ChemWiki - User contributions [en]

Rep:MOD:XYK172019

2019-05-24T12:23:38Z

Xyk17: /* MO14 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:XYK17MO21newpic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 450 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character as expected.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:23:04Z

Xyk17: /* MO14 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:XYK17MO21newpic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 450 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:22:31Z

Xyk17: /* MO21 (HOMO) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:XYK17MO21newpic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:22:16Z

Xyk17: /* MO21 (HOMO) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21newpic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

File:XYK17MO21newpic.png

2019-05-24T12:21:55Z

Xyk17:

Rep:MOD:XYK172019

2019-05-24T12:12:25Z

Xyk17: /* Vibrations for BH3 */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:12:07Z

Xyk17: /* Vibrations for NH3 */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:11:29Z

Xyk17: /* [N(CH3)4]+ */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:11:15Z

Xyk17: /* [P(CH3)4]+ */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:10:55Z

Xyk17: /* Molecular orbitals */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals of [N(CH3)4]+ ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:08:46Z

Xyk17: /* Charge distribution */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast and compare against the large charge distribution range in |[P(CH3)4]+ molecule, shown by very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:07:34Z

Xyk17: /* Association energy */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1 <ref name="sourcetwo"/>''. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:06:45Z

Xyk17:

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 <ref name="sourcetwo"/>'' and also a strong bond C-H with bond energy of 411 kJ mol-1. <ref name="sourcetwo"/>'' Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcethree"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcethree"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcethree"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcethree"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Wired Chemist, http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, (accessed May 2019). </ref>
<ref name="sourcethree" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019).</ref></references>

Rep:MOD:XYK172019

2019-05-24T12:04:12Z

Xyk17: /* Association energy */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1 (to nearest 1 kJ mol-1)

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 and also a strong bond C-H with bond energy of 411 kJ mol-1. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-24T12:03:11Z

Xyk17: /* Association energy */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak with bond energy of 135 kJ mol-1, and only small amount of energy is released for the binding of NH3 and BH3. This value is compared against moderately strong C-C with bond energy of 346 kJ mol-1 and also a strong bond C-H with bond energy of 411 kJ mol-1. Besides, it is most likely that B-N has a great bond length.

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-24T11:57:18Z

Xyk17:

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for angle deformation, and mode 5 and mode 6 which is responsible for bond stretch. Theoretically there should be 4 vibrational peaks in total, as each set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive.

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T22:41:42Z

Xyk17: /* MO14 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 300 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T22:41:31Z

Xyk17: /* MO14 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 350 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T22:41:20Z

Xyk17: /* MO14 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png | 600 px]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T22:40:07Z

Xyk17: /* MO14 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 700 px]]

MO 14 has the lowest energy among all three of the MOs chosen, therefore it has the greatest bonding character.

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T22:39:02Z

Xyk17: /* MO14 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png]]

LCAO representation:

[[File:XYK17MO14picnew.png | 500 px]]

[[File:XYK17MO14pic2.png | 500 px]]

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

File:XYK17MO14pic2.png

2019-05-23T22:38:53Z

Xyk17:

File:XYK17MO14picnew.png

2019-05-23T22:37:59Z

Xyk17:

Rep:MOD:XYK172019

2019-05-23T22:03:33Z

Xyk17: /* Molecular orbitals */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

==== MO14 (occupied) ====

Energy: -0.62250 a.u. (doubly degenerate)

Symmetry: e

Real MO:

[[File:XYK17MO14.png]]

LCAO representation:

[[File:XYK17MO14pic.png | 500 px]]

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

File:XYK17MO14pic.png

2019-05-23T22:03:22Z

Xyk17:

File:XYK17MO14.png

2019-05-23T22:03:06Z

Xyk17:

Rep:MOD:XYK172019

2019-05-23T21:07:50Z

Xyk17: /* References */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

== References ==
<references>

<ref name="sourceone" > P. Hunt, ''Hunt Research Group Teaching'', (accessed May 2019). </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T21:01:53Z

Xyk17: /* MO18 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T21:01:37Z

Xyk17: /* MO18 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T21:01:25Z

Xyk17: /* MO18 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 600 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T21:01:11Z

Xyk17: /* MO21 (HOMO) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |600 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T20:59:58Z

Xyk17: /* MO18 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:XYK17MO18pic2.png | 700 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T20:59:32Z

Xyk17: /* MO18 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

[[File:MO18pic2.png | 500 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

File:XYK17MO18pic2.png

2019-05-23T20:58:15Z

Xyk17:

Rep:MOD:XYK172019

2019-05-23T19:32:35Z

Xyk17: /* Charge distribution */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used as a contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T19:32:11Z

Xyk17: /* Charge distribution */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

Large, same range of colour was used to visualise the both the charge distribution. It is because this can be used to contrast, and to show the large charge distribution range in |[P(CH3)4]+ molecule with very different colour intensities.

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.

According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T19:24:03Z

Xyk17: /* MO18 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u. (triply degenerate)

Symmetry: t1

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T19:06:11Z

Xyk17: /* Molecular orbitals */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:MO18picnew.png | 500 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

File:MO18picnew.png

2019-05-23T19:05:06Z

Xyk17:

Rep:MOD:XYK172019

2019-05-23T19:02:35Z

Xyk17: /* MO18 (occupied) */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

[[File:XYK17MO18pic.png | 450 px]]

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

File:XYK17MO18pic.png

2019-05-23T19:02:19Z

Xyk17:

Rep:MOD:XYK172019

2019-05-23T18:37:11Z

Xyk17: /* Molecular orbitals */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T18:36:28Z

Xyk17:

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

==== MO21 (HOMO) ====

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO:

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

==== MO18 (occupied) ====

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T18:34:53Z

Xyk17:

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===

E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

=== Optimisation ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

=== Frequency analysis ===

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

==== Optimisation ====

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

MO21 (HOMO)

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO:

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

MO18 (occupied)

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T18:23:01Z

Xyk17: /* BH3 */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

==== Optimisation ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

==== Frequency analysis ====

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

Optimised N-H bond distance: 1.01789 Angstrom

Optimised H-N-H bond angle: 37.119o

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===
E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

MO21 (HOMO)

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO:

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

MO18 (occupied)

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T18:21:38Z

Xyk17: /* Molecular orbitals */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

Optimised B-H bond distance: 1.19266 Angstrom

Optimised H-B-H bond angle: 120.00o

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

Optimised N-H bond distance: 1.01789 Angstrom

Optimised H-N-H bond angle: 37.119o

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===
E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

MO21 (HOMO)

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO:

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

[[File:MO21pic2.png |550 px]]

MO18 (occupied)

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

File:MO21pic2.png

2019-05-23T18:19:52Z

Xyk17:

Rep:MOD:XYK172019

2019-05-23T18:17:39Z

Xyk17: /* Molecular orbitals */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

Optimised B-H bond distance: 1.19266 Angstrom

Optimised H-B-H bond angle: 120.00o

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

Optimised N-H bond distance: 1.01789 Angstrom

Optimised H-N-H bond angle: 37.119o

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===
E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

MO21 (HOMO)

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO:

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |450 px]]

MO18 (occupied)

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

Rep:MOD:XYK172019

2019-05-23T18:16:10Z

Xyk17: /* Molecular orbitals */

== BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytable.png]]

Optimised B-H bond distance: 1.19266 Angstrom

Optimised H-B-H bond angle: 120.00o

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000638 0.001800 YES
RMS Displacement 0.000417 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_BH3_SYM_OPT_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -0.1187 -0.0048 0.0010 42.2482 42.2484 43.3387
Low frequencies --- 1163.5889 1213.5519 1213.5521
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for BH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|93
|A1
|yes
|out-of-plane bend
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|1214
|14
|E
|very slight
|bend/angle deformation
|-
|2580
|0
|A1
|no
|symmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|-
|2713
|126
|E
|yes
|asymmetric bond stretch
|}

