==Revision Section==

===BH<sub>3</sub>===

[[File:Bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

[[Media:BH3 2 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -1.1800 -1.0028 -0.0055 4.1927 11.0182 11.0637
Low frequencies --- 1162.9912 1213.1792 1213.1819
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BH3 2 OPT jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:Bh3 spectrum jg2016.PNG|800px]]

{| class="wikitable" border="1"
|+ Vibration Analysis
! Frequency/cm<sup>-1</sup> !! Intensity !! Symmetry !! IR Active? !! Type of Vibration
|-
| 1164 || 93 || A2" || Yes || Out of plane Bend
|-
| 1214 || 14 || E' || Slightly || Bend
|-
| 1214 || 14 || E' || Slightly || Asymmetric in plane Bend
|-
| 2580 || 0 || A1' || No || Symmetric Stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|}

There are less than 6 peaks in the IR spectrum of BH<sub>3</sub> even though there are 6 distinct vibrations because the A1' vibration at 2580 cm<sup>-1</sup> doesn't produce a change in dipole moment and so is IR inactive and will not produce a peak at all. In addition, there are 2 vibrations which have the exact same symmetry and energy at 1214 cm<sup>-1</sup> and so their individual peaks will superimpose to only show 1 peak. The exact same situation is happening with the 2 vibrations at 2713 cm<sup>-1</sup> so these 2 vibrations will be superimposed and only show 1 peak. This explains why only 3 peaks are seen in this spectrum.

[[File:Bh3 mo jg2016.PNG|800px]]
<ref name="hunt" />

{| class="wikitable" border="1"
|+ Vibration Analysis
! 1a<sub>1</sub>' !! 2a<sub>1</sub>' !! 1e' !! 1e' !! 1a<sub>2</sub>'' !! 3a<sub>2</sub>' !! 2e' !! 2e'
|-
| [[File:Bh3 1a1' jg2016.PNG|200px]] || [[File:Bh3 a1' jg2016.PNG|200px]] || [[File:Bh3 e' jg2016.PNG|200px]] || [[File:Bh3 e'2 jg2016.PNG|200px]] || [[File:Bh3 a1'' jg2016.PNG|200px]] || [[File:Bh3 a'' jg2016.PNG]] || [[File:Bh3 2e' jg2016.PNG|200px]] || [[File:Bh3 2e'2 jg2016.PNG|200px]]
|}

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

[[File:Nh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[Media:NH3 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3 FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

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

[[File:Nh3bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

[[Media:NH3BH3 FREQ 2 jg2016.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1240 17.1263 37.1338
Low frequencies --- 265.7821 632.2034 639.3485
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3BH3 FREQ 2 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Association Energy===

E(NH<sub>3</sub>)=-56.55777 A.U.

E(BH<sub>3</sub>)=-26.61532 A.U.

E(NH<sub>3</sub>BH<sub>3</sub>)=-83.22469 A.U.

ΔE=E(NH<sub>3</sub>BH<sub>3</sub>)-[E(NH<sub>3</sub>)+E(BH<sub>3</sub>)]=0.0516 A.U.=135 kJ mol<sup>-1</sup>

==BBr<sub>3</sub>==

[[File:Bbr3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
</pre>

{{DOI|10042/202450}}

<pre>
Low frequencies --- -2.3055 -0.0029 -0.0018 0.0774 0.7534 0.7534
Low frequencies --- 155.9402 155.9405 267.6894
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Bbr3 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

==Investigating Aromaticity==

===Benzene===

[[File:Benzene summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

[[Media:BENZENE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0009
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BENZENE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Borazine===

[[File:Borazine summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

[[Media:BORAZINE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -0.0010 -0.0010 -0.0010 3.5555 4.4272 6.8943
Low frequencies --- 289.7109 289.7845 404.4187
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BORAZINE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Analysis===

====Charge Distribution====

{| class="wikitable" border="1"
|+ MOs
| [[File:Benzene charge distribution jg2016.PNG|500px|thumb|left|Benzene charge distribution]] || [[File:Borazine charge distribution jg2016.PNG|500px|thumb|right|Borazine charge distribution]]
|}

In benzene all the atoms involved in the aromaticty (the carbons) have the same, slight negative charge of -0.239 and therefore all the hydrogens also have the same positive 0.239 charge. In borazine the boron atoms have a +0.747 charge while all the nitrogen atoms have a -1.102 charge. The hydrogen atoms bonded to the boron atoms have a -0.077 charge and the hydrogen atoms bonded to the nitrogen atoms have a +0.432 charge.

Carbon and hydrogen have similar electronegativities and so there is minimal charge separation between the carbon and hydrogen bond in benzene. Nitrogen is more electronegative than Boron and so in the aromatic ring of borazine there will be a build up of electron density at the nitrogen atoms and a deficiency of electrons at the boron atoms. Hydrogen is less electronegative than nitrogen and so the hydrogens bonded to nitrogen will have a very positive charge. Boron and hydrogen have very similar electronegativities but the boron atoms in aromatic ring are partially positive so the hydrogens attached to boron in borazine have a very small negative charge.

====Molecular Orbitals====

{| class="wikitable" border="1"
|+ MOs
! Benzene !! Borazine !! Deconstructed orbital
|-
| [[File:MO 1 - Benzene - 0.43854 jg2016.PNG|thumb]] || [[File:MO 1 - Borazine - 0.43198 jg2016.PNG|thumb]] || [[File:MO 1 jg2016.png|200px]] || These orbitals are MO 14 in benzene and MO 15 in borazine. Both are made up from a superposition of 6 px orbitals and are very similar between the molecules. MO 15 in borazine has lobes which are slightly skewed towards the nitrogen atoms compared to the symmetrical lobes in MO 14 of benzene, this is due to nitrogen having lower energy px orbitals and so contributing more to the electrond denisty of this MO. As such the borazine MO has a lower symmetry than the benzene MO but both have no character from the hydrogen atoms. These orbitals help make up the sigma framework of the molecule and show weak bonding character as there are 3 nodes but they are all going through nuclei in the molecule and not between them.
|-
| [[File:MO_2_-_Benzene_-_0.35997_jg2016.PNG|thumb]] || [[File:MO 2 - Borazine - 0.36130 jg2016.PNG|thumb]] || [[File:MO 2 jg2016.png|200px]] || These orbitals are MO 17 in both benzene and borazine. Both are made up from a superposition of 6 pz orbitals and are very similar between the molecules. It can be seen however that there is slightly more electron density around the nitrogen atoms in the aromatic ring compared to the boron atoms in borazine which is different to benzene where the electron density around all 6 carbon atoms are identical. MO 17 in benzene is therefore more symmetric than MO 17 in borazine because of this. These orbitals help make up the pi bonding framework of each molecule and show strong bonding character as it concentrates electron density between the nuclei.
|-
| [[File:MO 3 - Benzene - 0.24691 jg2016.PNG|thumb]] || [[File:MO 3 - Borazine - 0.27591 jg2016.PNG|thumb]] || [[File:MO 3 jg2016.png|200px]] || These orbitals are MO 21 in benzene and MO 20 in borazine. Both are made up of a superposition of 6 pz orbitals but 3 adjacent orbitals are in an opposite phase to the other p orbitals. This produces bonding character between 3 atoms on each side of the molecule but it also has anti-bonding character through the centre of the molecule where there is a nodal plane. The MO in benzene is more symmetrical than the MO in borazine as the nodal plane is also a mirror plane. This cannot be said for the MO in borazine because The side which has 2 boron atoms and 1 nitrogen atoms has less electron density than the side which has 2 nitrogen atoms and 1 boron atom. This is due to nitrogen having lower energy p orbitals than boron and so providing a bigger contribution to the bonding MO than boron. These orbitals are overall bonding and are part of the pi framework of each molecule.
|}

====Aromaticty====

Aromaticty in its most basic sense describes a molecule with a delocalised cyclic pi electron system. Traditionally a molecule was described as aromatic if it had 4n+2 pi electrons and was cyclic and planar. This produced an aromatic stabilisation energy which made these molecules more stable when compared to its theoretical non aromatic structure, and had bond lengths in between single and double bonds. This simple description of aromaticty doesn't account for the molecules which exhibit aromaticity even though they aren't planar and undermines the contribution of sigma bonding to the aromatic character of some molecules.<ref name="aromaticity" />

Originally delocalisation of electrons around an aromatic molecule was thought to be due to pz orbital overlap but through calculations using molecular orbital theory it can be seen that other atomic orbitals will combine to form molecular orbitals which delocalise electrons around the molecule. For example, MO 14 for benzene shown above is not formed from the linear combination of pz orbitals above and below the plane of the molecules but px orbitals in the plane of the molecule. This produces a delocalised sigma framework which will be equally as responsible for stabilising aromatic compounds as the pi bonding system. This means that stating overlapping pz orbitals as a description for aromaticity is inaccurate because many other atomic orbitals in each atom will be responsible for producing MOs which delocalise electrons around the molecule and producing the stabilising effect attributed to aromaticity.

==References==
<references>
<ref name="hunt">Hunt.P (2018). Molecular Orbitals in Inorganic Chemistry. Tutorial after Lecture 4 Notes. [pdf] Retrieved from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf.</ref>
<ref name="aromaticity">Palusiak, M. and Krygowski, T. (2007). Application of AIM Parameters at Ring Critical Points for Estimation of π-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings. Chemistry - A European Journal, 13(28), pp.7996-8006.</ref>
</references>

File:Bh3 a'' jg2016.PNG

2018-05-25T12:18:51Z

Jg2016:

Rep:Mod:jg2016-hunt

2018-05-25T12:13:28Z

Jg2016:

==Revision Section==

===BH<sub>3</sub>===

[[File:Bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

[[Media:BH3 2 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -1.1800 -1.0028 -0.0055 4.1927 11.0182 11.0637
Low frequencies --- 1162.9912 1213.1792 1213.1819
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BH3 2 OPT jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:Bh3 spectrum jg2016.PNG|800px]]

{| class="wikitable" border="1"
|+ Vibration Analysis
! Frequency/cm<sup>-1</sup> !! Intensity !! Symmetry !! IR Active? !! Type of Vibration
|-
| 1164 || 93 || A2" || Yes || Out of plane Bend
|-
| 1214 || 14 || E' || Slightly || Bend
|-
| 1214 || 14 || E' || Slightly || Asymmetric in plane Bend
|-
| 2580 || 0 || A1' || No || Symmetric Stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|}

There are less than 6 peaks in the IR spectrum of BH<sub>3</sub> even though there are 6 distinct vibrations because the A1' vibration at 2580 cm<sup>-1</sup> doesn't produce a change in dipole moment and so is IR inactive and will not produce a peak at all. In addition, there are 2 vibrations which have the exact same symmetry and energy at 1214 cm<sup>-1</sup> and so their individual peaks will superimpose to only show 1 peak. The exact same situation is happening with the 2 vibrations at 2713 cm<sup>-1</sup> so these 2 vibrations will be superimposed and only show 1 peak. This explains why only 3 peaks are seen in this spectrum.

[[File:Bh3 mo jg2016.PNG|800px]]
<ref name="hunt" />

{| class="wikitable" border="1"
|+ Vibration Analysis
! 1a<sub>1</sub>' !! 2a<sub>1</sub>' !! 1e' !! 1e' !! 1a<sub>2</sub>'' !! 3a<sub>2</sub>' !! 2e' !! 2e'
|-
| [[File:Bh3 1a1' jg2016.PNG|200px]] || [[File:Bh3 a1' jg2016.PNG|200px]] || [[File:Bh3 e' jg2016.PNG|200px]] || [[File:Bh3 e'2 jg2016.PNG|200px]] || [[File:Bh3 a1'' jg2016.PNG|200px]] || [[File:Bh3 2e' jg2016.PNG|200px]] || [[File:Bh3 2e'2 jg2016.PNG|200px]]
|}

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

[[File:Nh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[Media:NH3 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3 FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

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

[[File:Nh3bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

[[Media:NH3BH3 FREQ 2 jg2016.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1240 17.1263 37.1338
Low frequencies --- 265.7821 632.2034 639.3485
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3BH3 FREQ 2 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Association Energy===

E(NH<sub>3</sub>)=-56.55777 A.U.

E(BH<sub>3</sub>)=-26.61532 A.U.

E(NH<sub>3</sub>BH<sub>3</sub>)=-83.22469 A.U.

ΔE=E(NH<sub>3</sub>BH<sub>3</sub>)-[E(NH<sub>3</sub>)+E(BH<sub>3</sub>)]=0.0516 A.U.=135 kJ mol<sup>-1</sup>

==BBr<sub>3</sub>==

[[File:Bbr3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
</pre>

{{DOI|10042/202450}}

<pre>
Low frequencies --- -2.3055 -0.0029 -0.0018 0.0774 0.7534 0.7534
Low frequencies --- 155.9402 155.9405 267.6894
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Bbr3 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

==Investigating Aromaticity==

===Benzene===

[[File:Benzene summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

[[Media:BENZENE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0009
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BENZENE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Borazine===

[[File:Borazine summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

[[Media:BORAZINE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -0.0010 -0.0010 -0.0010 3.5555 4.4272 6.8943
Low frequencies --- 289.7109 289.7845 404.4187
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BORAZINE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Analysis===

====Charge Distribution====

{| class="wikitable" border="1"
|+ MOs
| [[File:Benzene charge distribution jg2016.PNG|500px|thumb|left|Benzene charge distribution]] || [[File:Borazine charge distribution jg2016.PNG|500px|thumb|right|Borazine charge distribution]]
|}

In benzene all the atoms involved in the aromaticty (the carbons) have the same, slight negative charge of -0.239 and therefore all the hydrogens also have the same positive 0.239 charge. In borazine the boron atoms have a +0.747 charge while all the nitrogen atoms have a -1.102 charge. The hydrogen atoms bonded to the boron atoms have a -0.077 charge and the hydrogen atoms bonded to the nitrogen atoms have a +0.432 charge.

Carbon and hydrogen have similar electronegativities and so there is minimal charge separation between the carbon and hydrogen bond in benzene. Nitrogen is more electronegative than Boron and so in the aromatic ring of borazine there will be a build up of electron density at the nitrogen atoms and a deficiency of electrons at the boron atoms. Hydrogen is less electronegative than nitrogen and so the hydrogens bonded to nitrogen will have a very positive charge. Boron and hydrogen have very similar electronegativities but the boron atoms in aromatic ring are partially positive so the hydrogens attached to boron in borazine have a very small negative charge.

====Molecular Orbitals====

{| class="wikitable" border="1"
|+ MOs
! Benzene !! Borazine !! Deconstructed orbital
|-
| [[File:MO 1 - Benzene - 0.43854 jg2016.PNG|thumb]] || [[File:MO 1 - Borazine - 0.43198 jg2016.PNG|thumb]] || [[File:MO 1 jg2016.png|200px]] || These orbitals are MO 14 in benzene and MO 15 in borazine. Both are made up from a superposition of 6 px orbitals and are very similar between the molecules. MO 15 in borazine has lobes which are slightly skewed towards the nitrogen atoms compared to the symmetrical lobes in MO 14 of benzene, this is due to nitrogen having lower energy px orbitals and so contributing more to the electrond denisty of this MO. As such the borazine MO has a lower symmetry than the benzene MO but both have no character from the hydrogen atoms. These orbitals help make up the sigma framework of the molecule and show weak bonding character as there are 3 nodes but they are all going through nuclei in the molecule and not between them.
|-
| [[File:MO_2_-_Benzene_-_0.35997_jg2016.PNG|thumb]] || [[File:MO 2 - Borazine - 0.36130 jg2016.PNG|thumb]] || [[File:MO 2 jg2016.png|200px]] || These orbitals are MO 17 in both benzene and borazine. Both are made up from a superposition of 6 pz orbitals and are very similar between the molecules. It can be seen however that there is slightly more electron density around the nitrogen atoms in the aromatic ring compared to the boron atoms in borazine which is different to benzene where the electron density around all 6 carbon atoms are identical. MO 17 in benzene is therefore more symmetric than MO 17 in borazine because of this. These orbitals help make up the pi bonding framework of each molecule and show strong bonding character as it concentrates electron density between the nuclei.
|-
| [[File:MO 3 - Benzene - 0.24691 jg2016.PNG|thumb]] || [[File:MO 3 - Borazine - 0.27591 jg2016.PNG|thumb]] || [[File:MO 3 jg2016.png|200px]] || These orbitals are MO 21 in benzene and MO 20 in borazine. Both are made up of a superposition of 6 pz orbitals but 3 adjacent orbitals are in an opposite phase to the other p orbitals. This produces bonding character between 3 atoms on each side of the molecule but it also has anti-bonding character through the centre of the molecule where there is a nodal plane. The MO in benzene is more symmetrical than the MO in borazine as the nodal plane is also a mirror plane. This cannot be said for the MO in borazine because The side which has 2 boron atoms and 1 nitrogen atoms has less electron density than the side which has 2 nitrogen atoms and 1 boron atom. This is due to nitrogen having lower energy p orbitals than boron and so providing a bigger contribution to the bonding MO than boron. These orbitals are overall bonding and are part of the pi framework of each molecule.
|}

====Aromaticty====

Aromaticty in its most basic sense describes a molecule with a delocalised cyclic pi electron system. Traditionally a molecule was described as aromatic if it had 4n+2 pi electrons and was cyclic and planar. This produced an aromatic stabilisation energy which made these molecules more stable when compared to its theoretical non aromatic structure, and had bond lengths in between single and double bonds. This simple description of aromaticty doesn't account for the molecules which exhibit aromaticity even though they aren't planar and undermines the contribution of sigma bonding to the aromatic character of some molecules.<ref name="aromaticity" />

Originally delocalisation of electrons around an aromatic molecule was thought to be due to pz orbital overlap but through calculations using molecular orbital theory it can be seen that other atomic orbitals will combine to form molecular orbitals which delocalise electrons around the molecule. For example, MO 14 for benzene shown above is not formed from the linear combination of pz orbitals above and below the plane of the molecules but px orbitals in the plane of the molecule. This produces a delocalised sigma framework which will be equally as responsible for stabilising aromatic compounds as the pi bonding system. This means that stating overlapping pz orbitals as a description for aromaticity is inaccurate because many other atomic orbitals in each atom will be responsible for producing MOs which delocalise electrons around the molecule and producing the stabilising effect attributed to aromaticity.

