ChemWiki - User contributions [en]

TAw0133700117

2019-05-20T10:36:01Z

Taw17: /* N(CH3)4+ Orbitals */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04 (2). Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===
Three valence orbitals for this compound were examined. A LCAO MO diagram was drawn for each MO. In the LCAO diagrams, the green arrows represent the bonding interactions, and the pink arrows represent the antibonding interactions.

====MO 8====
[[File:TW_MO8.png]]
[[File:TW_N(CH4)3_Orb8.PNG]]

==== MO 10====
[[File:TW_MO10.png]]
[[File:TW_N(CH4)3_Orb10.PNG]]

==== MO21 ====
[[File:TW_MO21.png]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-20T10:33:41Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04 (2). Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===
Three valence orbitals for this compound were examined. A LCAO MO diagram was drawn for each MO.

====MO 8====
[[File:TW_MO8.png]]
[[File:TW_N(CH4)3_Orb8.PNG]]

==== MO 10====
[[File:TW_MO10.png]]
[[File:TW_N(CH4)3_Orb10.PNG]]

==== MO21 ====
[[File:TW_MO21.png]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-20T10:31:14Z

Taw17: /* NI3 */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===
Three valence orbitals for this compound were examined. A LCAO MO diagram was drawn for each MO.

====MO 8====
[[File:TW_MO8.png]]
[[File:TW_N(CH4)3_Orb8.PNG]]

==== MO 10====
[[File:TW_MO10.png]]
[[File:TW_N(CH4)3_Orb10.PNG]]

==== MO21 ====
[[File:TW_MO21.png]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-20T10:25:22Z

Taw17: /* N(CH3)4+ Orbitals */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===
Three valence orbitals for this compound were examined. A LCAO MO diagram was drawn for each MO.

====MO 8====
[[File:TW_MO8.png]]
[[File:TW_N(CH4)3_Orb8.PNG]]

==== MO 10====
[[File:TW_MO10.png]]
[[File:TW_N(CH4)3_Orb10.PNG]]

==== MO21 ====
[[File:TW_MO21.png]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-20T10:23:31Z

Taw17: /* N(CH3)4+ Orbitals */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===

====MO 8====
[[File:TW_MO8.png]]
[[File:TW_N(CH4)3_Orb8.PNG]]

==== MO 10====
[[File:TW_MO10.png]]
[[File:TW_N(CH4)3_Orb10.PNG]]

==== MO21 ====
[[File:TW_MO21.png]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-20T10:22:44Z

Taw17: /* N(CH3)4+ Orbitals */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===

[[File:TW_MO8.png]]
[[File:TW_N(CH4)3_Orb8.PNG]]
[[File:TW_MO10.png]]
[[File:TW_N(CH4)3_Orb10.PNG]]
[[File:TW_MO21.png]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-20T10:22:09Z

Taw17: /* N(CH3)4+ Orbitals */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===

[[File:TW_MO_8.png]]
[[File:TW_MO10.png]]
[[File:TW_MO21.png]]
[[File:TW_N(CH4)3_Orb8.PNG]]
[[File:TW_N(CH4)3_Orb10.PNG]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

File:TW MO8.png

2019-05-20T10:21:06Z

Taw17: Taw17 uploaded a new version of File:TW MO8.png

TAw0133700117

2019-05-20T10:20:24Z

Taw17: /* N(CH3)4+ Orbitals */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===

[[File:TW_MO_8.PNG]]
[[File:TW_MO10.PNG]]
[[File:TW_MO21.PNG]]
[[File:TW_N(CH4)3_Orb8.PNG]]
[[File:TW_N(CH4)3_Orb10.PNG]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-20T10:19:15Z

Taw17: /* N(CH3)4+ Orbitals */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===

[[File:TW_MO8.PNG]]
[[File:TW_MO10.PNG]]
[[File:TW_MO21.PNG]]
[[File:TW_N(CH4)3_Orb8.PNG]]
[[File:TW_N(CH4)3_Orb10.PNG]]
[[File:TW_N(CH4)3_Orb21.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

File:TW N(CH4)3 Orb21.PNG

2019-05-20T10:17:44Z

Taw17:

File:TW N(CH4)3 Orb10.PNG

2019-05-20T10:17:28Z

Taw17:

File:TW N(CH4)3 Orb8.PNG

2019-05-20T10:17:16Z

Taw17:

File:TW MO21.png

2019-05-20T10:16:56Z

Taw17:

File:TW MO10.png

2019-05-20T10:16:30Z

Taw17:

File:TW MO8.png

2019-05-20T10:16:10Z

Taw17:

TAw0133700117

2019-05-17T15:45:27Z

Taw17: /* N(CH3)4+ Orbitals */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T15:40:08Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

=== N(CH3)4+ Orbitals ===

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T15:38:56Z

Taw17:

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 = -135 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.184 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T12:10:42Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results. [NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T12:08:06Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

The top two pictures refer to the charge distribution on N(CH3)4+ and the bottom two refer to P(CH3)4+.

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T12:04:55Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]

[[File:TW_N(CH3)4+_chargedist.PNG]]

[[File:TW_P(CH3)4+_chargetable.PNG]]

[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T12:04:40Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P = 2.19, C = 2.55 and N = 3.04. Since P is less electronegative than C, the electron density resides on the carbon atoms which is why P is predicted to have a positive charge. N, on the other hand, is more electronegative than C and as a result withdraws electron density from the methyl groups, giving it a negative charge and making the charge on the C atoms more positive. The charges on the H atoms remain fairly constant at 0.298 for P(CH3)4+ and 0.269 for N(CH3)4+. This is because the inductive effect of changing the heteroatom falls away rapidly with distance.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

The formal positive charge on the N atom for this molecule using a traditional description is due to the N atom forming a dative bond to a methyl group. As a result, compared, to a neutral nitrogen atom, the nitrogen atom in this compound has one less electron. In reality, and as shown by the charge distributions, the positive charge is not located on a single atom but is actually spread out across the molecule. It is distributed over the H atoms on the methyl groups. In actual fact, the N atom actually has a negative charge. This is because the N atom is very electronegative and withdraws electron density from the methyl groups.

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T11:30:58Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P =

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T11:28:56Z

Taw17: /* References */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_c`hargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P =

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T11:28:47Z

Taw17: /* References */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_c`hargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P =

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referencesː

(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.
(2) J.E. Huheey, E.A. Keiter, and R.L. Keiter in Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition, HarperCollins, New York, USA, 1993.

TAw0133700117

2019-05-17T11:28:23Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_c`hargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

As can be seen by the tables and the charge distribution pictures, the heteroatom in each compound affects how electrons are distributed. The charge on the P atom was worked out to be 1.667 whereas the charge on the N atom was calculated to be -0.295. In the N(CH3)4+ and P(CH3)4+, the charges on carbon were -1.060 and -0.483 respectively. These observations can be explained by the electronegatives of the atoms involvedː P =

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T11:00:02Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! N
| -0.295
|-
! C
| -0.483
|-
! H
| 0.269
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1.667
|-
! C
| -1.060
|-
! H
| 0.298
|}

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:58:01Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|}

{| class="wikitable" style="text-align:center"
!Atom!! P(CH3)4+ Charges
|-
! P
| 1
|-
! C
| 2
|-
! O
| 3
|}

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:57:17Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|}

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

-

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:56:22Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

-

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:56:12Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|
[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

-

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:55:49Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

{| class="wikitable" style="text-align:center"
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|-

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:55:14Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|-

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:54:51Z

Taw17: /* References */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|-

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

ǃǃǃ P(CH3)4+ Charges

TAw0133700117

2019-05-17T10:54:31Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|-

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:53:57Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|-

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:53:09Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges
|-
! 1
| 1
|-
! 2
| 2
|-
! 3
| 3
|-

ǃǃǃ P(CH3)4+ Charges

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:52:30Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges ǃǃǃ P(CH3)4+ Charges
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|-

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:52:08Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:51:19Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges ǃǃǃ P(CH3)4+ Charges
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|-

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:48:14Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges ǃǃǃ P(CH3)4+ Charges
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|-

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:47:12Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges ǃǃǃ P(CH3)4+ Charges
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|-

!×!! 1 !! 2 !! 3
|-
! 1
| 1 || 2 || 3
|-
! 2
| 2 || 4 || 6
|-
! 3

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!×!! N(CH3)4+ Charges !! P(CH3)4+ Charges !! 3
|-
! 1
| 1 || 2 || 3
|-
! 2
| 2 || 4 || 6
|-
! 3
| 3 || 6 || 9
|}

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:46:21Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges ǃǃ P(CH3)4+ Charges
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|-

!×!! 1 !! 2 !! 3
|-
! 1
| 1 || 2 || 3
|-
! 2
| 2 || 4 || 6
|-
! 3

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!×!! N(CH3)4+ Charges !! P(CH3)4+ Charges !! 3
|-
! 1
| 1 || 2 || 3
|-
! 2
| 2 || 4 || 6
|-
! 3
| 3 || 6 || 9
|}

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:45:39Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges ǃǃ P(CH3)4+ Charges
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|-

!×!! 1 !! 2 !! 3
|-
! 1
| 1 || 2 || 3
|-
! 2
| 2 || 4 || 6
|-
! 3

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!×!! N(CH3)4+ Charges !! 2 !! 3
|-
! 1
| 1 || 2 || 3
|-
! 2
| 2 || 4 || 6
|-
! 3
| 3 || 6 || 9
|}

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:43:59Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ Charges ǃǃ P(CH3)4+ Charges
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|}

!×!! 1 !! 2 !! 3
|-
! 1
| 1 || 2 || 3
|-
! 2
| 2 || 4 || 6
|-
! 3

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:43:15Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ ǃǃ P(CH3)4+
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|}

!×!! 1 !! 2 !! 3
|-
! 1
| 1 || 2 || 3
|-
! 2
| 2 || 4 || 6
|-
! 3

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:40:59Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?


)̞

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ ǃ ǃ P(CH3)4+ ǃ
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|}

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:39:23Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?