[[File:XYK17irspectrumnew.png]]

There are 6 vibrational modes as [3(4)-6]= 6, with two sets of degenerate vibrations: mode 2 and mode 3 which is responsible for bond stretch, and mode 5 and mode 6 which is responsible for angle deformation. Theoretically there should be 4 vibrational peaks in total, as one set of degenerate vibrations will result in a single peak. However experimentally there were only 3 peaks in the IR spectrum, and the vibrational peak at 2580 cm-1 was not observed. This is because in order for a vibrational mode to absorb infrared light, there must be an overall change in the dipole moment of the molecule. The vibrational mode at 2580 cm-1 is a completely symmetric stretch and its dipoles cancel off, therefore it is IR inactive

=== Molecular orbitals ===
[[File:XYK17finalmo.png |700 px]]

''MO diagram taken from <ref name="sourceone"/>''

It can be seen that the LCAO molecular orbitals (MO) are not significantly different from the real MOs, except that the real MOs have more diffuse and larger orbitals. The phases between them are the same. We can say that LCAO is an useful approximation and that we can use MO theory (and MO diagrams) to mostly understand the bonding and reactivity of a molecule - a qualitative analysis.

== NH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablenh3.png]]

Optimised N-H bond distance: 1.01789 Angstrom

Optimised H-N-H bond angle: 37.119o

<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000221 0.001800 YES
RMS Displacement 0.000096 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_NH3_FREQ.LOG| nh3_frequency.log]]

<pre>
Low frequencies --- -28.3223 -28.3221 -25.0345 0.0014 0.0016 0.0040
Low frequencies --- 1088.2807 1693.7780 1693.7780
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibrations for NH3 ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1088
|146
|A1
|yes
|out-of-plane bend
|-
|1694
|14
|E
|very slight
|bend
|-
|1694
|14
|E
|very slight
|bend
|-
|3462
|1
|A1
|no
|symmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|-
|3591
|0
|E
|no
|asymmetric stretch
|}

[[File:XYK17irspectrumnh3.png | 550 px]]

== NH3BH3 ==

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytablebh3nh3.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.000788 0.001800 YES
RMS Displacement 0.000450 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_NEWBH3NH3_FREQ.LOG| bh3nh3_frequency.log]]

<pre>
Low frequencies --- -0.0197 -0.0023 0.0009 21.7711 21.7729 48.1543
Low frequencies --- 267.7721 631.8557 640.1246
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_NEWBH3NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association energy ===
E(BH3)= -26.61532349 a.u.

E(NH3)= -56.55776871 a.u.

E(NH3BH3)= -83.22468864 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(BH3)+E(NH3)]

= -83.22468864 - [(-26.61532349)+(-56.55776871)]

= -0.05159644 a.u.

= -135 kJ mol-1

The B-N dative bond is quite weak as only 135 kJ mol-1 amount of energy is released for the binding of NH3 and BH3. This value is compared against

== NI3 ==
Calculation method: RB3LYP

Basis set: Gen

[[File:XYK17summarytableni3new.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000108 0.000450 YES
RMS Force 0.000037 0.000300 YES
Maximum Displacement 0.000774 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
</pre>

Frequency file: [[Media:NI3_PP_RUN_FREQ.LOG| ni3_frequency.log]]

<pre>
Low frequencies --- -4.6918 -0.0003 -0.0003 -0.0002 3.0873 4.4353
Low frequencies --- 101.2739 101.3616 148.3436
</pre>

<jmol><jmolApplet>
<title>optimised NI3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NI3_PP_RUN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I bond distance: 2.1837 Angstrom

== Mini Project - Ionic liquids ==
=== [N(CH3)4]+ ===

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletma.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000118 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_TMA_FREQ.LOG| [N(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0009 -0.0006 -0.0006 18.2688 18.2688 18.2688
Low frequencies --- 184.2396 289.9254 289.9254
</pre>

