=='''BH3'''==

==== ''Link to the BH3 log file'' ====

[[File:FP2_BH3_FREQ.LOG]]

==== ''Method and Basis set'' ====

Method: B3LYP
Basis Set: 6-31G

==== ''Optimisation of the BH3 molecule''====

The BH3 summary file showing the optimisation of the molecule delivering D3h point group:

[[File:Bh3summary3817.PNG]]

The Item table section of the summary file showing that the calculation has converged:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.914919D-10
Optimization completed.
-- Stationary point found.

</pre>

==== ''Frequency Analysis of BH3'' ====

<pre>
Low frequencies --- -0.9385 -0.8438 -0.0054 5.8634 11.7841 11.8214

Low frequencies --- 1162.9968 1213.1829 1213.1856
</pre>

A frequency table to show the vibrational frequencies of the vibrational modes of the BH3 molecule:

[[File:Freqtable23817.PNG]]

==== ''Jmol of BH3 Molecule'' ====

<jmol><jmolApplet>
<title> BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FP2_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''BH3 IR spectrum'' ====

The IR spectrum of the optimised BH3 moleucle

[[File:IRspectra3817.PNG]]

In the IR there are fewer than 6 peaks, despite there being 6 vibrations as there are two doubly degenerate vibrations. These are the two bends at 1213.18 and the two asymmetric stretches at 2715.44. As a result, these four vibrations only result in 2 peaks. In addition, the symmetrical vibration mode at 2582.27 cm-1 does not lead to an overall change in dipole of the molecule and hence is not observed in the spectrum.

==== ''The Molecular Orbital Diagram of BH3'' ====

An annotated Molecular Orbital Diagram for the BH3 molecule, modified from: Hunt, P 2018, Molecular Orbitals Problem Class One Answers (Lecture Notes), Imperial College London, delivered 2018.
The diagram includes snapshots of the real MOs next to the LCAOs predicted from a qualitative combination of fragment orbitals.

[[File:Modiagram_BH3817.PNG]]

Questions relating to the orbital diagram above:

1. Are there any significant differences between the real and LCAO MOs?

The LCAO orbitals qualitatively determined in the diagram result in MOs that have localised orbitals on each atom simply combined. The reality is that the orbitals are much more diffuse in nature and occupy larger regions of space, spanning multiple atoms. As a result our 'paper method' LCAO gives slightly misleading representation of the electron density distribution in the molecule. In addition, the LCAO can also give incorrect energy orderings of the orbitals, however, in this case the ordering appears to be correct as we are dealing with a relatively simple molecule with a few atomic orbitals.

2. What does this say about the accuracy and usefulness of qualitative MO theory?

Molecular Orbital theory is a valid simple alternative to Valence Bond Theory, which simply predicts electrons localised between two bonds, instead of the reality of more diffuse orbitals predicted by the Schrodinger Equation. As mentioned above, the energy orderings here are correct, specifically and most importantly, the positioning and orbital type of the HOMO/LUMO region and as such qualitative MO theory appears to correctly predict energy levels in this case. However, as previously mentioned, as the complexity of the molecular increases, its usefulness may be impaired.

=='''Association Energy Calculation from Total Energies of Ammonia and Borane'''==

==== ''Link to the NH3 file'' ====

[[File:FP_NH3_FREQ3131.LOG]]

==== ''NH3 optimisation'' ====

Method: B3LYP/6-31G

Table showing the NH3 Optimisation and confirming symmetry point group as C3v:

[[File:Nh3freqtab3817.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== ''NH3 Frequency Analysis'' ====

<pre>

Low frequencies --- -11.6527 -11.6490 -0.0041 0.0333 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736

</pre>

==== ''NH3 Jmol file'' ====

<jmol><jmolApplet>
<title> BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FP_NH3_FREQ3131.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''Link to the NH3BH3 Log file'' ====

[[File:FP_NH3BH3_FREQ.LOG]]

==== ''NH3BH3 Optimisation'' ====
B3LYP/6-31G Level

[[File:Nh3bh3_opttable3817.PNG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000132 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000391 0.001200 YES
Predicted change in Energy=-2.114129D-07
Optimization completed.
-- Stationary point found.