==References==
<references>
<ref name="hunt">Hunt.P (2018). Molecular Orbitals in Inorganic Chemistry. Tutorial after Lecture 4 Notes. [pdf] Retrieved from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf.</ref>
<ref name="aromaticity">Palusiak, M. and Krygowski, T. (2007). Application of AIM Parameters at Ring Critical Points for Estimation of π-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings. Chemistry - A European Journal, 13(28), pp.7996-8006.</ref>
</references>

Rep:Mod:jg2016-hunt

2018-05-25T12:12:54Z

Jg2016:

==Revision Section==

===BH<sub>3</sub>===

[[File:Bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

[[Media:BH3 2 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -1.1800 -1.0028 -0.0055 4.1927 11.0182 11.0637
Low frequencies --- 1162.9912 1213.1792 1213.1819
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BH3 2 OPT jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:Bh3 spectrum jg2016.PNG|800px]]

{| class="wikitable" border="1"
|+ Vibration Analysis
! Frequency/cm<sup>-1</sup> !! Intensity !! Symmetry !! IR Active? !! Type of Vibration
|-
| 1164 || 93 || A2" || Yes || Out of plane Bend
|-
| 1214 || 14 || E' || Slightly || Bend
|-
| 1214 || 14 || E' || Slightly || Asymmetric in plane Bend
|-
| 2580 || 0 || A1' || No || Symmetric Stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|}

There are less than 6 peaks in the IR spectrum of BH<sub>3</sub> even though there are 6 distinct vibrations because the A1' vibration at 2580 cm<sup>-1</sup> doesn't produce a change in dipole moment and so is IR inactive and will not produce a peak at all. In addition, there are 2 vibrations which have the exact same symmetry and energy at 1214 cm<sup>-1</sup> and so their individual peaks will superimpose to only show 1 peak. The exact same situation is happening with the 2 vibrations at 2713 cm<sup>-1</sup> so these 2 vibrations will be superimposed and only show 1 peak. This explains why only 3 peaks are seen in this spectrum.

[[File:Bh3 mo jg2016.PNG|800px]]
<ref name="hunt" />

{| class="wikitable" border="1"
|+ Vibration Analysis
! 1a<sub>1</sub>' !! 2a<sub>1</sub>' !! 1e' !! 1e' !! 1a<sub>2</sub>'' !! 3a<sub>2</sub>' !! 2e' !! 2e'
|-
| [[File:Bh3 1a1' jg2016.PNG|300px]] || [[File:Bh3 a1' jg2016.PNG|300px]] || [[File:Bh3 e' jg2016.PNG|300px]] || [[File:Bh3 e'2 jg2016.PNG|300px]] || [[File:Bh3 a1'' jg2016.PNG|300px]] || [[File:Bh3 2e' jg2016.PNG|300px]] || [[File:Bh3 2e'2 jg2016.PNG|300px]]
|}

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

[[File:Nh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[Media:NH3 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3 FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

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

[[File:Nh3bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

[[Media:NH3BH3 FREQ 2 jg2016.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1240 17.1263 37.1338
Low frequencies --- 265.7821 632.2034 639.3485
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3BH3 FREQ 2 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Association Energy===

E(NH<sub>3</sub>)=-56.55777 A.U.

E(BH<sub>3</sub>)=-26.61532 A.U.

E(NH<sub>3</sub>BH<sub>3</sub>)=-83.22469 A.U.

ΔE=E(NH<sub>3</sub>BH<sub>3</sub>)-[E(NH<sub>3</sub>)+E(BH<sub>3</sub>)]=0.0516 A.U.=135 kJ mol<sup>-1</sup>

==BBr<sub>3</sub>==

[[File:Bbr3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
</pre>

{{DOI|10042/202450}}

<pre>
Low frequencies --- -2.3055 -0.0029 -0.0018 0.0774 0.7534 0.7534
Low frequencies --- 155.9402 155.9405 267.6894
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Bbr3 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

==Investigating Aromaticity==

===Benzene===

[[File:Benzene summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

[[Media:BENZENE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0009
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BENZENE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Borazine===

[[File:Borazine summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

[[Media:BORAZINE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -0.0010 -0.0010 -0.0010 3.5555 4.4272 6.8943
Low frequencies --- 289.7109 289.7845 404.4187
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BORAZINE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Analysis===

====Charge Distribution====

{| class="wikitable" border="1"
|+ MOs
| [[File:Benzene charge distribution jg2016.PNG|500px|thumb|left|Benzene charge distribution]] || [[File:Borazine charge distribution jg2016.PNG|500px|thumb|right|Borazine charge distribution]]
|}

In benzene all the atoms involved in the aromaticty (the carbons) have the same, slight negative charge of -0.239 and therefore all the hydrogens also have the same positive 0.239 charge. In borazine the boron atoms have a +0.747 charge while all the nitrogen atoms have a -1.102 charge. The hydrogen atoms bonded to the boron atoms have a -0.077 charge and the hydrogen atoms bonded to the nitrogen atoms have a +0.432 charge.

Carbon and hydrogen have similar electronegativities and so there is minimal charge separation between the carbon and hydrogen bond in benzene. Nitrogen is more electronegative than Boron and so in the aromatic ring of borazine there will be a build up of electron density at the nitrogen atoms and a deficiency of electrons at the boron atoms. Hydrogen is less electronegative than nitrogen and so the hydrogens bonded to nitrogen will have a very positive charge. Boron and hydrogen have very similar electronegativities but the boron atoms in aromatic ring are partially positive so the hydrogens attached to boron in borazine have a very small negative charge.

