ChemWiki - User contributions [en]

IO:jh3416

2019-05-17T16:32:38Z

Jh3416: /* [P(CH3)4]+ */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

==BH3 Molecular Orbitals==

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a resemblance to the computed orbitals, as it can be seen the nodes are displayed in the same regions. The computed MO's show a more accurate picture in that the in-phase MO's are merged and the gaps present in the LCAO representation are not observed. Another notable difference can be seen in the 3a1' orbital, where the orbital coefficients are notably larger on the central atom in the LCAO representation. Hence the LCAO description is insufficient to accurately describe orbital coefficients and energy ordering, however it is useful for depicting the general shape and rough energy ordering of MO's.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

[[File:NR4_jh.PNG|thumb|center|400px]]

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:jh_MO21.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:jh_MO16.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:jh_MO7.PNG|400px]]

<references>

IO:jh3416

2019-05-17T16:32:08Z

Jh3416: /* BH3 Molecular Orbitals */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

==BH3 Molecular Orbitals==

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a resemblance to the computed orbitals, as it can be seen the nodes are displayed in the same regions. The computed MO's show a more accurate picture in that the in-phase MO's are merged and the gaps present in the LCAO representation are not observed. Another notable difference can be seen in the 3a1' orbital, where the orbital coefficients are notably larger on the central atom in the LCAO representation. Hence the LCAO description is insufficient to accurately describe orbital coefficients and energy ordering, however it is useful for depicting the general shape and rough energy ordering of MO's.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

[[File:NR4_jh.PNG|thumb|center|400px]]

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:jh_MO21.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:jh_MO16.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:jh_MO7.PNG|400px]]

<references>

IO:jh3416

2019-05-17T16:31:53Z

Jh3416: /* BH3 Molecular Orbitals */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

==BH3 Molecular Orbitals==

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a resemblance to the computed orbitals, as it can be seen the nodes are displayed in the same regions. The computed MO's show a more accurate picture in that the in-phase MO's are merged and the gaps present in the LCAO representation are not observed. Another notable difference can be seen in the 3a1' orbital, where the orbital coefficients are notably larger on the central atom in the LCAO representation. Hence the LCAO description is insufficient to accurately describe orbital coefficients and energy ordering, however it is useful for depicting the general shape and rough energy ordering of MO's.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

[[File:NR4_jh.PNG|thumb|center|400px]]

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:jh_MO21.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:jh_MO16.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:jh_MO7.PNG|400px]]

<references>

IO:jh3416

2019-05-17T16:25:39Z

Jh3416: /* MOS */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===BH3 Molecular Orbitals===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

[[File:NR4_jh.PNG|thumb|center|400px]]

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:jh_MO21.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:jh_MO16.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:jh_MO7.PNG|400px]]

<references>

IO:jh3416

2019-05-17T16:25:16Z

Jh3416: /* Charge Distribution */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

[[File:NR4_jh.PNG|thumb|center|400px]]

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:jh_MO21.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:jh_MO16.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:jh_MO7.PNG|400px]]

<references>

File:NR4 jh.PNG

2019-05-17T16:23:21Z

Jh3416:

IO:jh3416

2019-05-17T16:23:07Z

Jh3416: /* Charge Distribution */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

[[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:jh_MO21.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:jh_MO16.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:jh_MO7.PNG|400px]]

<references>

IO:jh3416

2019-05-17T16:22:24Z

Jh3416: /* [N(CH3)4]+ MO Analysis */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:jh_MO21.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:jh_MO16.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:jh_MO7.PNG|400px]]

<references>

File:Jh MO7.PNG

2019-05-17T16:20:23Z

Jh3416:

File:Jh MO16.PNG

2019-05-17T16:20:11Z

Jh3416:

File:Jh MO21.PNG

2019-05-17T16:19:57Z

Jh3416: Jh3416 uploaded a new version of File:Jh MO21.PNG

File:Jh MO21.PNG

2019-05-17T16:19:05Z

Jh3416: Jh3416 uploaded a new version of File:Jh MO21.PNG

File:MO 16jh3416.PNG

2019-05-17T16:15:53Z

Jh3416: Jh3416 uploaded a new version of File:MO 16jh3416.PNG

File:Jh MO21.PNG

2019-05-17T16:15:22Z

Jh3416:

IO:jh3416

2019-05-17T16:14:12Z

Jh3416: /* MO Analysis */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:MO_16jh3416.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:MO_7jh3416.PNG|400px]]

<references>

IO:jh3416

2019-05-17T16:12:34Z

Jh3416: Cha

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

='''Discussion'''=

==Charge Distribution==

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|Charge Distribution for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500[red] to +0.500{green}). Values: P = +1.568, C = -1.058/-1.060, H = +0.298]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|Charge Distribution for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> (scale -0.500{red} to +0.500{green}). Valuesː N = -0.295, C = -0.483, H=+0.269.]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:

'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==MO Analysis==

The Molecular Orbitals for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> were then computed. Of these, three occupied MO's were analysed further and a corresponding LCAO MO depiction was formed.

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:MO_16jh3416.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:MO_7jh3416.PNG|400px]]

<references>

IO:jh3416

2019-05-17T16:01:40Z

Jh3416: /* Charge Distribution */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

=Discussion=

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

[[File:PMe4_Charge_Dis_jh3416.PNG|thumb|left|400px|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>]] [[File:NMe4_Charge_Dis_jh3416.PNG|thumb|400px|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>]]

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

=='''MO Analysis'''==

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:MO_16jh3416.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:MO_7jh3416.PNG|400px]]

<references>

IO:jh3416

2019-05-17T15:56:20Z

Jh3416: /* Charge Distribution */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

=Discussion=

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''

[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]

'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]

Valuesː N -0.295, C -0.483, H=+0.269.

Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

=='''MO Analysis'''==

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:MO_16jh3416.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:MO_7jh3416.PNG|400px]]

<references>

IO:jh3416

2019-05-17T15:54:26Z

Jh3416: /* Discussion */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

=Discussion=

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

=='''MO Analysis'''==

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:MO_16jh3416.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:MO_7jh3416.PNG|400px]]

<references>

IO:jh3416

2019-05-17T15:54:04Z

Jh3416: /* MO Analysis */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

=='''MO Analysis'''==

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:MO_16jh3416.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:MO_7jh3416.PNG|400px]]

<references>

IO:jh3416

2019-05-17T15:53:42Z

Jh3416: /* MO Analysis */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]] [[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]] [[File:MO_16jh3416.PNG|400px]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]] [[File:MO_7jh3416.PNG|400px]]

<references>

IO:jh3416

2019-05-17T15:51:56Z

Jh3416: /* NI3 */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

==NI<sub>3</sub>==

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

<references>

IO:jh3416

2019-05-17T15:51:14Z

Jh3416: /* NH3 */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

=='''NH<sub>3</sub>'''==

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

<references>

IO:jh3416

2019-05-17T15:50:35Z

Jh3416: /* Additional BH3 */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

==Additional BH3==

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

<references>

IO:jh3416

2019-05-17T15:50:00Z

Jh3416: /* Basis Sets and Pseudo-Potentials */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.18936 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

<references>

IO:jh3416

2019-05-17T15:49:18Z

Jh3416: /* Basis Sets and Pseudo-Potentials */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

==='''Optimisation'''===

'''Nitrogen atom:''' 6-31G(d,p) basis set

'''2 x Iodine atoms:''' LanL2DZ psuedo potential

[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

<references>

IO:jh3416

2019-05-17T15:47:45Z

Jh3416:

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.

<ref name="MO">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

<references>

IO:jh3416

2019-05-17T15:45:30Z

Jh3416:

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name="Bonds"> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name="HBo"> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="EXP"> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

<references>

IO:jh3416

2019-05-17T15:42:18Z

Jh3416: /* Charge Distribution */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name=”Bond”> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name=”HB”> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name=”XP”> Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).</ref>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T15:39:34Z

Jh3416: /* BH3 */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name=”Bond”> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name=”HB”> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T15:39:23Z

Jh3416:

==BH3==
<ref name="EN">Alfred, A. 1961, Inorg. Nucl. Chem. 1961, 17, 215</ref>
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol)and Hydrazine N-N (297kj/mol)<ref name=”Bond”> Stevenson, D. P. The Strengths of Chemical Bonds. J. Am. Chem. Soc. 77, 2350 (1955).</ref>, but stronger than intermolecular Hydrogen bonding (approx 7kj/mol)<ref name=”HB”> Markovitch, O. & Agmon, N. Structure and Energetics of the Hydronium Hydration Shells. J. Phys. Chem. A 111, 2253–2256 (2007).</ref>; it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

Notably the Hydrogen charge distribution in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+ and [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+, 0.298 and 0.269 respectively, contradicts the typical valence bond treatment which would predict the hydrogens attached to the more electron deficient carbon atom would themselves be more electron deficient. The opposite is seen to be true in this case.

According to Valence Bond Theory, [NR<sub>4</sub>]<sup>[+]</sup> is conventionally displayed with a formal positive charge of +1 on the nitrogen atom to achieve a stable octet. This is calculated according to the following formula:
'''Formal charge = no. of valence e- - [ no. of e- in lone pairs + 1/2{no. of bonding e-}]'''
= 5 - (0 + ½(8)) = +1

This contradicts the data above, which shows nitrogen bearing a non-integer negative value for its relative charge. This highlights the limitations of valence bond theory in comparison to Molecular Orbital Theory in describing bonding in molecules.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:35:14Z

Jh3416: /* Association Energies */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

==='''NH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

==='''NH<sub>3</sub>BH<sub>3</sub>'''===

<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''Calculating the B-N Association Energy'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

The B-N dative bond is weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol), but stronger than intermolecular Hydrogen bonding (approx 7kj/mol); it is therefore reasonable to describe the bond as being of medium strength.

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:27:25Z

Jh3416: /* Association Energies */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH<sub>3</sub>'''

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''NH<sub>3</sub>BH<sub>3</sub>'''

B3LYP/6-31G(d,p) level

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:26:08Z

Jh3416: /* Association Energies */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

B3LYP/6-31G(d,p) level

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:24:59Z

Jh3416: /* BH3 */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

B3LYP/6-31G(d,p) level

[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:24:08Z

Jh3416: /* Discussion */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

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

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon because in this case the carbon atom is drawing most of the electron density.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:20:57Z

Jh3416: /* Discussion */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

==='''MO Analysis'''===

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:19:31Z

Jh3416: /* [N(Ch3)4]+ */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:19:22Z

Jh3416: /* [P(Ch3)4]+ */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:19:05Z

Jh3416: /* [N(Ch3)4]+ */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

=='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T13:18:35Z

Jh3416: /* Part 2ː Project */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

=Part 2ː Ionic Liquids=

==='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''===
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T11:12:01Z

Jh3416: /* Basis Sets and Pseudo-Potentials */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

===NI<sub>3</sub>===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

==='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''===
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T10:56:07Z

Jh3416: /* Discussion */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

'''NI3'''

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

==='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''===
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<sup>[1]</sup>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T10:53:52Z

Jh3416: /* References */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

'''NI3'''

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

==='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''===
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="Electronegativities" />
<references>
<ref name="Electronegativities">Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. ''Evaluation and Test of Pauling’s Electronegativity Scale.'' J. Phys. Chem. A 104, 5867–5871 (2000).</ref>
</references>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1] - ''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''

[2] - ''Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).''

IO:jh3416

2019-05-17T10:52:48Z

Jh3416: /* Discussion */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

'''NI3'''

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

==='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''===
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="Electronegativities" />
<references>
<ref name="Electronegativities">Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. ''Evaluation and Test of Pauling’s Electronegativity Scale.'' J. Phys. Chem. A 104, 5867–5871 (2000).</ref>
</references>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

==References==
[1]
[2] - Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. Evaluation and Test of Pauling’s Electronegativity Scale. J. Phys. Chem. A 104, 5867–5871 (2000).

IO:jh3416

2019-05-17T10:51:59Z

Jh3416: /* Discussion */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

'''NI3'''

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

==='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''===
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; +0.298
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15<ref name="Electronegativities" />
<references>
<ref name="Electronegativities">Murphy, L. R., Meek, T. L., Allred, A. L. & Allen, L. C. ''Evaluation and Test of Pauling’s Electronegativity Scale.'' J. Phys. Chem. A 104, 5867–5871 (2000).</ref>
</references>. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

IO:jh3416

2019-05-17T10:46:15Z

Jh3416: /* NMe4 */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

'''NI3'''

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

==='''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''===
<jmol><jmolApplet>
<title>Optimised molecule</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; ̟0.298.
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15[ref]. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

IO:jh3416

2019-05-17T10:44:55Z

Jh3416: /* PMe4 */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

'''NI3'''

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

===NMe4===
<jmol><jmolApplet>
<title>Optimised NMe4</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

=='''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>'''==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; ̟0.298.
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15[ref]. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

IO:jh3416

2019-05-17T10:44:02Z

Jh3416: /* Discussion */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

'''NI3'''

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

===NMe4===
<jmol><jmolApplet>
<title>Optimised NMe4</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

==PMe4==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

'''[P(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; ̟0.298.
'''[N(Ch<sub>3</sub>)<sub>4</sub>]<sup>+</sup>+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15[ref]. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]

IO:jh3416

2019-05-17T10:43:10Z

Jh3416: /* Discussion */

==BH3==

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''
[[File:BH3JH_SUM.PNG|400px]]

'''Item 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>

'''Frequency Analysis'''
[[File:JH3416_BH3_FREQ.LOG|linktofile]]

<pre>
Low frequencies --- -0.1187 -0.0049 0.0005 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

===Additional BH3===

'''BH3 Vibrational Modes'''

{| class="wikitable" border="1"
|+ IR Data
! No. !! wavenumber (cm⁻¹) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1 || 1164 || 92.5 || A2'' || YES || Out of Plane Bend
|-
| 2 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 3 || 1214 || 14.1 || E' || YES || Antisymmetric Bend
|-
| 4 || 2580 || 0.0 || A1' || NO || Symmetric Stretch
|-
| 5 || 2580 || 126.4 || E' || YES || Symmetric Stretch
|-
| 6 || 2713 || 126.4 || E' || YES || Symmetric Stretch
|}

[[File:Jh3416_IRspectrum_1.PNG]]

There are 6 vibrational modes in total, satisfying the 3N-6 rule for a non-linear molecule. The IR spectrum however only contains 3 peaks, and this can be explained by looking at the vibrational modes. 2 and 3 are degenerate vibrations, as are 5 and 6, and so will appear under the same peak. Vibration (4) has a very low intensity and so will not be experimentally observable.

===MOS===

The Molecular Orbitals for BH3 were then computed and compared with a qualitative LCAO MO Diagram, shown below.<ref name="ChemDraw" />
<references>

<ref name="ChemDraw">''Hunt, P (2018) Lecture 4: Advanced Molecular Orbital Diagrams, from CHEM5001 Molecular Orbitals in Inorganic Chemistry, Imperial College London, Sherfield Building on 9th November. Available from Blackboard [Accessed 07/06/2019].''</ref>
</references>

[[File:JH3416_BH3_MO_DIAGRAM.PNG|500px]]

From the diagram it can be seen that the molecular orbitals in the qualitative MO Diagram for BH3 bears a strong resemblance to the computed orbitals, with the same energy ordering observed. Hence in the case of a BH3 molecule it can be seen that qualitative MO theory is able to draw an accurate picture of the bonding in a molecule. Whilst it would not be possible to use it to calculate relative energy orderings, nonetheless it is a useful tool to describe structure and bonding in molecules.

==Association Energies==

'''NH3'''

RB3LYP, 6-31G(d,p)

[[File:NH3_OPT_SUMMARY_JH3416.PNG|400px]]

[[File:JH3416_NH3_FREQ.LOG|linktobfile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''Key data for NH3BH3'''

RB3LYP, 6-31G(d,p)

[[File:BH3NH3_JH3416_SUM.PNG|400px]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

[[File:JH_BH3NH3_FREQUENCY.LOG|linktofile]]

'''Jmol image'''
<jmol><jmolApplet>
<title>BH3NH3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH_BH3NH3_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -0.0007 -0.0005 -0.0003 17.2958 17.6386 37.4385
Low frequencies --- 265.8400 632.2182 639.3651

'''calculation'''
E(NH3)= -56.55776873 a.u.
E(BH3)= -26.61532349 a.u.
E(NH3BH3)= -83.22468891 a.u.

ΔE (a.u.) =E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u.

ΔE (kj/mol) = (-0.0516 x 6.022x10²³ x 4.3597 x 10⁻¹⁸)/1000
= -135 kj/mol.

Weaker than Diborane B-B (146kj/mol) and Hydrazine N-N (297kj/mol). Stronger than Hydrogen bonding (approx 7kj/mol)

==Basis Sets and Pseudo-Potentials==

'''NI3'''

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>JH3416_NI3_OPTV3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimised N-I Bond Distanceː'''
2.0300 Angstrom

'''Optimisation'''
[[File:NI3_FREQ_SUMMJH.PNG|400px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000552 0.001800 YES
RMS Displacement 0.000477 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:JH3416_NI3_OPTV3.LOG|linktofile]]

<pre>
Low frequencies --- -63.3725 -63.3698 -61.9250 -0.0012 0.0005 0.0042
Low frequencies --- 133.9842 133.9844 195.0370
</pre>

==Part 2ː Project==

- if a job has not converged in 50 steps you MUST get a deomonstrator or lecturer to look at it.
- for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

- use your data! at least 50% of the project should be centered around interpretation, compare and analyse your data, can you find a justification or interpreation for trends? Are you able to rationalize, using this information, some key property or chemistry of the compound?

- time management is key, the calculations are quick, analysis is much slower

- simply reporting your results will only gain you a maximum of 50% of the mark for the project

- follow as similar pattern of steps from the revision material, the instructions for the mini projects are less developed, because you are now expected to know the processes and you are expected to work with more independence.

===NMe4===
<jmol><jmolApplet>
<title>Optimised NMe4</title>
<color>black</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>NCH4_FREQ_JH3416V2.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Nme4_Freq_summ_jh3416.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000249 0.000450 YES
RMS Force 0.000036 0.000300 YES
Maximum Displacement 0.000850 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
</pre>

'''Frequency Analysis'''
[[File:NCH4_FREQ_JH3416V2.LOG|linktofile]]

<pre>
Low frequencies --- -0.0010 -0.0009 -0.0007 34.7114 34.7114 34.7114
Low frequencies --- 216.3615 315.7960 315.7960
</pre>

==PMe4==
<jmol><jmolApplet>
<title>Optimised PMe4</title>
<color>blue</color>
<size>200</size>
<script>frame x.y</script>
<uploadedFileContents>PME4_FREQ_JH3416V3.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Optimisation'''

[[File:Pme4newsumjh.PNG|300px]]

'''Item Table'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000175 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001028 0.001800 YES
RMS Displacement 0.000372 0.001200 YES

</pre>

'''Frequency Analysis'''
[[File:PME4_FREQ_JH3416V3.LOG|linktofile]]

<pre>
Low frequencies --- -0.0026 -0.0016 -0.0010 22.8333 22.8333 22.8333
Low frequencies --- 159.9394 194.7757 194.7757
</pre>

==Discussion==

'''Charge Distribution'''

''' [P(CH3)4]+'''
[[File:PMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː P; +1.568. C; -1.058/-1.060. H; ̟0.298.
''' [N(CH3)4]+'''
[[File:NMe4_Charge_Dis_jh3416.PNG|400px]]
Valuesː N -0.295, C -0.483, H=+0.269.

Phosphorus has a positive charge, indicating electron density is being drawn from the central phosphorous atom by the surrounding carbon atoms. In contrast, Nitrogen has a negative value of -0.295 indicating it is drawing electron density from the carbons. This can be explained by referring to their relative electronegativities; N = 3.04 > C = 2.55 > P = 2.15[ref]. The more electronegative atom draws electron density towards itself, so nitrogen has a negative charge relative to carbon, as it has a greater electronegativity, whereas phosphorus has a positive charge relative to carbon for the converse reason.

'''MO Analysis'''

[[File:Fragmentsjh3416.PNG|400px|alt text]]

'''MO 21 (HOMO)'''
[[File:MO_21_jh3416.PNG|400px]]

[[File:MO_21jh3416.PNG|400px|MO 21]]

'''MO 16'''
[[File:Mo_16jh3416.PNG ‎|400px]]
[[File:MO_16jh3416.PNG|400px|alt text]]

'''MO 7'''
[[File:MO7_jh3416.PNG|400px]]

[[File:MO_7jh3416.PNG|400px|alt text]]