)̞

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ ǃǃ P(CH3)4+ ǃǃ
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|}

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.

TAw0133700117

2019-05-17T10:38:58Z

Taw17: /* P(CH3)4+ and N(CH3)4+ Comparison */

=== BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_BH3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_BH3_FREQ.LOG| bh3_frequency.log]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0054 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A"2
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|1213
|14
|E'
|very slight
|in-plane bend
|-
|2582
|0
|A'1
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

[[File:TW_BH3_vibspectrum.PNG|400px]]

In the spectrum there are less than 6 peaks. This is because there are two sets of vibrations with degenerate energies, these sets occur at frequencies 1213 and 2715. As a result, 4 vibrations are represented by two peaks. There is also a stretch at 2583, however since it is a symmetric stretch, it is not IR active and as a result does not appear on the spectrum. Therefore, only 3 peaks should be seen in the spectrum.

==== BH3 Molecular Orbital Diagram ====
[[File:TW_BH3_MO_completediagram2.PNG]]

MO diagram referenced fromː Hunt, P, 2018, MO Problem Class, ICL, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/P1_BH3_MO_diagram.pdf

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?

The LCAO MOs show the individual contributions from the orbitals on each atom however the real MOs may be much larger and cover multiple atoms e.g. 2a1'. For the LCAO MOs, the orbital contribution coefficients have been estimated, whereas for the real MOs these values have been calculated and will be more representative of what is actually happening.

The energy ordering and shape of the LCAO MOs predicted by MO theory compare well to the real MOs. MO theory allows us to generate these properties without having to carry out the complex calculations involved in solving the Schrodinger equation. As a result, MO theory is quite useful and accurate.

=== NH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3_summary.PNG]]

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

Frequency analysis log file [[Media:TW_NH3_OPT_FREQ.LOG| NH3_frequency.log]]

<pre>
Low frequencies --- -0.0128 -0.0018 -0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===

'''B3LYP/6-31G(d.p) level'''

[[File:TW_NH3BH3_summary3.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NH3BH3_FREQ2.LOG| NH3BH3_frequency.log]]

<pre>
Low frequencies --- -5.6966 -0.3177 -0.0465 -0.0015 1.1645 1.2407
Low frequencies --- 263.2815 632.9623 638.4593
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NH3BH3_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy of N-B Bond ====
E(NH3) = -56.55776873 a.u.

E(BH3) = -26.61532364 a.u.

E(NH3BH3) = -83.22468893 a.u.

Association energy = E(NH3BH3) - [E(NH3)+E(BH3)] = -83.22468893 - (-26.61532364 + -56.5577687) = -0.05159659 a.u. = -135.466847 kJ/mol

Compared to a C-C bond, which has a bond dissociation energy of 347 kJ/mol (1), the B-N bond is quite weak despite being isoelectronic.

=== NI3 ===

'''B3LYP/6-31G(d,p)LANL2DZ level'''

[[File:TW_NI3_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000629 0.001200 YES
</pre>

Frequency analysis log file [[Media:TW_NI3_OPT_FREQ.LOG| NI3_frequency.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_NI3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond length is 2.18424 A.

DSpace?

=== N(CH3)4+ ===

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

[[File:TW_N(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000091 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000765 0.001800 YES
RMS Displacement 0.000405 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0009 -0.0007 -0.0002 35.2870 35.2870 35.2870
Low frequencies --- 217.1555 316.3089 316.3089
</pre>

<jmol><jmolApplet>
<title>N(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_N(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ ===

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

[[File:TW_P(CH3)4+_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

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

<pre>
Low frequencies --- -0.0003 0.0014 0.0015 24.7544 24.7544 24.7544
Low frequencies --- 160.0917 194.8201 194.8201
</pre>

<jmol><jmolApplet>
<title>P(CH3)4+</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>TW_P(CH3)4+_OPT_SYM_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== P(CH3)4+ and N(CH3)4+ Comparison ===

[[File:TW_N(CH3)4+_chargetable.PNG]]
[[File:TW_N(CH3)4+_chargedist.PNG]]
[[File:TW_P(CH3)4+_chargetable.PNG]]
[[File:TW_P(CH3)4+_chargedist.PNG]]

Compare the charge distribution for these cations, placing images side by side is not sufficient, list and discuss the charges. The key words here are "compare" and "discuss" just presenting the data is not sufficient, you must interpret your results.

[NR4]+ (R=alkyl) is often depicted as shown, with the positive charge placed on the nitrogen centre. Based on your results for [N(CH3)4]+, discuss the validity of this traditional description. You should consider the following:
What does the "formal" positive charge on the N represent in the traditional picture?
On what atoms is the positive charge actually located for this cation?


)̞

{| class="wikitable" style="text-align:center"
|+ style="white-space:nowrap" |Multiplication table
|-
!Atom!! N(CH3)4+ǃǃ P(CH3)4+
|-
! 1
| 1 || 2
|-
! 2
| 2 || 4
|-
! 3
| 3 || 6
|}

===References ===
Referenceː(1) Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition.