ChemWiki - User contributions [en]

Inorganic Computational Lab:gab116

2018-05-25T16:44:41Z

Gab116:

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2"
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the MO's location, basic shape and relative AO contribution, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The contributing AOs are the pz orbitals perpendicular to the ring plane and there are two nodal planes; one parallel to the ring going through the atoms (characteristic of pz orbitals) and one splitting the molecule in half. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. The contributing AOs are the px orbitals parallel to the ring plane and hence there are nodes on every atom in the ring. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase with no nodes, and hence only involve s orbitals. However, the shapes aren't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):

1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.

2. When placed in an external magnetic field, a pi electron ring current is induced.

3. Aromatics are involved in reactions where the pi structure is conserved.

Simple aromatic molecules obey the empirical Hückel's rule (source: J. Clayden, N. Greeves and S. Warren, Organic Chemistry, 2nd Edition, 2012, OUP, 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex interpretations of aromaticity can include sigma-only aromaticity. For example, there are main group hydride clusters that exhibit no pi aromaticity and only sigma aromaticity. σ-aromaticity and σ-antiaromaticity in saturated inorganic rings is examined in the following paper: Z.-H. Li, D. Moran, K.-N. Fan and P. von Ragué Schleyer, J. Phys. Chem. A, 2005, 109 (16), 3711–3716 (https://pubs.acs.org/doi/abs/10.1021/jp048541o).

Inorganic Computational Lab:gab116

2018-05-25T16:33:07Z

Gab116: /* Molecular Orbital Comparison */

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2"
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the MO's location, basic shape and relative AO contribution, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. The contributing AOs are the px orbitals and hence there are nodes on every atom in the ring. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase with no nodes, and hence only involve s orbitals. However, the shapes aren't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):

1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.

2. When placed in an external magnetic field, a pi electron ring current is induced.

3. Aromatics are involved in reactions where the pi structure is conserved.

Simple aromatic molecules obey the empirical Hückel's rule (source: J. Clayden, N. Greeves and S. Warren, Organic Chemistry, 2nd Edition, 2012, OUP, 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex interpretations of aromaticity can include sigma-only aromaticity. For example, there are main group hydride clusters that exhibit no pi aromaticity and only sigma aromaticity. σ-aromaticity and σ-antiaromaticity in saturated inorganic rings is examined in the following paper: Z.-H. Li, D. Moran, K.-N. Fan and P. von Ragué Schleyer, J. Phys. Chem. A, 2005, 109 (16), 3711–3716 (https://pubs.acs.org/doi/abs/10.1021/jp048541o).

Inorganic Computational Lab:gab116

2018-05-25T16:31:47Z

Gab116: /* Molecular Orbital Comparison */

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2"
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the MO's location, basic shape and relative AO contribution, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase with no nodes, and hence only involve s orbitals. However, the shapes aren't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):

1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.

2. When placed in an external magnetic field, a pi electron ring current is induced.

3. Aromatics are involved in reactions where the pi structure is conserved.

Simple aromatic molecules obey the empirical Hückel's rule (source: J. Clayden, N. Greeves and S. Warren, Organic Chemistry, 2nd Edition, 2012, OUP, 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex interpretations of aromaticity can include sigma-only aromaticity. For example, there are main group hydride clusters that exhibit no pi aromaticity and only sigma aromaticity. σ-aromaticity and σ-antiaromaticity in saturated inorganic rings is examined in the following paper: Z.-H. Li, D. Moran, K.-N. Fan and P. von Ragué Schleyer, J. Phys. Chem. A, 2005, 109 (16), 3711–3716 (https://pubs.acs.org/doi/abs/10.1021/jp048541o).

Inorganic Computational Lab:gab116

2018-05-25T16:29:34Z

Gab116: /* MO Diagram for BH3 */

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2"
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the MO's location, basic shape and relative AO contribution, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase. However, the shape isn't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):

1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.

