ChemWiki - User contributions [en]

Rep:Mod:Inorganic mm1517

2019-05-24T14:55:59Z

Mm1517: /* Summary Table */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2' '
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2' ' symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

Energy of NH3 at 6-31G basis set = -148492 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

Energy of NH3-BH3 at 6-31G basis set = -218506 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

Energy of NI3 at GEN basis set = -233167 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

Energy of [N(CH3)4]+ at 6-31G basis set = -562333 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

Energy of [P(CH3)4]+ at 6-31G basis set = -1314921 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:54:27Z

Mm1517: /* Summary Table */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2' '
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2' ' symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

Energy of NH3 at 6-31G basis set = -148492 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

Energy of NH3-BH3 at 6-31G basis set = -218506 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

Energy of NI3 at GEN basis set = -233167 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

Energy of [N(CH3)4]+ at 6-31G basis set = -562333 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:54:01Z

Mm1517: /* Summary Table */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2' '
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2' ' symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

Energy of NH3 at 6-31G basis set = -148492 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

Energy of NH3-BH3 at 6-31G basis set = -218506 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

Energy of NI3 at 6-31G basis set = -233167 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

Energy of [N(CH3)4]+ at 6-31G basis set = -562333 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:52:14Z

Mm1517: /* Summary Table */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2' '
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2' ' symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

Energy of NH3 at 6-31G basis set = -148492 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

Energy of NH3-BH3 at 6-31G basis set = -218506 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

Energy of NI3 at 6-31G basis set = -233167 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:50:55Z

Mm1517: /* Summary Table */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2' '
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2' ' symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

Energy of NH3 at 6-31G basis set = -148492 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

Energy of NH3-BH3 at 6-31G basis set = -218506 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:50:05Z

Mm1517: /* Summary Table */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2' '
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2' ' symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

Energy of NH3 at 6-31G basis set = -148492 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:48:27Z

Mm1517: /* Vibrational Spectrum */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2' '
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2' ' symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:47:57Z

Mm1517: /* Vibrational Spectrum */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2' '
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:47:42Z

Mm1517: /* Vibrational Spectrum */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|1214
|14
|E'
|Very slight
|In-plane bend
|-
|2580
|0
|A1'
|No
|Totally symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:41:51Z

Mm1517: /* LCAOs of 3 occupied valence MOs of [N(CH3)4]+ */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

The ligand FO consists of entirely s-orbitals, 2s on the carbon and 1s on the hydrogens. As they are all in phase, the interactions between them is purely bonding. In turn, the nitrogen FO is a 2s orbital, which is the same phase as the ligand FO. The resultant molecule MO has purely bonding interactions between same phase orbitals, therefore is bonding and is very low in energy. No nodal plane is seen.

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

As in the previous ligand FO, the 2s carbon orbital and the 1s hydrogen orbitals are all in phase, so have solely bonding interactions. However, despite the nitrogen FO also being a 2s orbital as before, it is now in opposite phase to the ligand FO. The final molecule MO therefore now has anti bonding interactions between the nitrogen and ligand FOs, as well as the bonding interactions both in the FOs and through space bonding interactions between the ligand FOs. The bonding interactions outweigh the anti bonding interactions son this molecule MO is overall bonding. No nodal plane is observed.

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

The nitrogen FO involved is now a 2p orbital. The ligand FOs adjacent to the nitrogen 2p lobes are in phase with it. Therefore there is both bonding interactions in the ligand FO, and a very strong bonding interaction between the ligand FO and the in-phase nitrogen 2p orbital. There is also weak bonding interactions between the two in-phase ligand FOs through space. An anti bonding bonding interaction exists in the molecule MO between the out of phase ligand FOs on opposite sides of the molecule. A nodal plane is observed in this MO. As there are no nodal planes seen along bonds, the bonding interactions are much stronger than the through space anti bonding interactions. To conclude, this MO is overall bonding.

Rep:Mod:Inorganic mm1517

2019-05-24T14:15:13Z

Mm1517: /* Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+ */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei. However in reality, the positive charges are infact located on the hydrogens, with the nitrogen having a negative charge. The charge range is small in [N(CH3)4]+, showing that the electronegativity difference is small between carbon and nitrogen, meaning the bond is less polar and is stronger.

However in [P(CH3)4]+ the charge range is much larger. This is because there is a larger electronegativity difference between phosphorus and carbon, hence the bond is more polar and is weaker. Additionally the phosphorus radii is much larger than the carbon radii, meaning the orbital sizes are mis-matched, so the orbital overlap is less efficient than the nitrogen carbon bond. Carbon has the more negative charge as it has a higher electronegative than the phosphorus, resulting in phosphorus having a positive charge.

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T14:05:53Z

Mm1517: /* Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+ */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

The nitrogen in [N(CH3)4]+ has a more positive charge than the carbons, despite being more electronegative. This is because in order to form the 4th bond, the nitrogen has used its lone pair of electrons, thus creating the formal charge of +1. The formal charge is the charge that would occur if the electrons were shared evenly between nuclei.

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:46:09Z

Mm1517: /* NI3 */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

Iodine has a significantly larger radii than nitrogen, as it is low down in Group 7. Therefore due to their mis-matched orbital sizes, the orbital overlap is inefficient, meaning the N-I bond distance increases and the strength of the bond weakens.

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:43:34Z

Mm1517: /* [P(CH3)4]+ */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:43:17Z

Mm1517: /* [N(CH3)4]+ */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:42:44Z

Mm1517: /* NI3 */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Method: B3LYP

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:42:26Z

Mm1517: /* NH3-BH3 */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:42:06Z

Mm1517: /* NH3 */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP

Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:41:56Z

Mm1517: /* NH3 */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

Method: B3LYP
Basis set: 6-31G

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:41:33Z

Mm1517: /* 6-31G Basis Set */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:41:21Z

Mm1517: /* 3-21G Basis Set */

== BH3 ==

=== 3-21G Basis Set ===

Method: B3LYP

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:40:27Z

Mm1517: /* Calculation of Association Energy */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1 [1]

[1] - J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:39:22Z

Mm1517: /* Calculation of Association Energy */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

The B-N bond in ammonia borane is dative, with the nitrogen donating a lone pair of electrons to the electron deficient boron atom. Due to the large electronegativity difference between boron and nitrogen, the assumption that the bond has ionic character can be made. -135 kJmol-1 is a moderately weak bond when compared to a C-C bond in isoelectronic ethane, which has an association energy of about 350 kJmol-1.

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:29:17Z

Mm1517: /* Frequency */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm NI3 freq.PNG]]

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

File:Mm NI3 freq.PNG

2019-05-24T13:28:54Z

Mm1517:

Rep:Mod:Inorganic mm1517

2019-05-24T13:22:11Z

Mm1517: /* Jmol Dynamic Image */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents><script>frame 1.13</script>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:18:09Z

Mm1517: /* Jmol Dynamic Image */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [P(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:17:43Z

Mm1517: /* Ionic Liquids */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

Frequency file: [[Media: MM P4 FREQ.LOG|MM P4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM P4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

File:MM P4 FREQ.LOG

2019-05-24T13:16:38Z

Mm1517:

Rep:Mod:Inorganic mm1517

2019-05-24T13:16:28Z

Mm1517: /* Frequency */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised [N(CH3)4]+ at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM N4 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:15:30Z

Mm1517: /* Frequency */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

Frequency file: [[Media: MM N4 FREQ.LOG|MM N4 FREQ.LOG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

File:MM N4 FREQ.LOG

2019-05-24T13:15:02Z

Mm1517:

Rep:Mod:Inorganic mm1517

2019-05-24T13:14:12Z

Mm1517: /* Frequency Analysis */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies in the summary table and the frequency analysis table are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:13:48Z

Mm1517: /* Frequency Analysis */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0249 -0.0032 -0.0005 17.1466 17.1490 37.2133
Low frequencies --- 265.8038 632.2133 639.3565
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:12:55Z

Mm1517: /* Frequency Analysis */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:12:06Z

Mm1517: /* Summary Table */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000569 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:11:16Z

Mm1517: /* Optimisation Table */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:10:26Z

Mm1517: /* Summary Table */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Optimisation Table ====

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:09:23Z

Mm1517: /* Association Energies */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:09:03Z

Mm1517: /* Frequency Analysis */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3-BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:08:07Z

Mm1517: /* Frequency Analysis */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:07:35Z

Mm1517: /* NH3 */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

<jmol><jmolApplet>
<title>Optimised NH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents> MM NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:06:23Z

Mm1517: /* Frequency Analysis */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

Frequency file: [[Media:MM NH3BH3 FREQ.LOG|MM NH3BH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

File:MM NH3BH3 FREQ.LOG

2019-05-24T13:05:51Z

Mm1517:

Rep:Mod:Inorganic mm1517

2019-05-24T13:05:27Z

Mm1517: /* Frequency Analysis */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T13:05:10Z

Mm1517: /* Frequency Analysis */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

Frequency file - [[Media: File:MM NH3 FREQ.LOG|File:MM NH3 FREQ.LOG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

File:MM NH3 FREQ.LOG

2019-05-24T13:04:11Z

Mm1517:

Rep:Mod:Inorganic mm1517

2019-05-24T12:57:58Z

Mm1517: /* Frequency */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T12:56:07Z

Mm1517: /* Calculation of Association Energy */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135 kJmol-1

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]

Rep:Mod:Inorganic mm1517

2019-05-24T12:53:40Z

Mm1517: /* MO Diagram */

== BH3 ==

=== 3-21G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 321g.PNG]]

The optimisation was successful, as the gradient is below 0.001. However, the point group was not as expected, it is Cs instead of D3h. Very small differences in the x, y and z coordinates result in a breakage of symmetry causing the incorrect point group. Additionally, Gaussian requires incredibly accurate numbers to get the precise symmetry of the molecule, something not achieved by merely building the molecule and running a basic optimisation.

Energy of BH3 at 3-21G basis set = -69477 kJmol-1

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

The table shows that the forces and displacements have successfully converged, so the optimisation is complete. This also informs us that the placements have converged, meaning that for a small displacement the energy remains unchanged.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 3-21G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 321G.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== 6-31G Basis Set ===

==== Summary table ====

[[File:Mm bh3 opt photo 631g.PNG]]

The optimisation was successful due to the gradient value being lower than 0.001. However, like the basis set 3-21G, the point group is Cs instead of D3h. The cause of this is the same for both basis sets, that differences inn the x, y and z coordinates result inn a breakage of symmetry, leading to an incorrect point group assignment.

Energy of BH3 at 6-31G basis set = -69879 kJmol-1

The energy of BH3 at 6-31G basis set cannot be compared to that of 3-21G, as they are in different basis sets.

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000653 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Both the force and displacement successfully converged, providing further evidence that the optimisation went to completion.

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised BH3 at 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM BH3 OPT 631g.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Frequency ====

Frequency file: [[Media:MM BH3 FREQ 631G.LOG| MM BH3 FREQ 631G.LOG]]

==== Vibrational Spectrum ====

<pre>
Low frequencies --- -0.1187 -0.0049 -0.0012 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry || IR active? || Type
|-
|1164
|93
|A2''
|Yes
|Out-of-plane bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|1214
|14
|E'
|Very slight
|Bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|-
|2713
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Mm bh3 freq spectrum 631g.PNG]]

6 vibrational frequecies are reported in the Gaussian file, however only 3 vibrations are observed on the graph. The peak at 1164 cm-1 corresponds to the A2 symmetry, which has a high intensity resulting in the tall height of the peak, and is IR-active so is seen. The two E' bends seen at 1214 cm-1 are degenerate, so are seen as a single peak with low intensity. However the A1' stretch at 2580 cm-1 is not observed. As this stretch is symmetric, there is no change in dipole moment and thus it is not IR active, so is not observed on the spectrum. Finally, the two E' asymmetric stretches at 2713 cm-1 are degenerate, so are seen as a single peak of high intensity.

==== Frequency Summary Table ====

[[File:Mm bh3 freq 631g photo.PNG]]

Frequency analysis is reliable and has gone to completion, as the gradient is lower than 0.001. In order to do the frequency analysis, the point group had to be changed from Cs to D3h, which was done by constraining the symmetry to D3h and re-running the optimisation.

==== MO Diagram ====

[[File:Mm bh3 MO diagram.PNG]]

This diagram was taken from Professor Hunts Lecture 4 Tutorial Problem Model Answers.

Link: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

== Association Energies ==

The energy of optimised BH3 at 6-31G was found to be -69879 kJmol-1
In order to compute a reaction energy, the energies of NH3 and NH3-BH3 are additionally required.

INCLUDE FREQUENCY FILE

=== NH3 ===

==== Summary Table ====

[[File:Mm nh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3 freq.PNG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== NH3-BH3===

==== Summary Table ====

[[File:Mm nh3bh3 opt.PNG]]

==== Frequency Analysis ====

[[File:Mm nh3bh3 freq.PNG]]

As the energies are identical up to the final 2 decimal places, it is confirmed that the minimum was found.

=== Calculation of Association Energy ===

E(BH3) = -26.61532350 a.u.

E(NH3) = -56.55776873 a.u.

E(NH3BH3) = -83.22468891 a.u.

ΔE = E(NH3BH3) - [E(NH3) + E(NB3)] = -0.05159668 a.u. = -135.4670833 kJmol-1

CHECK HOW MANY SIG FIG

state whether the dative B-N bond is strong or weak, and how you figured this out

== NI3 ==

Basis set: GEN

Optimised N-I distance = 2.183 Å

==== Summary Table ====

[[File:Mm NI3 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000062 0.000300 YES
Maximum Displacement 0.001258 0.001800 YES
RMS Displacement 0.000609 0.001200 YES
</pre>

==== Frequency ====

<pre>
Low frequencies --- -1.7762 -1.7378 -0.7562 -0.0031 0.0322 0.0731
Low frequencies --- 101.3566 101.3572 148.4310
</pre>

Frequency file: [[Media:MM NI3 OPT 3.LOG.LOG| MM NI3 OPT 3.LOG]]

==== Jmol Dynamic Image ====

<jmol><jmolApplet>
<title>Optimised NI3 at GEN</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>MM NI3 OPT 3.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Ionic Liquids ==

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

==== Summary Table ====

[[File:Mm n4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000212 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm n4 freq.PNG]]

<pre>
Low frequencies --- 0.0013 0.0013 0.0014 21.4206 21.4206 21.4206
Low frequencies --- 188.2035 292.4104 292.4104
</pre>

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

==== Summary Table ====

[[File:Mm p4 opt.PNG]]

==== Optimisation Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000147 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
</pre>

==== Frequency ====

[[File:Mm p4 freq.PNG]]

<pre>
Low frequencies --- 0.0030 0.0039 0.0040 24.0415 24.0415 24.0415
Low frequencies --- 159.9379 194.7249 194.7249
</pre>

=== Charge Comparison of [N(CH3)4]+ and [P(CH3)4]+===

Colour range used = -1.667 to 1.667

[[File:Mm charge 1.PNG]]

The molecule on the left shows the charge distribution for [N(CH3)4]+ and on the right [P(CH3)4]+.

<pre>
Central Atom Carbon Hydrogen
Charges on [N(CH3)4]+ -0.295 -0.483 0.269
Charges on [P(CH3)4]+ 1.667 -1.060 0.298
</pre>

SEE QUESTIONS ON MO TO ANSWER
larger electronegativity difference between atoms, the more polarised the bond, and it is hence weaker.
additionally P has a larger radii than N, therefore the orbital overlap between P-C will be less efficient, making the bond weaker

=== LCAOs of 3 occupied valence MOs of [N(CH3)4]+ ===

[[File:Mm MO1.PNG|350px]] [[File:Mm MO1 L.PNG|350px]]

[[File:Mm MO2.PNG]] [[File:Mm MO2 L.PNG|300px]]

[[File:Mm MO3.PNG]] [[File:Mm MO3 L.PNG|350px]]