====Molecular Orbitals====

{| class="wikitable" border="1"
|+ MOs
! Benzene !! Borazine !! Deconstructed orbital
|-
| [[File:MO 1 - Benzene - 0.43854 jg2016.PNG|thumb]] || [[File:MO 1 - Borazine - 0.43198 jg2016.PNG|thumb]] || [[File:MO 1 jg2016.png|200px]] || These orbitals are MO 14 in benzene and MO 15 in borazine. Both are made up from a superposition of 6 px orbitals and are very similar between the molecules. MO 15 in borazine has lobes which are slightly skewed towards the nitrogen atoms compared to the symmetrical lobes in MO 14 of benzene, this is due to nitrogen having lower energy px orbitals and so contributing more to the electrond denisty of this MO. As such the borazine MO has a lower symmetry than the benzene MO but both have no character from the hydrogen atoms. These orbitals help make up the sigma framework of the molecule and show weak bonding character as there are 3 nodes but they are all going through nuclei in the molecule and not between them.
|-
| [[File:MO_2_-_Benzene_-_0.35997_jg2016.PNG|thumb]] || [[File:MO 2 - Borazine - 0.36130 jg2016.PNG|thumb]] || [[File:MO 2 jg2016.png|200px]] || These orbitals are MO 17 in both benzene and borazine. Both are made up from a superposition of 6 pz orbitals and are very similar between the molecules. It can be seen however that there is slightly more electron density around the nitrogen atoms in the aromatic ring compared to the boron atoms in borazine which is different to benzene where the electron density around all 6 carbon atoms are identical. MO 17 in benzene is therefore more symmetric than MO 17 in borazine because of this. These orbitals help make up the pi bonding framework of each molecule and show strong bonding character as it concentrates electron density between the nuclei.
|-
| [[File:MO 3 - Benzene - 0.24691 jg2016.PNG|thumb]] || [[File:MO 3 - Borazine - 0.27591 jg2016.PNG|thumb]] || [[File:MO 3 jg2016.png|200px]] || These orbitals are MO 21 in benzene and MO 20 in borazine. Both are made up of a superposition of 6 pz orbitals but 3 adjacent orbitals are in an opposite phase to the other p orbitals. This produces bonding character between 3 atoms on each side of the molecule but it also has anti-bonding character through the centre of the molecule where there is a nodal plane. The MO in benzene is more symmetrical than the MO in borazine as the nodal plane is also a mirror plane. This cannot be said for the MO in borazine because The side which has 2 boron atoms and 1 nitrogen atoms has less electron density than the side which has 2 nitrogen atoms and 1 boron atom. This is due to nitrogen having lower energy p orbitals than boron and so providing a bigger contribution to the bonding MO than boron. These orbitals are overall bonding and are part of the pi framework of each molecule.
|}

====Aromaticty====

Aromaticty in its most basic sense describes a molecule with a delocalised cyclic pi electron system. Traditionally a molecule was described as aromatic if it had 4n+2 pi electrons and was cyclic and planar. This produced an aromatic stabilisation energy which made these molecules more stable when compared to its theoretical non aromatic structure, and had bond lengths in between single and double bonds. This simple description of aromaticty doesn't account for the molecules which exhibit aromaticity even though they aren't planar and undermines the contribution of sigma bonding to the aromatic character of some molecules.<ref name="aromaticity" />

Originally delocalisation of electrons around an aromatic molecule was thought to be due to pz orbital overlap but through calculations using molecular orbital theory it can be seen that other atomic orbitals will combine to form molecular orbitals which delocalise electrons around the molecule. For example, MO 14 for benzene shown above is not formed from the linear combination of pz orbitals above and below the plane of the molecules but px orbitals in the plane of the molecule. This produces a delocalised sigma framework which will be equally as responsible for stabilising aromatic compounds as the pi bonding system. This means that stating overlapping pz orbitals as a description for aromaticity is inaccurate because many other atomic orbitals in each atom will be responsible for producing MOs which delocalise electrons around the molecule and producing the stabilising effect attributed to aromaticity.

==References==
<references>
<ref name="hunt">Hunt.P (2018). Molecular Orbitals in Inorganic Chemistry. Tutorial after Lecture 4 Notes. [pdf] Retrieved from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf.</ref>
<ref name="aromaticity">Palusiak, M. and Krygowski, T. (2007). Application of AIM Parameters at Ring Critical Points for Estimation of π-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings. Chemistry - A European Journal, 13(28), pp.7996-8006.</ref>
</references>

Rep:Mod:jg2016-hunt

2018-05-25T12:12:12Z

2018-05-25T11:52:06Z

Jg2016: /* BH3 */

==Revision Section==

===BH<sub>3</sub>===

[[File:Bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

[[Media:BH3 2 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -1.1800 -1.0028 -0.0055 4.1927 11.0182 11.0637
Low frequencies --- 1162.9912 1213.1792 1213.1819
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BH3 2 OPT jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:Bh3 spectrum jg2016.PNG|800px]]

{| class="wikitable" border="1"
|+ Vibration Analysis
! Frequency/cm<sup>-1</sup> !! Intensity !! Symmetry !! IR Active? !! Type of Vibration
|-
| 1164 || 93 || A2" || Yes || Out of plane Bend
|-
| 1214 || 14 || E' || Slightly || Bend
|-
| 1214 || 14 || E' || Slightly || Asymmetric in plane Bend
|-
| 2580 || 0 || A1' || No || Symmetric Stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|}

There are less than 6 peaks in the IR spectrum of BH<sub>3</sub> even though there are 6 distinct vibrations because the A1' vibration at 2580 cm<sup>-1</sup> doesn't produce a change in dipole moment and so is IR inactive and will not produce a peak at all. In addition, there are 2 vibrations which have the exact same symmetry and energy at 1214 cm<sup>-1</sup> and so their individual peaks will superimpose to only show 1 peak. The exact same situation is happening with the 2 vibrations at 2713 cm<sup>-1</sup> so these 2 vibrations will be superimposed and only show 1 peak. This explains why only 3 peaks are seen in this spectrum.

[[File:Bh3 mo jg2016.PNG|800px]]
<ref name="hunt" />

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

[[File:Nh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[Media:NH3 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3 FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

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

[[File:Nh3bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

[[Media:NH3BH3 FREQ 2 jg2016.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1240 17.1263 37.1338
Low frequencies --- 265.7821 632.2034 639.3485
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3BH3 FREQ 2 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Association Energy===

E(NH<sub>3</sub>)=-56.55777 A.U.

E(BH<sub>3</sub>)=-26.61532 A.U.

E(NH<sub>3</sub>BH<sub>3</sub>)=-83.22469 A.U.

ΔE=E(NH<sub>3</sub>BH<sub>3</sub>)-[E(NH<sub>3</sub>)+E(BH<sub>3</sub>)]=0.0516 A.U.=135 kJ mol<sup>-1</sup>

==BBr<sub>3</sub>==

[[File:Bbr3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
</pre>

{{DOI|10042/202450}}

<pre>
Low frequencies --- -2.3055 -0.0029 -0.0018 0.0774 0.7534 0.7534
Low frequencies --- 155.9402 155.9405 267.6894
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Bbr3 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

==Investigating Aromaticity==

===Benzene===

[[File:Benzene summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

[[Media:BENZENE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0009
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BENZENE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Borazine===

[[File:Borazine summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

[[Media:BORAZINE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -0.0010 -0.0010 -0.0010 3.5555 4.4272 6.8943
Low frequencies --- 289.7109 289.7845 404.4187
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BORAZINE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Analysis===

====Charge Distribution====

{| class="wikitable" border="1"
|+ MOs
| [[File:Benzene charge distribution jg2016.PNG|500px|thumb|left|Benzene charge distribution]] || [[File:Borazine charge distribution jg2016.PNG|500px|thumb|right|Borazine charge distribution]]
|}

In benzene all the atoms involved in the aromaticty (the carbons) have the same, slight negative charge of -0.239 and therefore all the hydrogens also have the same positive 0.239 charge. In borazine the boron atoms have a +0.747 charge while all the nitrogen atoms have a -1.102 charge. The hydrogen atoms bonded to the boron atoms have a -0.077 charge and the hydrogen atoms bonded to the nitrogen atoms have a +0.432 charge.

Carbon and hydrogen have similar electronegativities and so there is minimal charge separation between the carbon and hydrogen bond in benzene. Nitrogen is more electronegative than Boron and so in the aromatic ring of borazine there will be a build up of electron density at the nitrogen atoms and a deficiency of electrons at the boron atoms. Hydrogen is less electronegative than nitrogen and so the hydrogens bonded to nitrogen will have a very positive charge. Boron and hydrogen have very similar electronegativities but the boron atoms in aromatic ring are partially positive so the hydrogens attached to boron in borazine have a very small negative charge.

====Molecular Orbitals====

{| class="wikitable" border="1"
|+ MOs
! Benzene !! Borazine !! Deconstructed orbital
|-
| [[File:MO 1 - Benzene - 0.43854 jg2016.PNG|thumb]] || [[File:MO 1 - Borazine - 0.43198 jg2016.PNG|thumb]] || [[File:MO 1 jg2016.png|200px]] || These orbitals are MO 14 in benzene and MO 15 in borazine. Both are made up from a superposition of 6 px orbitals and are very similar between the molecules. MO 15 in borazine has lobes which are slightly skewed towards the nitrogen atoms compared to the symmetrical lobes in MO 14 of benzene, this is due to nitrogen having lower energy px orbitals and so contributing more to the electrond denisty of this MO. As such the borazine MO has a lower symmetry than the benzene MO but both have no character from the hydrogen atoms. These orbitals help make up the sigma framework of the molecule and show weak bonding character as there are 3 nodes but they are all going through nuclei in the molecule and not between them.
|-
| [[File:MO_2_-_Benzene_-_0.35997_jg2016.PNG|thumb]] || [[File:MO 2 - Borazine - 0.36130 jg2016.PNG|thumb]] || [[File:MO 2 jg2016.png|200px]] || These orbitals are MO 17 in both benzene and borazine. Both are made up from a superposition of 6 pz orbitals and are very similar between the molecules. It can be seen however that there is slightly more electron density around the nitrogen atoms in the aromatic ring compared to the boron atoms in borazine which is different to benzene where the electron density around all 6 carbon atoms are identical. MO 17 in benzene is therefore more symmetric than MO 17 in borazine because of this. These orbitals help make up the pi bonding framework of each molecule and show strong bonding character as it concentrates electron density between the nuclei.
|-
| [[File:MO 3 - Benzene - 0.24691 jg2016.PNG|thumb]] || [[File:MO 3 - Borazine - 0.27591 jg2016.PNG|thumb]] || [[File:MO 3 jg2016.png|200px]] || These orbitals are MO 21 in benzene and MO 20 in borazine. Both are made up of a superposition of 6 pz orbitals but 3 adjacent orbitals are in an opposite phase to the other p orbitals. This produces bonding character between 3 atoms on each side of the molecule but it also has anti-bonding character through the centre of the molecule where there is a nodal plane. The MO in benzene is more symmetrical than the MO in borazine as the nodal plane is also a mirror plane. This cannot be said for the MO in borazine because The side which has 2 boron atoms and 1 nitrogen atoms has less electron density than the side which has 2 nitrogen atoms and 1 boron atom. This is due to nitrogen having lower energy p orbitals than boron and so providing a bigger contribution to the bonding MO than boron. These orbitals are overall bonding and are part of the pi framework of each molecule.
|}

====Aromaticty====

Aromaticty in its most basic sense describes a molecule with a delocalised cyclic pi electron system. Traditionally a molecule was described as aromatic if it had 4n+2 pi electrons and was cyclic and planar. This produced an aromatic stabilisation energy which made these molecules more stable when compared to its theoretical non aromatic structure, and had bond lengths in between single and double bonds. This simple description of aromaticty doesn't account for the molecules which exhibit aromaticity even though they aren't planar and undermines the contribution of sigma bonding to the aromatic character of some molecules.<ref name="aromaticity" />

Originally delocalisation of electrons around an aromatic molecule was thought to be due to pz orbital overlap but through calculations using molecular orbital theory it can be seen that other atomic orbitals will combine to form molecular orbitals which delocalise electrons around the molecule. For example, MO 14 for benzene shown above is not formed from the linear combination of pz orbitals above and below the plane of the molecules but px orbitals in the plane of the molecule. This produces a delocalised sigma framework which will be equally as responsible for stabilising aromatic compounds as the pi bonding system. This means that stating overlapping pz orbitals as a description for aromaticity is inaccurate because many other atomic orbitals in each atom will be responsible for producing MOs which delocalise electrons around the molecule and producing the stabilising effect attributed to aromaticity.

==References==
<references>
<ref name="hunt">Hunt.P (2018). Molecular Orbitals in Inorganic Chemistry. Tutorial after Lecture 4 Notes. [pdf] Retrieved from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf.</ref>
<ref name="aromaticity">Palusiak, M. and Krygowski, T. (2007). Application of AIM Parameters at Ring Critical Points for Estimation of π-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings. Chemistry - A European Journal, 13(28), pp.7996-8006.</ref>
</references>

2018-05-24T18:08:56Z

Jg2016: /* Analysis */

Rep:Mod:jg2016-hunt

2018-05-24T18:07:08Z

Jg2016: /* Analysis */

Rep:Mod:jg2016-hunt

2018-05-24T18:06:43Z

Jg2016: /* Analysis */

Rep:Mod:jg2016-hunt

2018-05-24T18:05:45Z

Jg2016: /* Analysis */

2018-05-24T17:57:04Z

Jg2016:

==Revision Section==

===BH<sub>3</sub>===

Borane

[[File:Bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

[[Media:BH3 2 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -1.1800 -1.0028 -0.0055 4.1927 11.0182 11.0637
Low frequencies --- 1162.9912 1213.1792 1213.1819
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BH3 2 OPT jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable" border="1"
|+ Vibration Analysis
! Frequency/cm<sup>-1</sup> !! Intensity !! Symmetry !! IR Active? !! Type of Vibration
|-
| 1164 || 93 || A2" || Yes || Out of plane Bend
|-
| 1214 || 14 || E' || Slightly || Bend
|-
| 1214 || 14 || E' || Slightly || Asymmetric in plane Bend
|-
| 2580 || 0 || A1' || No || Symmetric Stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|}

[[File:Bh3 spectrum jg2016.PNG|500px]]

There are less than 6 peaks in the IR spectrum of BH<sub>3</sub> even though there are 6 distinct vibrations because the A1' vibration at 2580 cm<sup>-1</sup> doesn't produce a change in dipole moment and so is IR inactive and will not produce a peak at all. In addition, there are 2 vibrations which have the exact same symmetry and energy at 1214 cm<sup>-1</sup> and so their individual peaks will superimpose to only show 1 peak. The exact same situation is happening with the 2 vibrations at 2713 cm<sup>-1</sup> so these 2 vibrations will be superimposed and only show 1 peak. This explains why only 3 peaks are seen in this spectrum.

[[File:Bh3 mo diagram jg2016.PNG]]

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

Ammonia

[[File:Nh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[Media:NH3 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3 FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

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

[[File:Nh3bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

[[Media:NH3BH3 FREQ 2 jg2016.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1240 17.1263 37.1338
Low frequencies --- 265.7821 632.2034 639.3485
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3BH3 FREQ 2 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Association Energy===

E(NH<sub>3</sub>)=-56.55777 A.U.

E(BH<sub>3</sub>)=-26.61532 A.U.

E(NH<sub>3</sub>BH<sub>3</sub>)=-83.22469 A.U.

ΔE=E(NH<sub>3</sub>BH<sub>3</sub>)-[E(NH<sub>3</sub>)+E(BH<sub>3</sub>)]=0.0516 A.U.=135 kJ mol<sup>-1</sup>

==Day 1: New==

===BBr<sub>3</sub>===

[[File:Bbr3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
</pre>

{{DOI|10042/202450}}

<pre>
Low frequencies --- -2.3055 -0.0029 -0.0018 0.0774 0.7534 0.7534
Low frequencies --- 155.9402 155.9405 267.6894
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Bbr3 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

==Investigating Aromaticity==

===Benzene===

[[File:Benzene summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

[[Media:BENZENE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0009
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BENZENE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Borazine===

[[File:Borazine summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

[[Media:BORAZINE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -0.0010 -0.0010 -0.0010 3.5555 4.4272 6.8943
Low frequencies --- 289.7109 289.7845 404.4187
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BORAZINE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Analysis===

[[File:Benzene charge distribution jg2016.PNG|500px]]
[[File:Borazine charge distribution jg2016.PNG|500px]]

In benzene all the atoms involved in the aromaticty (the carbons) have the same, slight negative charge of -0.239 and therefore all the hydrogens also have the same positive 0.239 charge. In borazine the boron atoms have a +0.747 charge while all the nitrogen atoms have a -1.102 charge. The hydrogen atoms bonded to the boron atoms have a -0.077 charge and the hydrogen atoms bonded to the nitrogen atoms have a +0.432 charge.

Carbon and hydrogen have similar electronegativities and so there is minimal charge separation between the carbon and hydrogen bond in benzene. Nitrogen is more electronegative than Boron and so in the aromatic ring of borazine there will be a build up of electron density at the nitrogen atoms and a deficiency of electrons at the boron atoms. Hydrogen is less electronegative than nitrogen and so the hydrogens bonded to nitrogen will have a very positive charge. Boron and hydrogen have very similar electronegativities but the boron atoms in aromatic ring are partially positive so the hydrogens attached to boron in borazine have a very small negative charge.

====Molecular Orbitals====

[[File:MO 1 - Benzene - 0.43854 jg2016.PNG]]
[[File:MO 1 - Borazine - 0.43198 jg2016.PNG]]

[[File:MO_2_-_Benzene_-_0.35997_jg2016.PNG]]
[[File:MO 2 - Borazine - 0.36130 jg2016.PNG]]

[[File:MO 3 - Benzene - 0.24691 jg2016.PNG]]
[[File:MO 3 - Borazine - 0.27591 jg2016.PNG]]

{| class="wikitable" border="1"
|+ MOs
! Benzene !! Borazine !! Deconstructed orbital
|-
|-
| [[File:MO 1 - Benzene - 0.43854 jg2016.PNG]] || [[File:MO 1 - Borazine - 0.43198 jg2016.PNG]] || [[File:MO 1 jg2016.png|200px]]
|-
| [[File:MO_2_-_Benzene_-_0.35997_jg2016.PNG]] || [[File:MO 2 - Borazine - 0.36130 jg2016.PNG]] || [[File:MO 2 jg2016.png|200px]]
|-
| [[File:MO 3 - Benzene - 0.24691 jg2016.PNG]] || [[File:MO 3 - Borazine - 0.27591 jg2016.PNG]] || [[File:MO 3 jg2016.png|200px]]
|}

Rep:Mod:jg2016-hunt

2018-05-24T17:56:39Z

Jg2016: /* Molecular Orbitals */

==Revision Section==

===BH<sub>3</sub>===

Borane

[[File:Bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

[[Media:BH3 2 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -1.1800 -1.0028 -0.0055 4.1927 11.0182 11.0637
Low frequencies --- 1162.9912 1213.1792 1213.1819
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BH3 2 OPT jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable" border="1"
|+ Vibration Analysis
! Frequency/cm<sup>-1</sup> !! Intensity !! Symmetry !! IR Active? !! Type of Vibration
|-
| 1164 || 93 || A2" || Yes || Out of plane Bend
|-
| 1214 || 14 || E' || Slightly || Bend
|-
| 1214 || 14 || E' || Slightly || Asymmetric in plane Bend
|-
| 2580 || 0 || A1' || No || Symmetric Stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch in plane
|}

[[File:Bh3 spectrum jg2016.PNG|500px]]

There are less than 6 peaks in the IR spectrum of BH<sub>3</sub> even though there are 6 distinct vibrations because the A1' vibration at 2580 cm<sup>-1</sup> doesn't produce a change in dipole moment and so is IR inactive and will not produce a peak at all. In addition, there are 2 vibrations which have the exact same symmetry and energy at 1214 cm<sup>-1</sup> and so their individual peaks will superimpose to only show 1 peak. The exact same situation is happening with the 2 vibrations at 2713 cm<sup>-1</sup> so these 2 vibrations will be superimposed and only show 1 peak. This explains why only 3 peaks are seen in this spectrum.

[[File:Bh3 mo diagram jg2016.PNG]]

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

Ammonia

[[File:Nh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[Media:NH3 FREQ jg2016.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3 FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

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

[[File:Nh3bh3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

[[Media:NH3BH3 FREQ 2 jg2016.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1240 17.1263 37.1338
Low frequencies --- 265.7821 632.2034 639.3485
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>NH3BH3 FREQ 2 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Association Energy===

E(NH<sub>3</sub>)=-56.55777 A.U.

E(BH<sub>3</sub>)=-26.61532 A.U.

E(NH<sub>3</sub>BH<sub>3</sub>)=-83.22469 A.U.

ΔE=E(NH<sub>3</sub>BH<sub>3</sub>)-[E(NH<sub>3</sub>)+E(BH<sub>3</sub>)]=0.0516 A.U.=135 kJ mol<sup>-1</sup>

==Day 1: New==

===BBr<sub>3</sub>===

[[File:Bbr3 summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
</pre>

{{DOI|10042/202450}}

<pre>
Low frequencies --- -2.3055 -0.0029 -0.0018 0.0774 0.7534 0.7534
Low frequencies --- 155.9402 155.9405 267.6894
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Bbr3 jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

==Investigating Aromaticity==

===Benzene===

[[File:Benzene summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

[[Media:BENZENE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0009
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BENZENE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Borazine===

[[File:Borazine summary jg2016.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

[[Media:BORAZINE FREQ jg2016.LOG]]

<pre>
Low frequencies --- -0.0010 -0.0010 -0.0010 3.5555 4.4272 6.8943
Low frequencies --- 289.7109 289.7845 404.4187
</pre>

<jmol>
<jmolApplet>
<size>350</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>BORAZINE FREQ jsmol jg2016.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===Analysis===

[[File:Benzene charge distribution jg2016.PNG|500px]]
[[File:Borazine charge distribution jg2016.PNG|500px]]

In benzene all the atoms involved in the aromaticty (the carbons) have the same, slight negative charge of -0.239 and therefore all the hydrogens also have the same positive 0.239 charge. In borazine the boron atoms have a +0.747 charge while all the nitrogen atoms have a -1.102 charge. The hydrogen atoms bonded to the boron atoms have a -0.077 charge and the hydrogen atoms bonded to the nitrogen atoms have a +0.432 charge.

Carbon and hydrogen have similar electronegativities and so there is minimal charge separation between the carbon and hydrogen bond in benzene. Nitrogen is more electronegative than Boron and so in the aromatic ring of borazine there will be a build up of electron density at the nitrogen atoms and a deficiency of electrons at the boron atoms. Hydrogen is less electronegative than nitrogen and so the hydrogens bonded to nitrogen will have a very positive charge. Boron and hydrogen have very similar electronegativities but the boron atoms in aromatic ring are partially positive so the hydrogens attached to boron in borazine have a very small negative charge.

====Molecular Orbitals====

[[File:MO 1 - Benzene - 0.43854 jg2016.PNG]]
[[File:MO 1 - Borazine - 0.43198 jg2016.PNG]]

[[File:MO_2_-_Benzene_-_0.35997_jg2016.PNG]]
[[File:MO 2 - Borazine - 0.36130 jg2016.PNG]]

[[File:MO 3 - Benzene - 0.24691 jg2016.PNG]]
[[File:MO 3 - Borazine - 0.27591 jg2016.PNG]]

{| class="wikitable" border="1"
|+ MOs
! Benzene !! Borazine !! Deconstructed orbital
|-
|-
| [[File:MO 1 - Benzene - 0.43854 jg2016.PNG]] || [[File:MO 1 - Borazine - 0.43198 jg2016.PNG]] || [[File:MO 1 jg2016.png|500px]]
|-
| [[File:MO_2_-_Benzene_-_0.35997_jg2016.PNG]] || [[File:MO 2 - Borazine - 0.36130 jg2016.PNG]] || [[File:MO 2 jg2016.png|500px]]
|-
| [[File:MO 3 - Benzene - 0.24691 jg2016.PNG]] || [[File:MO 3 - Borazine - 0.27591 jg2016.PNG]] || [[File:MO 3 jg2016.png|500px]]
|}