2. When placed in an external magnetic field, a pi electron ring current is induced.

3. Aromatics are involved in reactions where the pi structure is conserved.

Simple aromatic molecules obey the empirical Hückel's rule (source: J. Clayden, N. Greeves and S. Warren, Organic Chemistry, 2nd Edition, 2012, OUP, 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex interpretations of aromaticity can include sigma-only aromaticity. For example, there are main group hydride clusters that exhibit no pi aromaticity and only sigma aromaticity. σ-aromaticity and σ-antiaromaticity in saturated inorganic rings is examined in the following paper: Z.-H. Li, D. Moran, K.-N. Fan and P. von Ragué Schleyer, J. Phys. Chem. A, 2005, 109 (16), 3711–3716 (https://pubs.acs.org/doi/abs/10.1021/jp048541o).

Inorganic Computational Lab:gab116

2018-05-25T16:27:52Z

Gab116: /* The Concept of Aromaticity */

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2"
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase. However, the shape isn't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):

1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.

2. When placed in an external magnetic field, a pi electron ring current is induced.

3. Aromatics are involved in reactions where the pi structure is conserved.

Simple aromatic molecules obey the empirical Hückel's rule (source: J. Clayden, N. Greeves and S. Warren, Organic Chemistry, 2nd Edition, 2012, OUP, 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex interpretations of aromaticity can include sigma-only aromaticity. For example, there are main group hydride clusters that exhibit no pi aromaticity and only sigma aromaticity. σ-aromaticity and σ-antiaromaticity in saturated inorganic rings is examined in the following paper: Z.-H. Li, D. Moran, K.-N. Fan and P. von Ragué Schleyer, J. Phys. Chem. A, 2005, 109 (16), 3711–3716 (https://pubs.acs.org/doi/abs/10.1021/jp048541o).

Inorganic Computational Lab:gab116

2018-05-25T16:21:28Z

Gab116: /* Vibrational spectrum for BH3 */

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2"
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase. However, the shape isn't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):

1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.

2. When placed in an external magnetic field, a pi electron ring current is induced.

3. Aromatics are involved in reactions where the pi structure is conserved.

All aromatic molecules obey the empirical Hückel's rule (source: J. Clayden, N. Greeves and S. Warren, Organic Chemistry, 2nd Edition, 2012, OUP, 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex interpretations of aromaticity can include sigma-only aromaticity. For example, there are main group hydride clusters that exhibit no pi aromaticity and only sigma aromaticity. σ-aromaticity and σ-antiaromaticity in saturated inorganic rings is examined in the following paper: Z.-H. Li, D. Moran, K.-N. Fan and P. von Ragué Schleyer, J. Phys. Chem. A, 2005, 109 (16), 3711–3716 (https://pubs.acs.org/doi/abs/10.1021/jp048541o).

Inorganic Computational Lab:gab116

2018-05-25T16:21:16Z

Gab116: /* Vibrational spectrum for BH3 */

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase. However, the shape isn't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):

1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.

2. When placed in an external magnetic field, a pi electron ring current is induced.

3. Aromatics are involved in reactions where the pi structure is conserved.

All aromatic molecules obey the empirical Hückel's rule (source: J. Clayden, N. Greeves and S. Warren, Organic Chemistry, 2nd Edition, 2012, OUP, 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex interpretations of aromaticity can include sigma-only aromaticity. For example, there are main group hydride clusters that exhibit no pi aromaticity and only sigma aromaticity. σ-aromaticity and σ-antiaromaticity in saturated inorganic rings is examined in the following paper: Z.-H. Li, D. Moran, K.-N. Fan and P. von Ragué Schleyer, J. Phys. Chem. A, 2005, 109 (16), 3711–3716 (https://pubs.acs.org/doi/abs/10.1021/jp048541o).

Inorganic Computational Lab:gab116

2018-05-25T16:17:29Z

Gab116:

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1
|no
|symmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase. However, the shape isn't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):

1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.

2. When placed in an external magnetic field, a pi electron ring current is induced.

3. Aromatics are involved in reactions where the pi structure is conserved.

All aromatic molecules obey the empirical Hückel's rule (source: J. Clayden, N. Greeves and S. Warren, Organic Chemistry, 2nd Edition, 2012, OUP, 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex interpretations of aromaticity can include sigma-only aromaticity. For example, there are main group hydride clusters that exhibit no pi aromaticity and only sigma aromaticity. σ-aromaticity and σ-antiaromaticity in saturated inorganic rings is examined in the following paper: Z.-H. Li, D. Moran, K.-N. Fan and P. von Ragué Schleyer, J. Phys. Chem. A, 2005, 109 (16), 3711–3716 (https://pubs.acs.org/doi/abs/10.1021/jp048541o).