<jmol><jmolApplet>
<title>optimised [N(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMA_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

[[File:XYK17summarytabletmp.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000507 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

Frequency file: [[Media:XYK17_TMP_FREQ.LOG| [P(CH3)4]+_frequency.log]]

<pre>
Low frequencies --- -0.0023 -0.0020 -0.0013 24.0125 24.0125 24.0125
Low frequencies --- 159.9844 194.7639 194.7639
</pre>

<jmol><jmolApplet>
<title>optimised [P(CH3)4]+ molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XYK17_TMP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Charge distribution ===
[[File:XYK17chargedistributionsnew.png | 800 px]]

{| class="wikitable"
!Structure
!Charge on central atom (N/P)
!Charge on C atom
!Charge on H atom
|-
|[N(CH3)4]+
|<nowiki>-0.295</nowiki>
|<nowiki>-0.483</nowiki>
|0.269
|-
|[P(CH3)4]+
|1.667
|<nowiki>-1.060</nowiki>
|0.298
|}

[N(CH3)4]+:

Nitrogen and carbon have negative charge distribution, with carbon being more negatively charged although C(2.55)<ref name="sourcetwo"/> is less electronegative than N(3.04). Whereas hydrogen has positive charge distribution, as agreed with theory as it is least electronegative (2.20)<ref name="sourcetwo"/>. The charge distribution shows that the central atom N tends to draw electron density from the H atoms in the methyl groups, therefore the positive charge is on the H atoms.
According to the commonly used Lewis structure, the +1 formal charge of the molecule is assigned to the central atom N, but the charge distribution calculated above do not support this assignment. It shows that the most positive potentials appear on the Hs, and the positive charge is spread equally over the Hs. The N in [N(CH3)4]+ carries a +1 charge if it shares bonding electrons equally with the C in methyl group, but we know that N is more electronegative than H, so the Lewis structure does not give accurate charge information for the ions.

[P(CH3)4]+:

The charge distribution agrees with the values of electronegativities (P:2.19, C:2.55, H:2.20)<ref name="sourcetwo"/> - as C atom is most electronegative, it tends to attract the shared pair of electrons more strongly towards itself, resulting in greater electron charge cloud which develops negative charge. Whereas P which is the most electropositive atom, has the most positive charge. The difference in charge distribution in the molecule is fairly large, as shown by the greatly different colour intensities.

Comparison:

Considering the electronegativities of the central atom(N: 3.04, P: 2.19)<ref name="sourcetwo"/>, N is more electronegative than P, which is reflected in the charge distribution where N has negative charge of -0.269 in N(CH3)4]+ whereas P have positive charge of +1.667 [P(CH3)4]+. In N(CH3)4]+, the most electron density is towards the N atoms and C atoms, whereas in N(CH3)4]+, the most electron density is towards the C atoms in methyl group. But in both molecule, H atoms have positive charges. Besides, it can be seen that the P-C bond in [P(CH3)4]+ has a much greater charge distribution difference compared to N-C bond in N(CH3)4]+, therefore P-C is mostly likely to be a more polar bond, and this might result in its greater reactivity due to the greater polarity.

=== Molecular orbitals ===

MO21 (HOMO)

Energy: -0.57936 a.u. (triply degenerate)

Symmetry: t2

Real MO:

[[File:XYK17MO21.png]]

LCAO representation:

[[File:MO21pic.png |500 px]]

MO18 (occupied)

Energy: -0.58038 a.u.

Point group:

Real MO:

[[File:XYK17MO18.png]]

LCAO representation:

== References ==
<references>

<ref name="sourceone" > J. I. Steinfeld, J. S. Francisco, W. L. Hase, ''Chemical Kinetic and Dynamics'', Prentice Hall, United States, 1998. </ref>
<ref name="sourcetwo" > Science Notes, https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/, (accessed May 2019) </ref></references>

File:XYK17 MO21pic.png

2019-05-23T18:15:21Z

Xyk17: