Rep:Mod:mwt12

Inorganic Computational Project - Michelle Tan

Optimising a BH₃ Molecule

The BH₃ molecule was drawn and the structure optimized using the level of theory B3LYP/3-21G

Optimizing a BH3 Molecule (B3LYP/3-21G) Log File Link - Figure 1.1 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000217 0.000450 YES RMS Force 0.000105 0.000300 YES Maximum Displacement 0.000692 0.001800 YES RMS Displacement 0.000441 0.001200 YES Predicted change in Energy=-1.635268D-07 Optimization completed. -- Stationary point found. BH3 Molecule

From the summary table displayed, the gradient is smaller than 0.0001 and very close to zero showing that the molecule has a minimum energy. In the item table all the rows say 'converged' indicating that the optimization has been succesful.

Gaussian is also able to draw a total energy curve and RMS curve to show the gradual shift towards the optimum structure with the lowest energy. From both graphs it is evident that there is a gradual decrease in the total energy and RMS towards a minimum which corresponds to the minimum energy structure. This is the process that occurs during every optimisation and how close you get to the minimum depends on how alike the drawn structure is to the minimum energy structure and the method and basis set employed.

Total Energy and RMS Curves - Figure 1.2 Total Energy Graph RMS Graph

Now the BH₃ Molecule was optimized using a higher level of theory to get a more accurate representation of the molecule.

Level of Theory: B3lYP/6-31G (d,p)

Optimizing a BH3 Molecule (B3LYP/6-31G (d,p)) Log File Link - Figure 1.3 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000012 0.000450 YES RMS Force 0.000008 0.000300 YES Maximum Displacement 0.000064 0.001800 YES RMS Displacement 0.000039 0.001200 YES Predicted change in Energy=-1.128830D-09 Optimization completed. -- Stationary point found. BH3 Molecule Optimized using 6-31G(dp) Level of theory

Geometry Data - Figure 1.4 r(B-H) Å θ(H-B-H) degrees(º) 1.19 Å (3.s.f) 120.0°

Optimising a GaBr₃ Molecule using Pseudo potentials (B3LYP/LanL2DZ)

A GaBr₃ was drawn and its point group restricted to the point group D_3h. The optimization was run using 'B3LYP/LanL2DZ' basis set which utilizes a medium level of theory to optimize the GaBr₃ Molecule.

Optimizing a GaBr3 Molecule (B3LYP/LanL2DZ)) Log File Link - Figure 1.5 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000000 0.000450 YES RMS Force 0.000000 0.000300 YES Maximum Displacement 0.000003 0.001800 YES RMS Displacement 0.000002 0.001200 YES Predicted change in Energy=-1.307742D-12 Optimization completed. -- Stationary point found. GaBr3 Molecule Optimized using Pseudo potentials (LanL2DZ)

Geometry Data - Figure 1.6 DOI r(Br-Ga) Å θ(Br-Ga-Br) degrees(º) DOI:10042/195150 2.35 Å (3.s.f) 120.0°

Optimising a BBr₃ Molecule using a mixture of Basis Sets and pseudo potentials (B3LYP/GEN)

There is a need to mix basis sets and pseudopotentials when your molecule has a heavy atom and a light atom. A heavy atom requires a pseudo-potential and the light atom requires the consideration of the whole basis set.

Optimizing a BBr3 Molecule (B3LYP/6-31G(d,p)LANL2DZ)) Log File Link - Figure 1.7 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000008 0.000450 YES RMS Force 0.000005 0.000300 YES Maximum Displacement 0.000034 0.001800 YES RMS Displacement 0.000023 0.001200 YES Predicted change in Energy=-3.670918D-10 Optimization completed. -- Stationary point found. BBr3 Molecule Optimized using B3LYP/6-31G(d,p)LANL2DZ (Mixture of Pseudo-potentials and basis sets)

Geometry Data - Figure 1.8 DOI r(B-Br) Å θ(Br-B-Br) degrees(º) DOI:10042/195192 1.93 Å (3.s.f) 120.0°

Geometry Discussion:

Combined Geometry Data - Figure 1.9 Molecule r (Å) Literature Value θ (degrees(º)) BH3 1.19 Å (3.s.f) 1.19 Å 120.0° GaBr3 2.35 Å (3.s.f) 2.34Å 120.0° BBr3 1.93 Å (3.s.f) 1.90 Å 120.0°

Changing the ligand

BH₃ and BBr₃ are similar as they have a central atom connected to 3 other smaller atoms and the central atom is sp² hybridized. The ligands are in a trigonal planar configuration with 120.0° angles which ensures that the ligands are as far apart as possible. However, their bond lengths differ due to the van der waals radii of hydrogen and bromine (120 ppm ,190 ppm , respectively). Since bromine has such a large van der waals radius it inherently has a larger steric bulk and therefore will require a greater distance between the central boron for all 3 atoms to be accommodated. The bond length obtained for BBr₃ agrees well with the literature value 190 ppm. Although there is no reported B-Br bond length in the condensed phase, the reported values were taken from gas electron diffraction data. Both molecules exhibit the expected 120.0° that a trigonal planar molecule would have (VSEPR theory).Therefore it can be concluded that longer bond lengths are required to allow the same 120° angle (L-M-L (M = central atom)) to be achieved for the bulkier Br atom (when compared to the H atom). The primary factor affecting the nature of bonding is matching the size of the central boron atomic orbital and the atomic orbital of hydrogen and bromine. There is stronger and better orbital overlap between the hydrogen 1s orbital and the boron 2p orbital than the bromine 4p orbital and the boron 2p orbital. Bromine and hydrogen have van der waals radii of 190 ppm and 120 ppm respectively and when compared to Boron's van der waals radius of 180 ppm it is evident that although the van der waals radii of boron and bromine 'match' better they are too big to come into close contact with each other resulting in a weaker and longer bond when compared with the B-H bond. This is reflected in the bond dissociation energies of B-H ( 389 kj/mol) and B-Br (377 kj/mol) . One can also comment on the polarity of the bond which can be probed by analyzing the relative electronegativities of hydrogen and bromine when compared with boron. χ(Electronegativity (Xα)): Boron (3.4), H (7.97) and Br (7.24) . Therefore it can be deduced that the B-Br bond is less polarized than the B-H bond and therefore exhibits a greater degree of covalent bonding than electrostatic bonding. Pauling noted that an increase in the polarity of the bond led to an increase in the bond strength and therefore the B-H bond being more polar than the B-Br would be stronger and shorter which is reflected in the data above.

Changing the central atom

Changing the central atom from Ga to B results in an overall reduction in the L-M bond length due to the size of the atom. Ga has a van der waals radius of 238 ppm. whilst boron has a van der waals radius of 205 ppm (n.b. both values are the radii of elements in AX_n molecules reduced to zero charge on the metal atom.) Nevertheless, both central atoms are in Group 3 with 3 valence electrons each thereby supporting the computationally-calculated bond angles (L-E-L) of 120°. Gallium is in period 3 and therefore has occupied d-orbitals which the boron doesn't possess which additionally adds to the steric bulk of the gallium atom. Its electron cloud is therefore more diffuse and less contracted than the boron's electron cloud hence supporting the longer bond length between gallium and bromine than between boron and bromine.

Further Discussion

A bond is an aspect that is difficult to delineate as it is not clear at what point you would consider an 'interaction' between atoms, a bond. There are differing ways of visualizing molecules and hence different views on what evidence supports the presence of a bond or not. IUPAC's description of a bond is when the 'forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity'. When visualizing the molecule using spectroscopy, there is an observed existence of electron density between the two nuclei. .

There is a range of weak, medium and strong bonds. Strong bonds would be those in a crystal of sodium chloride which is an electrostatic interaction between the sodium cations and the chloride anions which on average have a bond strength of 756 kj/mol . A medium strength bond would be approximately the strength of a carbonyl (C=O) bond which has a bond strength of 192 kj/mol (in CO₂). A weak bond would be the bond between 2 oxygens that is often exploited in epoxidation reactions with peroxides or in the Baeyer Villiger Reaction which only possesses a bond strength of 35 kj/mol .

Gaussview at times does not draw bonds but this does not mean that there is no bond between the atoms. It removes the bond because the distance between the atoms is outside the expected value for the bond length between the two atoms. In reality, the range from an interaction to a bond is continuous and not discrete.

Frequency analysis of BH₃

Frequency Analysis of BH3 Log File Link - Figure 2.0 Summary Table Low Frequencies Low frequencies --- -12.3889 -12.3823 -7.7287 -0.0002 0.0237 0.4048 Low frequencies --- 1162.9692 1213.1354 1213.1356

IR Frequency Analysis of BH3 Molecule - Table 1.1 Wavenumber Intensity IR active? Type 1163 93 Yes Bend 1213 14 Yes Bend 1213 14 Yes Bend 2583 0 No Stretch 2716 126 Yes Stretch 2716 126 Yes Stretch

IR Spectrum and Diagrams - Figure 2.1 Graph Diagram

The frequency function in gaussian calculates the second derivatives of energy which allows a stationary point to be characterized. If the output gives a negative eigenvalue or imaginary vibrational frequency this implies that there is a negative curvature at this point, thus corresponding to an energy maximum (Transition structure). Conversely, if the output is real and positive then the geometry of the structure is converging or has converged to an energy minimum. The frequency function of gaussian was then employed to confirm that the optimized structure that was found is indeed a minimum as the optimization may not have found the global minimum but instead the local minimum. There is also a chance we have found a 'saddle point' in which case we have calculated a transition structure rather than a minimum. At a minimum point, we can traverse the potential energy surface in any direction and the energy will always rise, however, for a transition structure, movement in one direction will lead to a reduction in energy which corresponds to the reaction path. Therefore, the frequency calculation must be done in order to identify which stationary point was found.

Upon running the first frequency calculation at the same level of theory (B3LYP/6-31G), the IR vibrations were found and none were imaginary, implying that there is no negative force constant. No imaginary frequencies correlates to the fact that this optimized structure is not a transition structure and is in fact a minimum on the potential energy surface.

The frequency calculations were also used to determine IR/Raman modes that can be used to compare with experimental findings.

After the frequency calculation was run, there was 6 vibrations displayed in the table. However, there are less than six peaks (only 3 peaks observed) in the spectrum because there are 2 vibrations that are degenerate and therefore have the same energy and appear as a single peak instead of two distinct peaks in the IR spectrum.There are some vibrations that are due to bends and some due to stretches. It is evident that the stretches are higher in energy than the bends. One of the stretches has a 0 intensity because it is a symmetrical stretch which doesn't result in a change in dipole moment and therefore does not appear on an IR spectrum.

Frequency analysis of GaBr₃

Frequency Analysis of GaBr3 Log File Link DOI:10042/195203 - Figure 2.2 Summary Table Low Frequencies Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540 Low frequencies --- 76.3920 76.3924 99.6767

From the frequency analysis done it is evident that there are no imaginary frequencies inferring that a minimum point has been reached. This is further supported by relatively low 'low frequencies' that are tending towards 0.

IR Frequency Analysis of GaBr3 Molecule - Table 1.2 Wavenumber Intensity IR active? Type 76 3 Yes Bend 76 3 Yes Bend 100 9 Yes Bend 197 0 No Stretch 316 57 Yes Stretch 316 57 Yes Stretch

IR Spectrum and Diagrams - Figure 2.3 Graph Diagram

The large difference in the value for the frequencies of BH₃ compared to GaBr₃ is due to the rigidity of the bonds and how flexible the molecule is especially when considering its bending and stretching modes. The bond dissociation energy of the Ga-Br bond is 402±13 kj/mol compared with the bond dissociation energy of the B-H bond which is 345.2 ± 2.5 kj/mol . This supports the computational findings which show a higher frequency for the BH₃ bending and stretching modes compared to those of GaBr₃.

There has also been a reordering of modes in particular, the A2" umbrella motion which was observed in the log files of both the respective molecules. For the BH₃ molecule, the A2" umbrella motion occurs at 1163 cm^-1 with an intensity of 93 whilst for the GaBr₃ molecule this motion has shifted to 100 cm^-1 with a much lower intensity of 9. The nature of this vibration has changed because the bond lengths have changed. The bond length B-H is 1.19 Å whereas the Ga-Br bond length is much longer at 2.35 Å hence there will be an increase in the frequency of the vibration for the shorter bond (B-H bond) and a reduction in the frequency for the longer (Ga-Br) Bond. This finding can be further supported by considering the equation that relates frequency with force constant (k) and reduced mass(μ). As you increase the rigidity and strength of the bond you increase the force constant of the bond which will therefore increase the frequency. Additionally, when you increase the mass of your molecule you essentially increase the reduced mass of the molecule which will decrease the vibrational frequency of that bond. In all of these considerations, we are assuming that the bond behaves like a harmonic oscillator. The bond oscillates around a mean position which corresponds to the equilibrium bond length. From the animations it was observed that the hydrogens in BH₃ move more than the central boron atom due to the difference in mass. When the movement of the hydrogen was compared to the bromine in GaBr₃, the movement was greater. However, when comparing the movement of Boron and the Gallium, the Gallium moves more than the Boron. This is because in a molecule of GaBr₃ the bromine is heavier than the gallium and therefore the gallium appears to oscillate more than the bromine. In a molecule of BH₃ the hydrogen is much lighter than the boron and therefore the boron appears to oscillate less than the hydrogens.

To ensure that the frequency calculation is valid, one must carry out the frequency calculation using exactly the same basis set and method as the prior optimisation. Computing the frequency with a different basis set and method to the optimisation would not be able to act as proof that the optimisation has led to a minimum energy conformation. When doing comparisons between molecules, data from calculations using the same basis set and method can only be used to yield meaningful deductions otherwise the inferences made are futile. The 'low frequencies' reported are the "-6" that is in the formula for calculating the number of vibrational modes of a molecule. These low frequencies are essentially the translations and rotations at the center of mass of the molecule that do not give rise to a peak on the IR spectrum. If you use a higher level of theory to compute the optimization and frequency calculations, these 6 frequencies will tend to converge to 0.

MO analysis of BH₃

MO Diagram of LCAO Molecular orbitals and 'real' Molecular orbitals DOI:10042/195320 // Log File Link - Figure 2.4

There are a lot of similarities between the real MOs and those inferred from using MO theory. Although some of the orbitals do not look exactly the same the number of nodes observed correlates well. When we deduce molecular orbitals manually we localize the molecular orbitals on the atoms that they belong to. However, this is not necessarily true as the molecular orbitals of individual atoms overlap to form a delocalized electron cloud. What maintains the same is the number of nodes in each of the molecular orbitals deduced and the "real" molecular orbitals. The highest energy molecular orbitals (4 MOs) are actually 2 sets of degenerate pairs. This demonstrates the fundamental usefulness and accuracy of qualitative MO theory and the ability to predict MOs that look very close to the real MOs is a very powerful tool to have.

NBO Analysis of NH₃

Optimizing a NH3 Molecule (B3LYP/6-31G (d,p)) Log File Link - Figure 2.5 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000006 0.000015 YES RMS Force 0.000004 0.000010 YES Maximum Displacement 0.000012 0.000060 YES RMS Displacement 0.000008 0.000040 YES Predicted change in Energy=-9.846063D-11 Optimization completed. -- Stationary point found. NH3 Molecule

Frequency Analysis of NH3 Log File Link - Figure 2.6 Summary Table Low Frequencies Low frequencies --- -0.0138 -0.0030 -0.0010 7.0781 8.0927 8.0932 Low frequencies --- 1089.3840 1693.9368 1693.9368

From the frequency analysis we can confirm that we have accurately optimized the molecule as there reported low frequencies are within 15cm^-1 and are all close to 0.

IR Frequency Analysis of NH3 Molecule - Table 1.3 Wavenumber Intensity IR active? Type 1089 145 Yes Bend 1694 14 Very Slight Bend 1694 14 Very Slight Bend 3461 1 No Stretch 3590 0 No Stretch 3590 0 No Stretch

IR Spectrum and Diagrams - Figure 2.7 Graph Diagram

NBO Analysis of NH3 Population Analysis File Log File Link - Figure 2.8 Molecule with Charge Distribution NB. The Color ranges from red to green showing a charge ranging from -1.125 to 1.125 respectively. NBO Charges: H Charge = 0.375 N Charge = -1.125

From the diagram above it is evident that the central nitrogen is much more electronegative than the surrounding hydrogens and this is denoted by the red nitrogen atom.

We can use the population analysis that was done to analyse the contribution of each atom to a bond and the relative hybridisation of each bond. The nitrogen contributes 68.83% towards the N-H bond whilst the hydrogen contributes 31.17%. This disparity is due to the electronegativity of the nitrogen atom compared to the hydrogen. Therefore the greater electron density around the nitrogen would allow it to contribute greater electron density towards the bond.

All the N-H bonds are observed to have the same energy of -0.64017 AU , the core orbital has an energy of -14.16768 AU and the lone pair on the nitrogen has an energy of -0.31757 AU. This demonstrates the reason why we leave off the very low energy core orbitals on MO diagrams.

Association Energies of Ammonia-Borane

Introduction

Ammonia Borane is considered one of the future sources of clean energy. In an age where we are becoming so reliant on energy we require new sources of energy as our current energy sources will soon run out. Hence, chemical hydrogen storage may be the solution for cleaner energy, as it is able to release H₂ through thermolysis without emitting CO₂. Its discovery happened in the military, when they were looking for a clean source of H₂ for use in HF Laser systems As N-B is isoelectronic with C-C, ammonia boranes are considered to be the inorganic analogue of commonly used hydrocarbon fuels. However, a significant difference is that ammonia borane is a solid rather than a gas at room temperature due to the strong dipole in B-N and strong intermolecular interactions compared to hydrocarbons. As they are solids, they exhibit greater densities than gaseous hydrocarbons and are therefore easier to handle and store. The energetics of H₂ release from NH₃BH₃ is substantially different from C₂H₆ as hydrogen release from ammonia borane is exothermic whilst it is endothermic for hydrocarbons. This difference stems from the relatively weak dative σ B-H and N-H bond in ammonia borane that will readily lose H₂ to form a much stronger B-N σ bond and dative π bond in BH₂NH₂. This can continue to release hydrogen until a total of 3 equivalents of H₂ is produced and the by product is a single BN unit.

Optimizing Ammonia Borane

Optimizing a NH3BH3 Molecule (B3LYP/6-31G (d,p)) Log File Link - Figure 2.9 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000123 0.000450 YES Item Value Threshold Converged? Maximum Force 0.000002 0.000015 YES RMS Force 0.000001 0.000010 YES Maximum Displacement 0.000034 0.000060 YES RMS Displacement 0.000010 0.000040 YES Predicted change in Energy=-1.180615D-10 Optimization completed. -- Stationary point found. NH3BH3 Molecule

From the data above it is clear that the potential energy gradient is close to zero and upon inspecting the item table in the log file, all values have converged. However, it is sensible to support this information using a frequency analysis of the NH₃BH₃ molecule.

Frequency Analysis of NH3BH3 Log File Link - Figure 3.0 Summary Table Low Frequencies Low frequencies --- -1.9046 0.0004 0.0008 0.0011 2.2871 3.2630 Low frequencies --- 263.4739 632.9557 638.4484

From the frequency analysis, the data supports the fact that a minimum energy structure has been reached. This is because there were no observed imaginary frequencies and the low frequencies are all within 15 cm^-1 and tend towards 0.

IR Frequency Analysis of NH3BH3 Molecule - Table 1.3 Wavenumber Intensity IR active? Type 263 0 No Twist 633 14 Yes Symmetric stretch 638 4 Very Slight Twist 639 4 Very Slight Wag 1069 41 Yes Twist 1069 41 Yes Wag 1196 109 Yes Wag 1204 3 Very Slight Symmetric stretch 1204 3 Very Slight Scissor 1329 114 Yes Symmetric stretch 1676 28 Yes Scissor 1676 28 Yes Scissor 2472 67 Yes Symmetric stretch 2532 231 Yes Anti-symmetric Stretch 2532 231 Yes Anti-symmetric Stretch 3464 3 Very Slight Symmetric stretch 3581 28 Yes Anti-symmetric Stretch 3581 28 Yes Anti-symmetric Stretch

IR Spectrum and Diagrams - Figure 3.1 Graph

NBO Analysis of Ammonia Borane

The NBO charges on atoms of Ammonia Borane were computed.

NBO Analysis of Ammonia Borane Log File Link - Figure 3.2 Molecule with Charge Distribution NB. The Color ranges from red to green showing a charge ranging from -0.962 and + 0.962 respectively. NBO Charges: B Charge = -0.171 H1= -0.059 (hydrogen attached to boron) N Charge = -0.962 H2 (hydrogen attached to nitrogen) Charge = 0.436

Figure 3.3 Atom Hybridisation Nitrogen s(21.53%) p(78.41%) Hydrogen attached to Nitrogen s(99.90%) p(0.10%) Boron s(28.18%) p(71.73%) Hydrogen attached to Boron s(99.97%) p(0.03%)

From the NBO analysis of ammonia borane, Nitrogen contributes 72.14% to the N-H bond whilst hydrogen contributes 27.86%. In the B-H bond boron contributes 46.88% to the bond whilst H contributes 53.12%. In the B-N bond, there is a much more polarized contribution between Nitrogen and Boron. Nitrogen contributes 81.88% to the B-N bond whilst Boron only contributes 18.12%. In both bonds which contain nitrogen - the strongly polarized contributions from each atom can be attributed to the fact that nitrogen is substantially more electronegative than boron or hydrogen and therefore will attract most of the electron density towards itself. This therefore supports the fact that most of bond is contributed by the extra electron density around the nitrogen.

From the table above, both nitrogen and boron are sp3 hybridized shown by the relative s and p contributions. This therefore supports the optimized structure that exhibits 3 sp3 orbitals that are 107° apart that then overlap with the s orbitals of the hydrogens.

Determining the Energy of the bond:

BH₃ + NH₃ --> NH₃BH₃

E(NH₃)= -56.5577687 AU

E(BH₃)= -26.61532360 AU

E(NH₃BH₃)= -83.2246891 AU

Dissociation Energy:

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -83.2246891 - (-56.5577687-26.61532360) = -0.05159675 AU = -135.5 kj/mol

Referring to the previous discussion regarding the strength of weak, medium and strong bonds. From the dissociation energy calculated above, the association of NH₃ and BH₃ to form a B-N bond within NH₃BH₃ would be considered a medium strength bond.

It is published in the literature that the strength of this B-N bond is -113.8 kj/mol which is relatively close to the energy calculated. The discrepancy could be due to the method and basis set used.

Since ethane and aminoborane are isoelectronic - we can do a similar analysis on ethane. However, it is apparent that the C-C and N-B bonds are very different so by probing the NBO charges we can begin to understand their differences using computational methods.

Optimizing an Ethane molecule

Firstly the ethane molecule was optimised using the level of theory: 6-31G (dp).

Optimizing an Ethane Molecule (B3LYP/6-31G) Log File Link - Figure 3.4 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000003 0.000015 YES RMS Force 0.000001 0.000010 YES Maximum Displacement 0.000015 0.000060 YES RMS Displacement 0.000006 0.000040 YES Predicted change in Energy=-9.162134D-11 Optimization completed. -- Stationary point found. Ethane Molecule

The optimized structure has a reported point group of C1 but in reality it should be D_3d. This was achieved by symmetrizing the molecule which produced a D_3d point group. One should note that the optimized structure is the staggered conformation of ethane as expected.

Frequency Analysis of Ethane Log File Link - Figure 3.5 Summary Table Low Frequencies Low frequencies --- -11.2259 -4.4534 -1.9221 0.0007 0.0011 0.0013 Low frequencies --- 312.9100 827.8967 827.9437

IR Frequency Analysis of an Ethane Molecule - Table 1.4 Wavenumber Intensity IR active? Type 312 0 No Twist 828 5 Very Slight Wag 828 5 Very Slight Wag 1005 0 No Symmetric Stretch 1226 0 No Wag 1226 0 No Wag 1419 0 No Wag 1441 0 No Wag 1517 0 No Scissor 1517 0 No Scissor 1522 7 Very Slight Scissor 1522 7 Very Slight Scissor 3043 0 No Symmetric stretch 3044 58 Yes Anti-symmetric Stretch 3099 0 No Anti-symmetric Stretch 3099 0 No Anti-symmetric Stretch 3122 70 Yes Anti-symmetric Stretch 3122 70 Yes Anti-symmetric Stretch

IR Spectrum - Figure 3.6 Graph

From the frequency analysis, the data supports the fact that a minimum energy structure has been reached. This is because there were no observed imaginary frequencies and the low frequencies are all within 15 cm^-1 and tend towards 0.

Consequently the NBO charges on the carbon atoms were computed.

NBO Analysis of Ethane's Population Analysis File DOI:10042/195277 // Log File Link - Figure 3.7 Molecule with Charge Distribution NB. The Color ranges from red to green showing a charge ranging from -0.687 to 0.687 respectively. NBO Charges: C Charge = -0.687 H Charge = 0.229

Combined NBO Analysis of Ethane and Ammonia Borane - Table 1.5 Molecule Atom Charge Ethane C -0.687 Ethane H 0.229 Ammonia Borane N -0.962 Ammonia Borane H (attached to N) 0.436 Ammonia Borane B -0.171 Ammonia Borane H (attached to B) -0.059

From the NBO analysis that was carried out, we can see that the difference in charges between B and N is much greater than for the C-C bond. The difference in charge between the boron and nitrogen in ammonia borane is 0.791 whilst the difference in charge between the two carbons is 0. Thereby implying that the B-N bond is much more polarized than the corresponding C-C bond hence supporting the fact that it is much stronger than the C-C bond in the hydrocarbon. This is therefore exploited as it affects the physical properties of the ammonia borane such as the its state at room temperature, which is solid as opposed to hydrocarbons which are commonly liquids. The strength of the B-N bond compared to a C-C bond also affects its energetic properties (discussed previously in the introduction). One can also note that the hydrogens no longer have the same charge distribution across the molecule and are heavily affected the electronegativity of the atom that they are adjacent to. The hydrogens that are attached to the nitrogen are much more electropositive than those attached to the boron further reaffirming the strong electronegativity of nitrogen when compared to boron. Chemically, we can manipulate the charges on the carbon or nitrogen by changing the substituents on these respective atoms. The findings yielded from this investigation are shown below.

Addition of an Electron withdrawing atom to Ethane

Optimizing a Fluoroethane Molecule (B3LYP/6-31G) Log File Link - Figure 3.8 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000007 0.000015 YES RMS Force 0.000003 0.000010 YES Maximum Displacement 0.000041 0.000060 YES RMS Displacement 0.000021 0.000040 YES Predicted change in Energy=-9.256399D-10 Optimization completed. -- Stationary point found. Ethane Molecule substituted with a fluorine

Frequency Analysis of Fluoroethane Log File Link - Figure 3.9 Summary Table Low Frequencies Low frequencies --- -0.0015 -0.0014 -0.0005 2.0214 5.2890 10.0160 Low frequencies --- 266.8509 406.5208 815.9337

IR Spectrum and Diagrams - Figure 4.0 Table Graph

From the frequency analysis, the data supports the fact that a minimum energy structure has been reached. This is because there were no observed imaginary frequencies and the low frequencies are all within 15 cm^-1 and tend towards 0.

Consequently the NBO charges on the atoms within the molecule were computed.

NBO Analysis of Fluoroethane's Population Analysis File DOI:10042/195281 // Log File Link - Figure 4.1 Molecule with Charge Distribution NB. The Color ranges from red to green showing a charge ranging from -0.734 to 0.734 respectively. NBO Charges: C1 Charge = -0.734 H1 Charge = 0.240 C2 Charge = 0.012 F=-0.389 H2 = 0.196 (where C1 is the carbon adjacent to C2 (attached to fluorine)).

As you can see from just adding a fluorine onto one of the carbons (C2) there is a significant change in the charges of the surrounding atoms. The very electronegative fluorine has made the carbon adjacent to it more electropositive and the attached hydrogens less electropositive when compared to a molecule of ethane. The addition of the fluorine has also influenced the adjacent carbon (C1) by making it more negatively charged to counterbalance the increased positive charge on C2. Subsequently, the hydrogens attached to C1 have become more electropositive to counterbalance the increased negative charge distribution on C1.

Addition of Electron withdrawing group to Ammonia Borane

If we wanted to weaken the N-B bond in Ammonia borane we would add an electronegative group which would withdraw electrons away from the B-N bonds thus weakening it. The fluorine was arbitrarily chosen to be attached to the boron.

Optimizing a Fluorine substituted Ammonia Borane (B3LYP/6-31G) Log File Link - Figure 4.2 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000001 0.000015 YES RMS Force 0.000001 0.000010 YES Maximum Displacement 0.000032 0.000060 YES RMS Displacement 0.000012 0.000040 YES Predicted change in Energy=-4.922417D-11 Optimization completed. -- Stationary point found. Jmol diagram cannot be displayed as the optimized structure does not contain a bond between boron and nitrogen and therefore cannot be converted into a mol file.The bond length has extended longer than expected for a B-N bond and therefore will not be recognised by gaussian as a bond.

Frequency Analysis of Fluorine Substituted Ammonia Borane Log File Link - Figure 4.3 Summary Table Low Frequencies Low frequencies --- -0.0018 -0.0017 -0.0016 3.7086 5.0371 7.1603 Low frequencies --- 175.8245 304.7295 544.1697

IR Spectrum and Diagrams - Figure 4.4 Table Graph

From the frequency analysis, the data supports the fact that a minimum energy structure has been reached. This is because there were no observed imaginary frequencies and the low frequencies are all within 15 cm^-1 and tend towards 0.

Consequently the NBO charges on the Boron, Nitrogen and hydrogen atoms were computed.

NBO Analysis of Fluorine Substituted Ammonia Borane DOI:10042/195280 // Log File Link - Figure 4.5 Molecule with Charge Distribution NB. The Color ranges from red to green showing a charge ranging from -1.006 to 1.006 respectively. NBO Charges: B Charge = 0.471 H1 Charge = -0.122 F Charge = -0.527 N Charge = -1.006 H2 = 0.435 (H2 are the hydrogens attached to the nitrogen and H1 are the hydrogens attached to the boron) The distance between B-N is 170 ppm and from the charge distribution image one can observe that the bond is not present in gaussian as this length has extended beyond the length of a regular B-N bond as designated by gaussian.

The charge distribution on the nitrogen and bonded hydrogens has not changed significantly from the ammonia borane. However, there is a significant change in the charge distribution at the boron. The boron has become much more electropositive due to the very electronegative fluorine atom that is now attached directly to it. This changes the nature of the B-N bond as the fluorine is withdrawing electron density away from the central bond thereby making it weaker. It can also be noted that the difference in charge distribution between B/N has now increased and the bond has become more polar. This therefore can imply that the substituted ammonia borane may be more stable as ions where the fluorine can stabilize the positive charge on boron.

Projects

Ionic liquids are becoming a field of great interest amongst researchers due to their unique properties. They are often an ionic pair that is present in a liquid at room temperature. Ionic liquids commonly constitute a long and flat organic cation and a polyatomic anion with delocalized charge. Since there is such a large range of ions that can be used to form varying ionic liquids, the tunability of these substances is often exploited. They also have good solvent properties some of which include: 1) Their ability to solubilize a wide range of organic, inorganic and polymeric compounds which would not be soluble without the presence of the ionic liquid. 2) Due to their low coordinating ability, they are often used as catalysts or solvents in reactions. 3) Their insolubility in certain solvents can make them highly useful in extraction applications which require multiphases. As there are a vast range of combinations of cations and anions to make an ionic liquid, it is feasibly impossible and would be costly to make every combination in the lab. Therefore computational methods are becoming increasingly popular in determining the right combination of a cation and an anion to make a 'designer solvent' with desired properties.

Part 1: Comparison of Onium Cations

Optimizing [N(CH3)4+] (B3LYP/6-31G) Log File Link- Figure 4.6 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000037 0.000450 YES RMS Force 0.000009 0.000300 YES Maximum Displacement 0.001606 0.001800 YES RMS Displacement 0.000330 0.001200 YES Predicted change in Energy=-2.670871D-08 Optimization completed. -- Stationary point found. N(CH3)4+

This molecule should exhibit a Td point group and after symmetrizing and ensuring that the bond angles were as close to the expected bond angles of a tetrahedral molecule, the Td point group was obtained (shown below).

Image showing expected point group of N(CH₃)₄⁺

Frequency Analysis of N(CH3)4+ Log File Link - Figure 4.7 Summary Table Low Frequencies Low frequencies --- -2.1414 -0.0006 0.0002 0.0007 5.1201 11.0111 Low frequencies --- 182.9081 288.1971 288.8046

From the frequency analysis, the data supports the fact that a minimum energy structure has been reached. This is because there were no observed imaginary frequencies and the low frequencies are all within 20-30 cm^-1 and tend towards 0. The range for the low frequencies is now slightly larger as the basis set and methods used are not good enough for this sized molecule.

Optimizing [P(CH3)4+] (B3LYP/6-31G) Log File Link - Figure 4.8 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000036 0.000450 YES RMS Force 0.000013 0.000300 YES Maximum Displacement 0.000372 0.001800 YES RMS Displacement 0.000129 0.001200 YES Predicted change in Energy=-2.803693D-08 Optimization completed. -- Stationary point found. P(CH3)4+

This molecule should exhibit a Td point group and after symmetrizing and ensuring that the bond angles were as close to the expected bond angles of a tetrahedral molecule, the Td point group was obtained (shown below).

Image showing expected point group of P(CH₃)₄⁺

Frequency Analysis of P(CH3)4+ Log File Link - Figure 4.9 Summary Table Low Frequencies Low frequencies --- -11.9206 -6.7850 -5.1345 -0.0033 -0.0032 -0.0030 Low frequencies --- 156.7331 191.6116 192.3976

From the frequency analysis, the data supports the fact that a minimum energy structure has been reached. This is because there were no observed imaginary frequencies and the low frequencies are all within 20-30 cm^-1 and tend towards 0.

Optimizing [S(CH3)3+] (B3LYP/6-31G) DOI:10042/195284 //Log File Link- Figure 5.0 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000103 0.000450 YES RMS Force 0.000041 0.000300 YES Maximum Displacement 0.001638 0.001800 YES RMS Displacement 0.000535 0.001200 YES Predicted change in Energy=-3.134776D-07 Optimization completed. -- Stationary point found. S(CH3)3+

This molecule should exhibit a C3v point group and after symmetrizing and ensuring that the bond angles were as close to the expected bond angles of a distorted trigonal pyramidal molecule, the C3v point group was obtained (shown below). It is slightly more distorted from a regular trigonal pyramidal structure as the bond angle is contracted from the expected 107.3° to 102.7°. This contraction could be due to the lengthening of the bond between the central sulphur and carbon of the methyl groups and therefore reduced steric hindrance enabling the methyl groups to become laterally closer in contact with each other.

Image showing expected point group of S(CH₃)₃⁺

Frequency Analysis of S(CH3)3+ DOI:10042/195285 // Log File Link - Figure 5.1 Summary Table Low Frequencies Low frequencies --- -10.2551 -5.3249 0.0022 0.0036 0.0045 11.3781 Low frequencies --- 162.6435 200.0775 200.6348

From the frequency analysis, the data supports the fact that a minimum energy structure has been reached. This is because there were no observed imaginary frequencies and the low frequencies are all within 20-30 cm^-1 and tend towards 0.

Geometry Data - Table 1.6 Molecule r (Å) θ (degrees(º)) N(CH3)4+ 1.51 109.5 P(CH3)4+ 1.82 109.5 S(CH3)3+ 1.82 102.7

The structure of N(CH₃)₄⁺ and P(CH₃)₄⁺ are the expected tetrahedral structure with bond angles of 109.5°. Whilst S(CH₃)₃⁺ has a smaller bond angle as sulphur has a van der waals radius of 1.80 Å and therefore the methyl groups can be laterally closer together as the bond length is sufficiently long enough to prevent steric clashes. It is interesting to note that the bond length of S-C is the same as P-C in this computation. Although phosphorous has a much larger van der waals radius compared to sulphur it needs to fit 4 methyl groups around it whereas sulphur only needs to fit 3. Therefore, although the two bond lengths are the same, there is an observed reduction in the bond angle in the sulphur complex.

We can draw direct comparisons between N(CH₃)₄⁺ and P(CH₃)₄⁺ as both the molecules are in the same geometrical arrangement (i.e. bond angles are the same). However, there is a difference in the bond lengths as shown in the geometry data table. The bond length between N-C is shorter than the same corresponding bond P-C. This could be rationalized by considering the electronegativity difference between N and P. From the charge distribution analysis it was observed that the electronegativity difference between N and C is greater than for P and C and this could infer a stronger more electrostatic-like bond. However, one must take into account the orbital size match which is better for N/C than P/C as P now has 3p orbitals which mismatch with the 2p orbital of C. Another factor is the steric hindrance of the now quite large phosphorous atom which exhibits a larger van der waals radius of 2.05 Å than the van der waals radius of N of 1.70 Å showing that in order to accommodate 4 methyl groups around the phosphorous, the bonds between phosphorous and carbon need to be elongated.

MO Analysis of the Onium Cations

From the MO analysis I have selected 5 very distinct non-core MOs to analyze. These have been selected as they show the range from strongly bonding to strongly anti-bonding.

Non-Core Molecular Orbitals of N(CH3)4+ - Figure 5.2 Molecular Orbital MO Number// Energy (AU) MO 6 // -1.19642 MO 10 // -0.80746 MO 13 // -0.69895 MO 15 // -0.62247 MO 21 // -0.57933

MO 6: Shows no nodes and is strongly bonding in character. The MO is delocalized over the whole molecule.

MO 10: Shows strong through space bonding interactions where the lobes are near in proximity to each which outweighs the 4 nodal planes that are weakly antibonding due to the weak interactions between the lobes of opposite phase. Therefore overall, we can consider this MO bonding in nature. The lobes are less delocalized than MO 6, however the orbital is delocalized across the methyl group.

MO 13: Exhibits an overall weakly bonding through space interaction, however it is less so than MO 10. It additionally shows 4 nodes which are weakly antibonding whilst having 2 nodal planes. One can observe that the majority of the MO is green and hence is mostly bonding however, there are more antibonding interactions within the MO because the relative surface area of antibonding interactions is greater than the corresponding bonding interactions. Hence, overall this is a weakly antibonding MO.

MO 15: There is an observed through space antibonding interactions on multiple occasions and there are 4 nodes and 2 nodal planes within this MO. Since the planes run all the way through the MO it can be inferred that these two nodal planes outweigh the distant through space bonding interactions between the elongated lobes of the MO. Therefore, it can be concluded that this MO is overall moderately antibonding.

MO 21: There are 5 nodes and 3 nodal planes within this MO with extremely weak through space bonding interactions however there are very strong antiboding interactions at each part of the MO. There are large surface areas where two lobes of opposite phase meet thus creating a large nodal surface. When comparing this overall, very strongly anti bonding MO, the lobes are very localized in comparison to the MO 6 which had a very delocalized MO diagram.

Charge Distribution of N(CH3)4+/P(CH3)4+/S(CH3)3+ - Figure 5.3 Complex Charge on N/P/S Charge on C Charge on H N(CH3)4+ -0.295 -0.463 0.269 P(CH3)4+ 1.667 -1.060 0.298 S(CH3)3+ 0.917 -0.846 0.279

Charge Distribution of Images of Onium Ions (NB. Red-Green refers to -1.667 to 1.667 respectively.) - Figure 5.4 N(CH3)4+ P(CH3)4+ S(CH3)3+ Log File Link Log File Link Log File Link

From the charge distribution images it is evident that the most electropositive atom is the phosphorous atom which correlates well with the reported electronegativities by Bartolotti et al. χ(Electronegativity (Xα)): P (5.01), N (6.97) and S (6.52) . In the molecule of N(CH₃)₄⁺ the nitrogen and carbon have similar charge density whereas for P(CH₃)₄⁺ and S(CH₃)₃⁺ there is a more discernable difference between the charge density on the phosphorous/sulphur and carbon. The S-C and P-C bonds appear to be more polarized than the N-C bond in these cation complexes. The hydrogens all exhibit a similar color indicating that the charge density at hydrogen is largely unchanged by the electronics of the central atom. The charge distribution differences cannot necessarily be compared directly with the electronegativity differences as they do not necessarily reinforce each other. In this example, there is a greater electronegativity difference between N and C however, the charge distribution shows that they have similar charge density.

NBO Analysis of Onium Cations

Relative Contribution to the C-X Bond (NBO Analysis) - Table 1.7 Molecule Contribution from X Hybridisation of X Contribution from C Hybridisation of C N(CH3)4+ 66.35% s(25.00%) p(74.97%) d(0.03%) 33.65% s(20.77%) p(79.06%) d(0.16%) P(CH3)4+ 40.43% s(25.00%) p(74.15%) d(0.85%) 59.57% s(25.24%) p(74.68%) d(0.08%) S(CH3)3+ 51.32% s(16.95%) p(82.41%) d(0.63%) 48.68% s(19.72%) p(80.14%) d(0.14%)

We can see from the NBO analysis that N and S contributes more to the bond than carbon. Conversely, C contributes more than P to the C-P bond. This can be explained by the relative electronegativities of each of the central atoms compared to carbon. For both nitrogen and sulphur, they are both more electronegative than carbon and therefore will have greater electron density in the vicinity of the atom. Hence they will be able to contribute more towards the bond with carbon. On the other hand, phosphorous is less electronegative than carbon and therefore we would expect the carbon to contribute more to the P-C bond which is supported by the data above. The polarization of the bond i.e. the charge distribution cannot be used to infer the contribution from each of the atoms. We would expect that the C-N bond would be δ- on the nitrogen and δ+ on the carbon however, the charge distribution data does not reflect this. This may be due to the limitation of the basis set and methods, if a higher level of theory was used the charge distribution could switch over thereby making the nitrogen more electronegative, as expected.

As expected from the geometry, both X and C have sp³ hybridisation however this is to varying degrees for each of the cations in questions. Both phosphorous and sulphur contain contributions from the d orbitals as they are in 3p orbitals which are closer to the 3d orbitals. However, this is not the case for nitrogen as it contains little to no contribution from d orbitals as it is too high in the periodic table to be able to involve d orbitals in bonding.

[NR4}+ is formally depicted as having a positive charge on the nitrogen center however, it is debatable as to whether the charge is actually localized on the central atom or delocalized over the whole molecule. This is also seen in an analogous example reported by Hunt et al. where the positive charge is delocalized around the aromatic imidazolium instead of being localized on one carbon atom.

Part 2: Influence of functional groups

I have optimized and completed a frequency analysis for 2 onium cations that can be used as the cationionic component in ionic liquids - ([N(CH₃)₃(CH₂OH)]+/[N(CH₃)₃(CH₂CN)]+)

Optimizing [N(CH3)3(CH2OH)]+ (B3LYP/6-31G) Log File Link - Figure 5.5 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000002 0.000015 YES RMS Force 0.000000 0.000010 YES Maximum Displacement 0.000039 0.000060 YES RMS Displacement 0.000009 0.000040 YES Predicted change in Energy=-3.143387D-11 Optimization completed. -- Stationary point found. [N(CH3)3(CH2OH)]+

Frequency Analysis of [N(CH3)3(CH2OH)]+ Log File Link - Figure 5.6 Summary Table Low Frequencies Low frequencies --- -8.4533 -5.0423 -1.1594 -0.0011 -0.0010 -0.0008 Low frequencies --- 131.1008 213.4660 255.7054

Since the low frequencies are near zero and all convergence criteria has been met I can conclude that a minimum energy structure has been obtained.

Optimizing [N(CH3)3(CH2CN)]+ (B3LYP/6-31G) Log File Link - Figure 5.7 Summary Table Item Table Molecule Item Value Threshold Converged? Maximum Force 0.000000 0.000015 YES RMS Force 0.000000 0.000010 YES Maximum Displacement 0.000002 0.000060 YES RMS Displacement 0.000000 0.000040 YES Predicted change in Energy=-6.238302D-13 Optimization completed. -- Stationary point found. [N(CH3)3(CH2CN)]+

Frequency Analysis of [N(CH3)3(CH2CN)]+ Log File Link - Figure 5.8 Summary Table Low Frequencies Low frequencies --- -2.6320 0.0003 0.0004 0.0005 7.1497 9.6684 Low frequencies --- 91.7740 154.0285 210.9274

Since the low frequencies are near zero and all convergence criteria has been met I can conclude that a minimum energy structure has been obtained.

MO and NBO Analysis

Charge Distribution of N(CH3)4+/[N(CH3)3(CH2OH)]+/[N(CH3)3(CH2CN)]+ - Table 1.8 Complex Charge on N Charge on C Charge on H Charge on O/H Charge on C/N N(CH3)4+ -0.295 -0.483 0.269 - - [N(CH3)3(CH2OH)]+ -0.322 -0.492(0.088) Variable -0.725/0.521 - [N(CH3)3(CH2CN)]+ -0.289 -0.489(-0.358) Variable - 0.209/-0.186

N.B: Charge in brackets refers to carbon attached to the OH/CN.

Charge Distribution Images of Substituted Onium Ions (NB. Red-Green refers to -0.725 and 0.725 respectively.) - Figure 5.9 N(CH3)4+ [N(CH3)3(CH2OH)]+ [N(CH3)3(CH2CN)]+ Log File Link Log File Link Log File Link

By changing the methyl group to an electron donating group to form [N(CH₃)₃(CH₂OH)]+, we have essentially increased the electron density at the nitrogen whereas by substituting the methyl group with an electron withdrawing group, the nitrogen becomes more electropositive compared to N(CH₃)₄⁺. However, making this deduction may not be conclusive as the charge distribution on the nitrogen in the 3 cases are very close to each other and as a result by just changing the method and basis set these increases and decreases in charge distribution at nitrogen when compared to N(CH₃)₄⁺ could switch for the substituted cations.

Firstly considering [N(CH₃)₃(CH₂OH)]+. Since oxygen is more electronegative than carbon it will be δ- compared to the carbon. This is reflected in a more positive charge distribution on the carbon (0.088) than on the oxygen (-0.725). This differs when considering [N(CH₃)₃(CH₂CN)]+, the carbon adjacent to the cyanide group becomes quite δ- compared to the same carbon in [N(CH₃)₃(CH₂OH)]+, because the carbon of the cyanide group is strongly δ+ due to the strong electronegativity of the nitrogen (in cyanide group). The electron density on the carbon will therefore have to be redistributed to the adjacent carbon which will therefore be more δ-.

The energies of the frontier orbitals was investigated and was found to have changed for each of these substituted cations.

Energies of LUMO and HOMO - Table 1.9 Complex Energies of HOMO (AU) Energy of LUMO (AU) HOMO-LUMO Gap N(CH3)4+ -0.57034 -0.13302 0.43732 [N(CH3)3(CH2OH)]+ -0.48763 -0.12459 0.36304 [N(CH3)3(CH2CN)]+ -0.50048 -0.18183 0.31865

As shown in the table above, the HOMO-LUMO gap has decreased in both instances (addition of electron donating and electron withdrawing substituents). This is because by adding an electron donating group you are increasing the ease at which electrons can be lost from the molecule and this has the effect of raising the HOMO. Conversely, upon addition of an electron withdrawing group, it becomes easier to add electrons to the molecule. This consequently lowers the energy of the LUMO. Therefore, overall it results in a reduction in the HOMO LUMO gap in both instances. This is reflected in the relative energies of the HOMO and LUMO in the substituted cations in comparison with the non-substituted cation. When considering the absolute energies of the HOMO and LUMO, it may not be useful to compare absolute values as the basis set and method used are not a high enough level of theory for meaningful deductions to be made. Therefore, it is just important to comment on the fact that in both cases where an electron donating and electron withdrawing group has been added the HOMO-LUMO gap has decreased. This may be purposely done to alter the chemical properties of these cations for applications as ionic liquids. It can also be noted, that the addition of an electron donating group could help to stabilize the positive charge that is formally on the nitrogen but in reality is delocalized across the molecule. This could help improve the lifetime of this cation and prevent reaction before its intended use as a component of an ionic liquid. It is also particularly important to note that the substituent will affect the ease at which the cation is formed in the first place. By placing an electron withdrawing group on the molecule, the the electron density is pulled away from the nitrogen lone pair which would result in a weaker N-H bond. This would therefore increase the ease at which the cation is formed by increasing the acidity of the hydrogen (attached to N). The opposite discussion applies for the electron donating group. It will also affect proton conductivity of the ionic liquid as the substituents will affect the proton accepting and donating ability of the respective ions.

The MOs generated by gaussian are essentially the total molecular density which is equivalent to the wavefunction squared. We can probe them to analyse the bonding and antibonding the characteristics of a molecule. We can use them as a tool to investigate the electronic interactions that are occurring within the molecule. By doing this computationally rather than in the lab is extremely powerful as the time it takes to run a calculation is usually faster than probing the electron density through x-ray diffraction or other spectroscopic techniques. Since molecular orbitals are made up of the atomic orbitals we usually estimate the the contribution from each atomic orbital, whether it be H₂ where the two AOs have the same orbital coefficients to HF where the orbital coefficients are quite different. In the MOs displayed in gaussian, these coefficients are computed more accurately depending on the basis set and method utilized.

Below we only consider the frontier orbitals and not all the molecular orbitals of the molecule as these are the most poignant MOs that are often the orbitals that interact, or the orbitals where electrons are removed or added.

Frontier Orbitals of N(CH3)4+/[N(CH3)3(CH2OH)]+/[N(CH3)3(CH2CN)]+ - Figure 6.0 LUMO Orbitals HOMO Orbitals The HOMO of N(CH3)4+ exhibits a larger and more uniform electron density cloud over the whole molecule. [N(CH3)3(CH2OH)]+ HOMO is less uniform and more skewed over to the oxygen which is electronegative in itself but inductively donates electron density towards the nitrogen therefore the lobes seems marginally larger than for the N(CH3)4+. Both the oxygen and the adjacent carbon are sp3 hybridized so we see some hybridized nature in the orbitals on the oxygen and carbon but in an antibonding fashion. The nitrogen is also electronegative and appears to pull the electron density away from the hydrogens and carbons on the left hand side. On the other hand the addition of a cyanide group (EWG) to form [N(CH3)3(CH2CN)]+ generates a HOMO that is also skewed, but now it seems as though the electron density is skewed to a larger degree towards the cyanide group. This is understandable because the cyanide group is electron withdrawing and will act to pull electron density away from other parts of the molecule. The LUMO of these 3 molecules also shows a change in the uniformity of the orbital. The N(CH3)4+ LUMO is quite symmetrical compared to the other two molecules as there are no additional substituents that are acting to change the electron density cloud in the molecule. The LUMO of [N(CH3)3(CH2OH)]+ seems to exhibit greater electron density around the oxygen whereas the LUMO of [N(CH3)3(CH2CN)]+ seems to show the electron density mostly on the nitrogen. In general we can compare these more complex molecular orbitals to the molecular orbitals of the individual components. The cyanide group exhibits the molecular orbitals given below. This is somewhat reflected in the MOs of [N(CH3)3(CH2CN)]+ as there is an observed π orbital with a nearby antibonding component contributed by the methylene group.

Molecular Orbital Diagram of CN-

It is interesting to take cross sections of the LUMO orbitals as it is evident that there are molecular orbitals that are not as discernable in the images above. To be able to visualize the inner orbitals, it is useful to utilize these cross sections.

Cross sections of Molecular Orbitals - Figure 6.1 LUMO Orbital of N(CH3)4+ LUMO Orbital of [N(CH3)3(CH2CN)]+ From the LUMO of the N(CH3)4+ we can see concentric orbitals showing the 1s and 2s orbitals of the nitrogen which we do not normally draw when we draw out MOs by hand but by utilizing computational power it is extremely useful to be able to see these molecular orbitals in its entirety without having to employ spectroscopy to observe the orbitals. There is therefore an inner cavity that is actually a nodal surface that is at the interface of a green s orbital with The cross section of the LUMO of [N(CH3)3(CH2CN)]+ shows a similar inner 1s orbital of the nitrogen however, the 2s orbital seems to have merged with the orbitals of carbons nearby to form one delocalized molecular orbital that spreads over the entire molecule. It is also easier to observe the π*-like component of the CΞN Bond.