</pre>

==== ''NH3BH3 Frequency Analysis'' ====

<pre>

Low frequencies --- -0.0570 -0.0490 -0.0073 10.1041 12.1139 14.5392

Low frequencies --- 265.8927 632.3719 640.1156

</pre>

==== ''NH3BH3 Jmol file'' ====

<jmol><jmolApplet>
<title> BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FP_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''Association Energy Calculation'' ====

From the 6-31G optimised structures:

E(BH3): -26.62523

E(NH3): -56.55776

E(BH3NH3): -83.22469

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE = -83.22469-(-56.55776-26.62523) AU

ΔE= -0.05106 AU

Thus ΔE = -135 kJ/mol

Is the B-N bond weak, medium or strong? What comparison have you made to come to this conclusion?

This dative covalent bond is relatively weak (-135 kJ/mol). The classification of bond strength can be clarified when you consider it in relation to other bonds, such as in comparison with other stronger bonds such as is C-C carbon bonds. The bond energy of these bonds is -346 kJ/mol. In addition, a more comparable bond strength is that of C-N (-305 kJ/mol) This is an example of a non-dative covalent bond involving the same atom, N. As a result, it can be concluded that dative covalent bonds, such as that calcualted for the above compound, are much weaker than non-dative bonds involving the same atoms. (Data from J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

=='''Using Basis Sets and Pseudo-Potentials for NI3'''==

==== ''Link to the NI3 log file'' ====

[[File:FP_NI3_FREQ1.LOG]]

==== ''Optimisation and Frequency Analysis of NI3'' ====

Method: B3LYP
Basis set: GEN

[[File:Ni3summ3817.PNG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.193442D-07
Optimization completed.
-- Stationary point found.

</pre>

<pre>

Low frequencies --- -12.3844 -12.3780 -5.6127 -0.0040 0.0194 0.0711
Low frequencies --- 100.9306 100.9314 147.2332

</pre>

==='' Jmol file''===

<jmol><jmolApplet>
<title> NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FP_NI3_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''The Optimised N-I Bond Distance'' ====

The optimised N-I distance: 2.184 Angstroms (3dp)

=='''Project: Ionic Liquids as Designer Solvents'''==

==== ''Optimisation and Frequency Analysis of [N(CH3)4]+'' ====

===== ''Link to the [N(CH3)4]+ Log file'' =====
[[File:N(CH3)4_FREQ3817.LOG]]

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

Method: B3LYP

Basis Set: 6-31G

[[File:Nch34freqtable3817.PNG]]

Item tableː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000079 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001538 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-9.571933D-08
Optimization completed.
-- Stationary point found.

</pre>

Low Frequenciesː

<pre >

Low frequencies --- 0.0009 0.0011 0.0011 34.9215 34.9215 34.9215
Low frequencies --- 218.3774 317.2079 317.2079

</pre>

Jmolː

<jmol><jmolApplet>
<title> NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>N(CH3)4_FREQ3817.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''Optimisation and Frequency Analysis of [P(CH3)4]+'' ====

===== ''Link to the [P(CH3)4]+ Log file'' =====

[[File:P(CH3)4_OPT_FREQ3817.LOG]]

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

Method: B3LYP

Basis Set: 6-31G

Frequency Optimisation Summary Tableː

[[File:Freqtable3817.PNG]]

Item tableː

<pre>

Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000050 0.000300 YES
Maximum Displacement 0.001219 0.001800 YES
RMS Displacement 0.001065 0.001200 YES
Predicted change in Energy=-1.200686D-06
Optimization completed.
-- Stationary point found.

</pre>

Low Frequenciesː

<pre>

Low frequencies --- -0.0025 -0.0020 -0.0013 52.5253 52.5253 52.5253
Low frequencies --- 189.2279 213.8449 213.8449

</pre>

Jmolː

<jmol><jmolApplet>
<title> NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>P(CH3)4_OPT_FREQ3817.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== ''Charge Distribution Comparisons'' ===

Charge Distribution analysis was conducted colouring atoms by charge within the same colour rangeː -0.470 - 0.470. This was chosen as the same range for both molecules and the largest range that allowed a clear comparison of the charge distribution without making any of the atoms too dark. This charge distribution clearly shows the difference in charge distribution between having a nitrogen atom as a central atom or a P atom.

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

[[File:Nchargeanal3817.PNG]]

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

[[File:Pchargeanal3817.PNG]]

===== Charge Comparison Analysis =====

Summary and Comparison Tableː

Discussion of Lewis Structure Representationː

=== ''LCAO MO Diagrams'' ===

Molecular Orbital Analysis Tableː

[[File:Motable23817.PNG]]

File:MoTable23817.PNG

2019-05-23T14:31:50Z

Fp3817:

Fp3917

2019-05-23T14:30:30Z

Fp3817: /* Project: Ionic Liquids as Designer Solvents */

=='''BH3'''==

==== ''Link to the BH3 log file'' ====

[[File:FP2_BH3_FREQ.LOG]]

==== ''Method and Basis set'' ====

Method: B3LYP
Basis Set: 6-31G

==== ''Optimisation of the BH3 molecule''====

The BH3 summary file showing the optimisation of the molecule delivering D3h point group:

[[File:Bh3summary3817.PNG]]

The Item table section of the summary file showing that the calculation has converged:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.914919D-10
Optimization completed.
-- Stationary point found.

</pre>

==== ''Frequency Analysis of BH3'' ====

<pre>
Low frequencies --- -0.9385 -0.8438 -0.0054 5.8634 11.7841 11.8214

Low frequencies --- 1162.9968 1213.1829 1213.1856
</pre>

A frequency table to show the vibrational frequencies of the vibrational modes of the BH3 molecule:

[[File:Freqtable23817.PNG]]

==== ''Jmol of BH3 Molecule'' ====

<jmol><jmolApplet>
<title> BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FP2_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''BH3 IR spectrum'' ====

The IR spectrum of the optimised BH3 moleucle

[[File:IRspectra3817.PNG]]

In the IR there are fewer than 6 peaks, despite there being 6 vibrations as there are two doubly degenerate vibrations. These are the two bends at 1213.18 and the two asymmetric stretches at 2715.44. As a result, these four vibrations only result in 2 peaks. In addition, the symmetrical vibration mode at 2582.27 cm-1 does not lead to an overall change in dipole of the molecule and hence is not observed in the spectrum.

==== ''The Molecular Orbital Diagram of BH3'' ====

An annotated Molecular Orbital Diagram for the BH3 molecule, modified from: Hunt, P 2018, Molecular Orbitals Problem Class One Answers (Lecture Notes), Imperial College London, delivered 2018.
The diagram includes snapshots of the real MOs next to the LCAOs predicted from a qualitative combination of fragment orbitals.

[[File:Modiagram_BH3817.PNG]]

Questions relating to the orbital diagram above:

1. Are there any significant differences between the real and LCAO MOs?

The LCAO orbitals qualitatively determined in the diagram result in MOs that have localised orbitals on each atom simply combined. The reality is that the orbitals are much more diffuse in nature and occupy larger regions of space, spanning multiple atoms. As a result our 'paper method' LCAO gives slightly misleading representation of the electron density distribution in the molecule. In addition, the LCAO can also give incorrect energy orderings of the orbitals, however, in this case the ordering appears to be correct as we are dealing with a relatively simple molecule with a few atomic orbitals.

2. What does this say about the accuracy and usefulness of qualitative MO theory?

Molecular Orbital theory is a valid simple alternative to Valence Bond Theory, which simply predicts electrons localised between two bonds, instead of the reality of more diffuse orbitals predicted by the Schrodinger Equation. As mentioned above, the energy orderings here are correct, specifically and most importantly, the positioning and orbital type of the HOMO/LUMO region and as such qualitative MO theory appears to correctly predict energy levels in this case. However, as previously mentioned, as the complexity of the molecular increases, its usefulness may be impaired.

=='''Association Energy Calculation from Total Energies of Ammonia and Borane'''==

==== ''Link to the NH3 file'' ====

[[File:FP_NH3_FREQ3131.LOG]]

==== ''NH3 optimisation'' ====

Method: B3LYP/6-31G

Table showing the NH3 Optimisation and confirming symmetry point group as C3v:

[[File:Nh3freqtab3817.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== ''NH3 Frequency Analysis'' ====

<pre>

Low frequencies --- -11.6527 -11.6490 -0.0041 0.0333 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736

</pre>

==== ''NH3 Jmol file'' ====

<jmol><jmolApplet>
<title> BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FP_NH3_FREQ3131.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''Link to the NH3BH3 Log file'' ====

[[File:FP_NH3BH3_FREQ.LOG]]

==== ''NH3BH3 Optimisation'' ====
B3LYP/6-31G Level

[[File:Nh3bh3_opttable3817.PNG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000132 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000391 0.001200 YES
Predicted change in Energy=-2.114129D-07
Optimization completed.
-- Stationary point found.

</pre>

==== ''NH3BH3 Frequency Analysis'' ====

<pre>

Low frequencies --- -0.0570 -0.0490 -0.0073 10.1041 12.1139 14.5392

Low frequencies --- 265.8927 632.3719 640.1156

</pre>

==== ''NH3BH3 Jmol file'' ====

<jmol><jmolApplet>
<title> BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FP_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''Association Energy Calculation'' ====

From the 6-31G optimised structures:

E(BH3): -26.62523

E(NH3): -56.55776

E(BH3NH3): -83.22469

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE = -83.22469-(-56.55776-26.62523) AU

ΔE= -0.05106 AU

Thus ΔE = -135 kJ/mol

Is the B-N bond weak, medium or strong? What comparison have you made to come to this conclusion?

This dative covalent bond is relatively weak (-135 kJ/mol). The classification of bond strength can be clarified when you consider it in relation to other bonds, such as in comparison with other stronger bonds such as is C-C carbon bonds. The bond energy of these bonds is -346 kJ/mol. In addition, a more comparable bond strength is that of C-N (-305 kJ/mol) This is an example of a non-dative covalent bond involving the same atom, N. As a result, it can be concluded that dative covalent bonds, such as that calcualted for the above compound, are much weaker than non-dative bonds involving the same atoms. (Data from J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed. (1993).

=='''Using Basis Sets and Pseudo-Potentials for NI3'''==

==== ''Link to the NI3 log file'' ====

[[File:FP_NI3_FREQ1.LOG]]

==== ''Optimisation and Frequency Analysis of NI3'' ====

Method: B3LYP
Basis set: GEN

[[File:Ni3summ3817.PNG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.193442D-07
Optimization completed.
-- Stationary point found.

</pre>

<pre>

Low frequencies --- -12.3844 -12.3780 -5.6127 -0.0040 0.0194 0.0711
Low frequencies --- 100.9306 100.9314 147.2332

</pre>

==='' Jmol file''===

<jmol><jmolApplet>
<title> NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FP_NI3_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''The Optimised N-I Bond Distance'' ====

The optimised N-I distance: 2.184 Angstroms (3dp)

=='''Project: Ionic Liquids as Designer Solvents'''==

==== ''Optimisation and Frequency Analysis of [N(CH3)4]+'' ====

===== ''Link to the [N(CH3)4]+ Log file'' =====
[[File:N(CH3)4_FREQ3817.LOG]]

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

Method: B3LYP

Basis Set: 6-31G

[[File:Nch34freqtable3817.PNG]]

Item tableː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000079 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001538 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-9.571933D-08
Optimization completed.
-- Stationary point found.

</pre>

Low Frequenciesː

<pre >

Low frequencies --- 0.0009 0.0011 0.0011 34.9215 34.9215 34.9215
Low frequencies --- 218.3774 317.2079 317.2079

</pre>

Jmolː

<jmol><jmolApplet>
<title> NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>N(CH3)4_FREQ3817.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== ''Optimisation and Frequency Analysis of [P(CH3)4]+'' ====

===== ''Link to the [P(CH3)4]+ Log file'' =====

[[File:P(CH3)4_OPT_FREQ3817.LOG]]

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

Method: B3LYP

Basis Set: 6-31G

Frequency Optimisation Summary Tableː

[[File:Freqtable3817.PNG]]

Item tableː

<pre>

Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000050 0.000300 YES
Maximum Displacement 0.001219 0.001800 YES
RMS Displacement 0.001065 0.001200 YES
Predicted change in Energy=-1.200686D-06
Optimization completed.
-- Stationary point found.

</pre>

Low Frequenciesː

<pre>

Low frequencies --- -0.0025 -0.0020 -0.0013 52.5253 52.5253 52.5253
Low frequencies --- 189.2279 213.8449 213.8449

</pre>

Jmolː

<jmol><jmolApplet>
<title> NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>P(CH3)4_OPT_FREQ3817.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== ''Charge Distribution Comparisons'' ===

Charge Distribution analysis was conducted colouring atoms by charge within the same colour rangeː -0.470 - 0.470. This was chosen as the same range for both molecules and the largest range that allowed a clear comparison of the charge distribution without making any of the atoms too dark. This charge distribution clearly shows the difference in charge distribution between having a nitrogen atom as a central atom or a P atom.

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

[[File:Nchargeanal3817.PNG]]

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

[[File:Pchargeanal3817.PNG]]

===== Charge Comparison Analysis =====

Summary and Comparison Tableː

Discussion of Lewis Structure Representationː

=== ''LCAO MO Diagrams'' ===

Molecular Orbital Analysis Tableː

[[File:Motable3817.PNG]]

Fp3917

2019-05-23T09:34:02Z

Fp3817: /* Association Energy Calculation */

Fp3917

2019-05-21T17:19:46Z

Fp3817: /* Association Energy Calculation */

Fp3917

2019-05-21T17:19:38Z

Fp3817: /* Association Energy Calculation */