is just optimised to a stationary point. By using the second derivative of this energy profile the vibrational analysis confirms that this stationary point is in fact a minima.
The 'low frequencies' correspond to the motions of the center of mass of the molecule being observed. Ideally they should be zero, and get smaller with the better method used as the center of mass is moving less.

=== Calculating Molecular Orbitals ===

Using the 6-31G(d,p) optimised BH3 molecule the molecule orbitals were calculated and can be found here: {{DOI|10042/146859}}

[[File:JLS_BH3_MO.png]]

Comparing the predicted orbitals in the molecular orbital diagram with that calculated there is reasonable agreement. The small constricted nature of the 1s orbital can be seen in both, the more diffuse nature of the higher energy orbitals is only really seen in the calculated orbitals opposed those from the MO diagram. Also, some of the contributions from specific orbitals to certain molecular orbitals are not in agreement, for example in 3a1' the computed contribution of the 2s orbital is smaller than that predicted. However, for a qualitative method the MO diagram is reasonably accurate and therefore useful to predict orbitals in smaller simpler molecules without computational methods.

==== NH3 ====

'''Optimisation'''
Using basis set 6-31G(d,p), NH3 was optimised. The bond angle between the N-H bonds was found to be 106° and the bond length was found to be 1.02 Å.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NH3_opt_summary.PNG]] || [[File:JLS_NH3_opt_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:NH3_OPT.LOG| here]]

'''Frequency analysis'''
Using the optimised molecule and setting the point group to C3v a frequency analysis was run as before, with basis set 6-31G(d,p) and the B3LYP method, to confirm the energy minima.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NH3_freq_summary.PNG]] || [[File:JLS_NH3_freq_lowfrequencies.PNG]]

|}

It can be seen that the the frequencies are low and that there is no negative frequencies showing the energy minima has been found.

[[File:JLS_NH3_freq_IR.PNG]]

{| class="wikitable" border="1"
|+ Frequency Data
! Vibration (cm-1) !! Intensity !! Active !! Type
|-
| 1089 || 145 || Yes || bend
|-
| 1694 || 14 || Yes || bend
|-
| 1694 || 14 || Yes || bend
|-
| 3461 || 1 || Slight || Stretch
|-
| 3590 || 0 || No || Stretch
|-
| 3590 || 0 || No || Stretch

|}

The log file can be found [[Media:JLS_NH3_FREQ.LOG| here]]

'''MO and NBO'''
[[File:JLS_NH3_charge_distribution.PNG|thumb|right|Charge distribution on an optimised NH3 molecule with red indicating negative charge and green positive charge ]]
The molecular orbitals were computed again using 6-31G(d,p) basis set and the B3LYP method with set C3v symmetry. The log file can be found here: {{DOI|10042/147006}}.

The charge distribution is shown, with nitrogen possessing a negative charge of -1.125 and the hydrogen's with 0.375 each.

=== Association Energies ===

==== Ammonia-Borane ====

Ammonia-borane is a Lewis acid-base complex where by definition the nitrogen is donating a pair of electrons to the boron however the nature of this bond is not so straight forward and can be investigated by examining association energies.
The energies of the reactants and products are needed to calculate reaction energy which will give the energy for the dative bond between nitrogen and hydrogen. NH3 and BH3 have already been calculated and so NH3BH3 was optimisation was run.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NH3BH3_OPT_summary.PNG]] || [[File:JLS_NH3BH3_OPT_file.PNG]] || <jmol><jmolApplet>
<title>Optimisied NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_NH3BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_NH3BH3_OPT.LOG| here]]

Frequency analysis was then also performed on NH3BH3

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NH3BH3_FREQ_summary.PNG]] || [[File:JLS_NH3BH3_FREQ_lowfrequencies.PNG]]

|}

The log file for the frequency analysis can be found [[Media:JLS_NH3BH3_FREQ.LOG| here]]

The energies calculated for the reagents and products were found to be:

{| class="wikitable" border="1"
|+ Energies
! !! NH3 !! BH3 !! NH3BH3
|-
| Energies (a.u) || -56.5577687 || -26.6153235 || -83.2246889

|}

The dissociation energy is given by ΔE=E(NH3BH3)-[E(NH3)+E(BH3)].
So ΔE= -0.0515967 a.u
ΔE= -135.44 KJ/mol
This is a relatively weak bond as in much smaller than the medium bond of C-H of 432.9 kJ/mol <ref name="CH" />, this is likely due to the nature of the dative covalent bond not being as strong as a fully covalent bond. However it is not a weak as that between Cs2 which is 43.5 kJ/mol <ref name="N2" />.

== Ionic Liquids: Designer Solvents ==

=== Onium Cations ===

==== [N(CH3)4]+ ====

The cation was optimised using 6-31G(d,p) basis set and the B3LYP method.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_NCH34_OPT_summary1.PNG]] || [[File:JLS_NCH34_OPT_file1.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_NCH34_OPT1.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_NCH34_OPT1.LOG| here]]

It was found that the optimised bond lengths were: N-C [1.51 Å], C-H [1.09 Å] and the bond angles around nitrogen was 109.5 ° but for the carbon there was less perfect sp3 hybridization as the angles between the hydrogens, 110.1 °, were larger than between the nitrogen and hydrogens, 108.9 °. This is likely due to the shorter C-H bond length meaning the hydrogens are physically closer to one another and therefore experience higher repulsion so are pushed further apart.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_NCH34_FREQ_summary1.PNG]] || [[File:JLS_NCH34_FREQ_low1.PNG]]

|}

The log file can be found [[Media:JLS_NCH34_FREQ1.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_NCH34_MO1.LOG| here]]

==== [P(CH3)4]+ ====

[P(CH3)4]+ was optimised using 6-31G(d,p) basis set and the B3LYP method.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_PCH34_OPT_summary1.PNG]] || [[File:JLS_PCH34_OPT_file1.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_PCH34_OPT1.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_PCH34_OPT.LOG| here]]

Analysis of the bond angles shows that the around the carbon, the angle between hydrogen and nitrogen is 109.9 ° compared to angle between the hydrogens at 109.0 °. The angle around the nitrogen is 109.5 °. The P-C bond is 1.82 Å and the C-H bond is 1.09 Å.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_PCH34_FREQ_summary1.PNG]] || [[File:JLS_PCH34_FREQ_low1.PNG]]

|}

The log file can be found [[Media:JLS_PCH34_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_PCH34_MO.LOG| here]]

==== [S(CH3)3]+ ====

[S(CH3)3]+ was optimised using 6-31G(d,p) basis set and the B3LYP method.

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_SCH33_OPT_summary.PNG]] || [[File:JLS_SCH33_OPT_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_SCH33_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_SCH33_OPT.LOG| here]]

[[File:JLS_SCH33_FREQ_summary.PNG|thumb|right|[S(CH3)3]+ showing different bond angles]]

The structure of the molecule is not planar, due to the lone pair situated on the sulphur. This means the angle between the carbons is 102.8 °. The angle between the hydrogen and sulphur is 107.3 ° for the hydrogens pointing 'up' and 110.6 for those pointing 'down'. This difference in angles is due to the different environments the hydrogens are in due to the unsymmetrical nature of the molecule. However, the both C-H bond lengths are 1.09 Å and the S-C length is 1.82 Å.

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_SCH33_FREQ_summary.PNG]] || [[File:JLS_SCH33_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_SCH33_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_SCH33_MO.LOG| here]]

==== Geometries comparison ====

The bond lengths and the bond angles of the above cations were taken from their optimised structure and compared in the table below.

{| class="wikitable" border="1"
|+ Geometries
! Molecule !! Central atom-C length (Å) !! C-H length (Å) !! Central atom-C-central atom angle (°) !! Central atom-C-H angle (°) !! H-C-H angle (°)
|-
| [N(CH3)4]+ || 1.51 || 1.09 || 109.5 || 108.9 || 110.1
|-
| [P(CH3)4]+ || 1.82 || 1.09 || 109.5 || 109.9 || 109.0
|-
| [S(CH3)3]+ || 1.82 || 1.09 || 102.8 || 110.6/107.3 ||111.1/109.4

|}

It can be seen that the bond length between N-C is significantly smaller than the P-C or S-C showing that is a stronger bond. This is due to the higher electronegativity of nitrogen and lower outer p orbitals that are at similar energy to carbon so have very good overlap leading to stronger interaction.

==== MO and NBO analysis of [N(CH3)4]+ ====

Using five different molecular orbitals found from calculations on the electronic structure of [N(CH3)4]+ to get a better picture of the different levels of bonding. Core electrons are not considered as they are so low in energy they are not involved in bonding. Bonding interaction are produced from in-phase overlap and anti-bonding from out-of-phase overlap. Boundaries between phase changes are defined as nodes and indicate anti-bonding character. Due to the smaller directionality and more diffuse nature pi interactions are weaker than sigma type.

[[File:JLS_6.PNG|thumb|right|First core orbital, energy level 6]]

The first non-core molecular orbital is highly bonding. This is likely due to bonding through the s-orbital interaction, leading to a highly bonding molecular orbital with no anti-bonding contribution.There are no nodes and all interactions are σ, this dense nature of the orbital creates the strong bonding and therefore stabilisation of the electrons in this orbital. The MO is very tight on the orbitals.

[[File:JLS_9.png|thumb|right|MO 8]]

This molecular orbital still shows large lobes of bonding in-phase interactions, probably between s-orbitals on the hydrogens and the carbon of predominately two of the methyl groups. There is also strong through bond interaction between the central nitrogen through hybridised sp3 and the corresponding phase s-orbital. However, there is also now some anti-bonding character in the molecule seen by the nodal plane which splits the molecular orbital. This means there will be some weak through space anti-bonding interactions which will slightly destabilise the orbital.

[[File:JLS_10.png|thumb|right|Level 10 MO]]

Again, this molecular orbital shows strong bonding interactions through bonds between the hydrogen and the carbon. Most likely between the s orbital of the hydrogen and the sp3 hybridised carbon orbital which would be pointing in the direction of the bond. This could then forms another bonding interaction with the s-orbital of the nitrogen. There is a spherical nodal plane around the central atom. There is also though-space anti-bonding interactions which are relatively close in space so will be relatively destabilising for through-space interactions. The atomic orbitals in the molecules are now getting more diffuse as the MOs are getting higher energy.

[[File:JLS_14_2.png|thumb|right|Level 14 MO]]

The MO at energy level 14 orbitals shows the lobes are spreading further across the molecule as they get more diffuse.There are two nodal planes, criss-crossing the central nitrogen atom. The atomic orbitals proposed to be involved are the sp3 of the carbon and s orbitals of the hydrogen. This lends to strong through bond bonding interactions, but then there is also weak through space anti-bonding interaction between the the opposite phase s orbitals of the methyl hydrogens. However, this has a minimal destabilising effect compared to the stabilising affect of the through bond bonding. There is also more even weaker through space anti-bonding interactions between the different methyl groups of opposite phase, but also stabilising through space bonding interactions that elongate the phases across the molecule.

[[File:JLS_18.png|thumb|right|Level 18 MO]]

The 18th molecular orbital a relatively high energy bonding orbital which can be explained by its increased anti-bonding nature in comparison to the MOs above. It has three nodal planes and features the interaction of mainly 3 of the CH3, with most of the electron density spread over two of the hyrdogens on these groups. The interacting orbitals are quite diffuse, espcially compared to level 6 meaning both bonding and antibonding interactions are weaker than in above orbitals. The bonding, stabilising effect comes from the interaction between the sp3 orbitals on the carbon with the s atomic orbitals on the hydrogens. This leads to quite strong through bonding interactions which outweighs the weaker through space anti-bonding interactions across nodes and so therefore overall the molecular orbital is still stabilising.

==== Charge Distribution Comparison ====

From the natural bond orbital analysis of the cations the distribution of charge across the molecules could be calculated over the molecule. The differing central atom can be seen, by the tables below, to greatly effect the way that charge is disbursed across the molecule.

{| class="wikitable" border="1"
|+ Charge Distribution
! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| [[File:JLS_NCH34_MO_charge.PNG]] || [[File:JLS_PCH34_MO_charge.PNG]] || [[File:JLS_SCH33_MO_charge.PNG]]

|}

{| class="wikitable" border="1"
|+ Charges
! Atom !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Central[N/P/S] || -0.295 || 1.667 || 0.917
|-
| C || -0.483 || -1.060 || -0.846
|-
| H || 0.269 || 0.298 || 0.297/0.279

|}

The central atoms differs in charge from -0.342 on the nitrogen to 1.667 on the phosphorus. The difference is due to the difference in electronegativity of the central atom compared to the carbon it is bonded too which has a Pauling electronegativity of 2.55<ref name="BondOrder" />. Nitrogen has a significantly higher electronegativity at 3.04<ref name="BondOrder" />. This results in a higher affinity for electrons so electron density is pulled closer to the central nitrogen atom opposed to the phosphorus or sulphur leading to a build up in negative charge at the centre. However, this charge distribution is differs a lot compared to that expected from neutral N(CH3)3 due to the positive charge.
This positive charge is formally assigned to the central atom as this is where the extra substituent is situated. However, for the [N(CH3)4]+ molecule, most of the positive charge is on the hydrogens. Contrary to the electronegativity data, the carbon is the most negatively charged atom in the molecule, this is due to the effect of the extra substituent on the central atom increasing the charge.

The phosphorus is the least electronegative, 2.19<ref name="BondOrder" />, and so this combined with the positive charge means it is the most positively charged central atom of the three molecules. This leads to the carbons having the most negative charge compared to in the other molecules as less electron density is built up on the centre. Also, being a larger atom with more electrons, there is more charge to be distributed which also explains the much more negative carbons. The carbons for [S(CH3)3]+ are still much more negative than for [N(CH3)4]+ but are less than [P(CH3)4]+ due to sulphur, although being the about the same size as phosphorus, it is more electronegative, 2.58<ref name="BondOrder" />, so more charge is pulled onto the central atom. Also, for the sulphur molecule there is one less substituent so there are fewer electrons.

==== [NR4]+ ====

In the traditional characterisation of [NR4]<suop>+ cations the charge is placed on the central nitrogen. This formal assignment is made as the nitrogen is the atom with the higher number of substituents and in basic valence bond theory would be the atom lacking one electron so would be positively charged. However, as can be seen from the charge distribution this is clearly not the case and the positive charge is actually distributed across the hydrogens. This shows that the formal description is not valid for the [N(CH3)4]<suop>+ molecule. However, it is more true for the the phosphorus and sulphur cations as these have more of a positive charge on the central atom.

==== Relative contributions of C-X ====

In comparison between the C-X bonds of the molecule the NBO analysis can be evaluated from the MO calculations run on the three different molecules. The nitrogen contributes 66% to the bond whereas phosphorus contributes 40% and sulphur contributes 51%. This correlates to the different electronegativities of the 3 atoms which are stated above. The higher the electronegativity the more the larger the pull on electrons in the bond and so the higher the contribution.
These relative contributions can also be seen in the charge distributions discussed above as it is seen that nitrogen has the highest percentage contribution and so has a higher amount of electron density on its centre and therefore has the more negative charge. And phosphorus which has the lowest contribution also has the most positive charge situated on it.

The NBO analysis also confirms that the central atom is sp3 hybridised as there is about a 25% contribution from s orbital and 75% from p orbital. This is in the 1:3 ratio as expected in sp3 hybridised orbitals. However, as discussed in the geometry analysis the sulphur molecule is not perfect sp3 hybridised and this is reflected in the s and p contributions as the s contribution is 20% and p is 80%, meaning that there is less s character to the bond than would be expected.

=== Influence of functional groups ===

'''[N(CH3)3(CH2OH)]+'''

[N(CH3)3(CH2OH)]+ was optimised using the B3LYP method and using the basis set 6-31G(d,p).

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_N(CH3)3(CH2OH)_OTP_summary.PNG]] || [[File:JLS_N(CH3)3(CH2OH)_OTP_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_N(CH3)3(CH2OH)_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2OH)_OPT.LOG| here]]

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_N(CH3)3(CH2OH)_FREQ_summary.PNG]] || [[File:JLS_N(CH3)3(CH2OH)_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2OH)_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_N(CH3)3(CH2OH)_MO.LOG| here]]

'''[N(CH3)3(CH2CN)]+'''

[N(CH3)3(CH2OH)]+ was optimised using the B3LYP method and using the basis set 6-31G(d,p).

{| class="wikitable" border="1"
|+ geometry data
! Summary Data !! Convergence !! Jmol
|-
| [[File:JLS_N(CH3)3(CH2CN)_OTP_summary.PNG]] || [[File:JLS_N(CH3)3(CH2CN)_OTP_file.PNG]] || <jmol><jmolApplet>
<title> Optimisied cation </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JLS_N(CH3)3(CH2CN)_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2CN)_OPT.LOG| here]]

{| class="wikitable" border="1"
|+ Frequency Data
! Summary Data !! Low frequencies
|-
| [[File:JLS_N(CH3)3(CH2CN)_FREQ_summary.PNG]] || [[File:JLS_N(CH3)3(CH2CN)_FREQ_low.PNG]]

|}

The log file can be found [[Media:JLS_N(CH3)3(CH2CN)_FREQ.LOG| here]]

The log file for the molecular optimisation calculations can be found [[Media:JLS_N(CH3)3(CH2CN)_MO.LOG| here]]

==== Charge distribution analysis ====

Using the molecular orbital calculation the charge distributions of the two optimised cations could be analysed. The table below shows the distribution of charge in both molecules;

{| class="wikitable" border="1"
|+ Charge Distributions
! [[File:JLS_N(CH3)3(CH2OH)_charge.PNG]] !! [[File:JLS_N(CH3)3(CH2CN)_charge.PNG]]

|}

The difference between in charge distribution can be explained by the nature of the attached functional group. The lone pairs on the oxygen in the OH group can be donated, this would explain why the central nitrogen has a more negative charge than in N(CH3)3(CH2CN)+. The attached carbon however is more positive which is due to oxygen being much higher in electronegativity than carbon so polarising the bond. The cyanide group however is electron withdrawing hence the carbon it attached to being less negatively charged than the other methyl groups. Also, it can be seen that more of the negative charge sits on the nitrogen in the functional group. Also, the nitrogen is slightly less negative than in N(CH3)4+ but not significantly so.

==== HOMO LUMO comparison ====

{| class="wikitable" border="1"
|+ HOMO
! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| [[File:JLS_NCH34_HOMO.PNG|thumb]] || [[File:JLS_N(CH3)3(CH2OH)_HOMO.PNG|thumb]] || [[File:JLS_N(CH3)3(CH2CN)_HOMO.PNG|thumb]]
|-
! colspan="3" | LUMO
|-
! [[File:JLS_NCH34_LUMO.PNG|thumb]] !! [[File:JLS_N(CH3)3(CH2OH)_LUMO.PNG|thumb]] !![[File:JLS_N(CH3)3(CH2CN)_LUMO.PNG|thumb]]

|}

== References ==
<references>

<ref name="BondOrder"> C. Housecroft, A. Sharpe, Inorganic Chemistry,2012, Pearson, 4 ed, 50 & 30. </ref>

<ref name="N2"> T. Ghanty and S. Ghosh, J. Phys. Chem., 1991, 6512–6514.</ref>

<ref name="CH"> G. K. Jarvis, K.-M. Weitzel, M. Malow, T. Baer, Y. Song and C. Y. Ng, Phys. Chem. Chem. Phys., 1999, 1, 5259–5262. </ref>
</references>