Inorganic Computational Lab:gab116

2018-05-25T15:31:50Z

Gab116: /* The Concept of Aromaticity */

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1
|no
|symmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase. However, the shape isn't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

Aromatic systems generally have the following properties (source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250):
1. They posses a resonance stability that mean their bond energies are more stable than their alkene equivalents and have bond lengths that are between single and double bonds.
2. When placed in an external magnetic field, a pi electron ring current is produced

All aromatic molecules obey the empirical Hückel's rule (source: 161); for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex descriptions of aromaticity can include sigma-aromaticity

== References ==

Inorganic Computational Lab:gab116

2018-05-25T14:48:04Z

Gab116:

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1
|no
|symmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase. However, the shape isn't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

All aromatic molecules obey the empirical Hückel's rule; for planar compounds with a cyclic, contiguous array of p-orbitals perpendicular to the plane of the rings, there must be 4n+2 p electrons, where n is a natural number. For example, benzene is sp2 hybridized and so there are 6 pz orbitals perpendicular to the plane and 6 p electrons involved in the aromaticity and hence n=1 and Hückel's rule is obeyed.

This rule leads to a simple description of aromaticity as the delocalised pi overlap of pz orbitals above and below the plane, as is shown in the image of MO 17 below.

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

In fact, bonding in aromatics involves a wide variety of AOs and overlaps, as can be seen from the MO comparison above. Not all aromatic MOs involve only pi orbitals and many can involve sigma interactions, including MO 7 above.

More complex descriptions of aromaticity can include sigma-aromaticity

== References ==

Inorganic Computational Lab:gab116

2018-05-24T20:07:14Z

Gab116:

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1
|no
|symmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

blue = nitrogen

pink = boron

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

These MOs are the HOMOs and are relatively similar pi MOs. The MO for borazine is less symmetric than the highly symmetric benzene MO. This is a result of the highly electronegative nitrogen atoms in borazine pulling the MO towards themselves, leading to an uneven distribution of electrons.
|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

These MOs are both low energy sigma bonding MOs and are entirely in phase. However, the shape isn't particularly similar. While the benzene MO is highly symmetric, the borazine MO is less so and features no contribution from the borons' hydrogen atoms.
|}

===The Concept of Aromaticity===

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

== References ==

Inorganic Computational Lab:gab116

2018-05-24T19:40:40Z

Gab116: /* Molecular Orbital Comparison */

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1
|no
|symmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

These MOs are similar and correspond to high energy sigma bonding MOs. While the benzene MO is highly symmetric, the MOs in borazine are slightly pulled towards the nitrogen atoms due to its high electronegativity.
|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

|}

===The Concept of Aromaticity===

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

== References ==

Inorganic Computational Lab:gab116

2018-05-24T19:17:59Z

Gab116:

== EX3 section ==

===BH3===

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

[[File:Gab116_bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1
|no
|symmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

====MO Diagram for BH3====

[[File:Gab116_bh3_freq_modiagram3.PNG]]

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

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

The real MOs are more diffuse than the LCAO MOs.

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

While qualitative MO theory is useful in terms of accurately predicting the location of the MOs, it is not able to predict the volume occupied by the real MOs.

===NH3===

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

[[File:Gab116_nh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3_FREQ.LOG| GAB116_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -8.4661 -8.4184 -0.0028 0.0337 0.1931 26.4322
Low frequencies --- 1089.7605 1694.1862 1694.1866
</pre>

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:Gab116_nh3bh3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000621 0.001800 YES
RMS Displacement 0.000355 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_NH3BH3_FREQ.LOG| GAB116_NH3BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0617 -0.0457 -0.0066 21.6788 21.6848 40.5422
Low frequencies --- 266.0173 632.3610 640.1362
</pre>

<jmol><jmolApplet>
<title>optimised NH3BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===B-N Dative Bond Energy in NH3BH3===

'''NH3 + BH3 -> H3B:NH3'''

E(NH3)= -56.55777 au to 5 decimal places

E(BH3)= -26.61532 au to 5 d.p.

E(NH3BH3)= -83.22469 au to 5 d.p.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au to 5 d.p. = -135 kJ/mol (to the nearest 1 kJ/mol)

(1.00000 au = 2625.5002 kJ/mol, source: http://www.colby.edu/chemistry/PChem/Hartree.html)

'''Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?'''

The B-N dative bond is medium strength, compared to the strong C-C bond in the similarly structured ethane and the weak intermolecular Hydrogen bond in water.

C-C bond energy= 348 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986). Hydrogen bond energy in water= 22 kJ/mol, (source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 674).

===BBr3===

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

[[File:Gab116_bbr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

Frequency analysis log file [[Media:Gab116_BBr3_FREQ_scanserver.log| Gab116_BBr3_FREQ_scanserver.LOG]]

{{DOI|10042/202458}}

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Gab116_BBr3_FREQ_scanserver.log</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Aromaticity ==

===Benzene===

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

[[File:Gab116_benzene_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000780 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BENZENE_FREQ.LOG| GAB116_BENZENE_FREQ.LOG]]

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0088 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

<jmol><jmolApplet>
<title>optimised Benzene molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

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

[[File:Gab116_borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000218 0.000450 YES
RMS Force 0.000069 0.000300 YES
Maximum Displacement 0.000332 0.001800 YES
RMS Displacement 0.000106 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BORAZINE_FREQ.LOG| GAB116_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -12.5959 -12.3825 -8.9170 -0.0099 0.0381 0.0783
Low frequencies --- 289.1143 289.1234 403.9108
</pre>

<jmol><jmolApplet>
<title>optimised Borazine molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NBO Charge Analysis===

[[File:Gab116_nbo_colours.PNG]]

{| class="wikitable" border="1"
|Benzene
|Borazine
|Comparison of charge distributions
|-
|[[File:Gab116_nbo_benzene.PNG|300px]]
|[[File:Gab116_nbo_borazine.PNG|300px]]
|While all components of the 6-membered ring in benzene have equal charge, the large difference in electronegativity between the boron and nitrogen in borazine means that there is an unequal distribution of charge, leading to partial ionic character. The carbons in benzene have a small relative charge of -0.239 while the hydrogens have a charge of +0.239, meaning that there is a small dipole between the carbons and hydrogens, which is due to their small difference in electronegativity. (Pauling value for carbon= 2.55, hydrogen= 2.20, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

In borazine, the nitrogens have a large relative charge of -1.102 and the borons have a charge of +0.747, meaning that there is a large dipole between the nitrogens and the borons. This is a result of their large difference in electronegativity. While all hydrogens on benzene have the same charge, the ones on borazine have different charges depending on whether they are connected to the negatively charged nitrogen or positively charged boron. The nitrogen connected hydrogens have a relative charge of +0.432, due to nitrogen being more electronegative than hydrogen. The boron connected hydrogens have a relative charge of -0.077, due to boron being less electronegative than hydrogen. (Pauling value for boron= 2.04, hydrogen=2.20, nitrogen= 3.04, source: P. Atkins and J. de Paula, Physical Chemistry, 10th Edition, 2014, OUP, 986).

The partial ionic character and unequal distribution of charge in borazine may help to explain its higher reactivity in comparison to be benzene.
|}

===Molecular Orbital Comparison===

{| class="wikitable" border="1"
|Benzene
|Borazine
|Discussion of comparative MOs
|-
|[[File:Gab116_benzene_HOMO.PNG|300px]]
|[[File:Gab116_borazine_HOMO.PNG|300px]]
|HOMO: MO 21 (benzene) and MO 21 (borazine)

|-
|[[File:Gab116_benzene_MO14.PNG|300px]]
|[[File:Gab116_borazine_MO15.PNG|300px]]
|MO 14 (benzene) and MO 15 (borazine)

|-
|[[File:Gab116_benzene_MO7.PNG|300px]]
|[[File:Gab116_borazine_MO7.PNG|300px]]
|MO 7 (benzene) and MO 7 (borazine)

|}

===The Concept of Aromaticity===

[[File:Gab116_benzene_MO17_pz.PNG|300px]]

== References ==

File:Gab116 benzene MO17 pz.PNG

2018-05-24T19:17:27Z

Gab116:

File:Gab116 borazine MO7.PNG

2018-05-24T18:51:30Z

Gab116:

File:Gab116 benzene MO7.PNG

2018-05-24T18:49:34Z

Gab116:

File:Gab116 borazine MO15.PNG

2018-05-24T18:49:14Z

Gab116:

File:Gab116 benzene MO14.PNG

2018-05-24T18:48:51Z

Gab116:

File:Gab116 borazine HOMO.PNG

2018-05-24T18:34:39Z

Gab116:

File:Gab116 benzene HOMO.PNG

2018-05-24T18:34:20Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-24T16:26:39Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-24T15:54:20Z

Gab116:

File:Gab116 nbo borazine.PNG

2018-05-24T15:27:44Z

Gab116:

File:Gab116 nbo benzene.PNG

2018-05-24T15:27:01Z

Gab116:

File:Gab116 nbo colours.PNG

2018-05-24T15:22:59Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-24T15:02:35Z

Gab116:

File:GAB116 BORAZINE FREQ.LOG

2018-05-24T15:00:53Z

Gab116:

File:Gab116 borazine freq summary.PNG

2018-05-24T14:58:31Z

Gab116:

File:GAB116 BENZENE FREQ.LOG

2018-05-24T14:27:48Z

Gab116:

File:Gab116 benzene freq summary.PNG

2018-05-24T14:24:44Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-23T17:45:03Z

Gab116:

File:Gab116 BBr3 FREQ scanserver.log

2018-05-23T17:28:54Z

Gab116:

File:Gab116 bbr3 freq summary.PNG

2018-05-23T17:24:49Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-23T15:20:47Z

Gab116: /* BH3 */

Inorganic Computational Lab:gab116

2018-05-23T15:20:33Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-23T14:50:36Z

Gab116: /* B-N Dative Bond Energy in NH3BH3 */

Inorganic Computational Lab:gab116

2018-05-23T14:50:04Z

Gab116: /* B-N Dative Bond Energy in NH3BH3 */

Inorganic Computational Lab:gab116

2018-05-23T14:48:38Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-22T19:45:15Z

Gab116:

File:GAB116 NH3BH3 FREQ.LOG

2018-05-22T19:42:33Z

Gab116:

File:Gab116 nh3bh3 freq summary.PNG

2018-05-22T19:40:00Z

Gab116:

File:GAB116 NH3 FREQ.LOG

2018-05-22T19:15:09Z

Gab116:

File:Gab116 nh3 freq summary.PNG

2018-05-22T19:12:48Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-22T18:18:44Z

Gab116: /* B3LYP/6-31G (d,p) level */

Inorganic Computational Lab:gab116

2018-05-22T18:04:10Z

Gab116: /* MO Diagram for BH3 */

Inorganic Computational Lab:gab116

2018-05-22T18:03:53Z

Gab116:

File:Gab116 bh3 freq modiagram3.PNG

2018-05-22T17:52:01Z

Gab116:

Inorganic Computational Lab:gab116

2018-05-22T16:50:24Z

Gab116:

== EX3 section ==

===BH3===

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

[[File:Gab116 bh3 freq summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1
|no
|symmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). As a result, there are three peaks in the spectrum even though there are six vibrations.

== Project section ==

== References ==

Inorganic Computational Lab:gab116

2018-05-22T16:49:23Z

Gab116:

== EX3 section ==

===BH3===

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

[[File:Gab116 bh3 freq summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:GAB116_BH3_FREQ.LOG| GAB116_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0056 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>GAB116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1
|no
|symmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|-
|2716
|126
|E
|yes
|asymmetric stretch
|}

|[[File:Gab116_bh3_freq_spectrum.PNG|400px]]

There are fewer vibrational peaks than there are vibrations as not all vibrations are IR active, e.g. at 2582 cm-1. In addition, there are two pairs of vibrations that occur at the same wavenumber and hence overlap (at 2716 cm-1 and 1213 cm-1). Hence there are three peaks in the spectrum, although there are six vibrations.

== Project section ==

== References ==

File:Gab116 bh3 freq spectrum.PNG

2018-05-22T16:42:51Z

Gab116: