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	<id>https://chemwiki.ch.ic.ac.uk/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=Asp216</id>
	<title>ChemWiki - User contributions [en]</title>
	<link rel="self" type="application/atom+xml" href="https://chemwiki.ch.ic.ac.uk/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=Asp216"/>
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	<updated>2026-04-08T03:05:01Z</updated>
	<subtitle>User contributions</subtitle>
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	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723977</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723977"/>
		<updated>2018-05-18T16:59:31Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. In borazine, more the lobes are larger on the boron atoms as the energy of the boron based fragment orbitals are closer to the energy of the MO and so have a larger contribution to the MO, due to boron being more electropositive. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital (MO7) in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine (MO7) spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. In benzene, each carbon atom has one electron situated in the p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; and borazine has a lone pair of electrons situated in each nitrogen p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbital, with the boron p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals empty. Both molecules are isoelectronic and isostructural and obey the 4n + 2 π electron rule (n=1) and are aromatic. As discussed early, borazine is less aromatic then benzene.&lt;br /&gt;
&lt;br /&gt;
However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene, cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, the behaviour of aromatic molecules can be explained, where valence bond theory fails. It can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3. It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723916</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723916"/>
		<updated>2018-05-18T16:49:27Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital (MO7) in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine (MO7) spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. In benzene, each carbon atom has one electron situated in the p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; and borazine has a lone pair of electrons situated in each nitrogen p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbital, with the boron p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals empty. Both molecules are isoelectronic and isostructural and obey the 4n + 2 π electron rule (n=1) and are aromatic. As discussed early, borazine is less aromatic then benzene.&lt;br /&gt;
&lt;br /&gt;
However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene, cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, the behaviour of aromatic molecules can be explained, where valence bond theory fails. It can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3. It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723911</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723911"/>
		<updated>2018-05-18T16:48:42Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. In benzene, each carbon atom has one electron situated in the p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; and borazine has a lone pair of electrons situated in each nitrogen p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbital, with the boron p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals empty. Both molecules are isoelectronic and isostructural and obey the 4n + 2 π electron rule (n=1) and are aromatic. As discussed early, borazine is less aromatic then benzene.&lt;br /&gt;
&lt;br /&gt;
However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene, cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, the behaviour of aromatic molecules can be explained, where valence bond theory fails. It can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3. It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723892</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723892"/>
		<updated>2018-05-18T16:45:30Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. In benzene, each carbon atom has one electron situated in the p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; and borazine has a lone pair of electrons situated in each nitrogen p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbital, with the boron p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals empty. Both molecules therefore obey the 4n + 2 π electron rule (n=1) and are aromatic. As discussed early, borazine is less aromatic then benzene.&lt;br /&gt;
&lt;br /&gt;
However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene, cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, the behaviour of aromatic molecules can be explained, where valence bond theory fails. It can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3. It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723844</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723844"/>
		<updated>2018-05-18T16:35:06Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. In benzene, each carbon atom has one electron situated in the p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; and borazine has a lone pair of electrons situated in each nitrogen p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbital, with the boron p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals empty. Both molecules therefore obey the 4n + 2 π electron rule (n=1) and are aromatic. As discussed early, borazine is less aromatic then benzene.&lt;br /&gt;
&lt;br /&gt;
However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene, cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3. It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723839</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723839"/>
		<updated>2018-05-18T16:34:20Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. In benzene, each carbon atom has one electron situated in the p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; and borazine has a lone pair of electrons situated in each nitrogen p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbital, with the boron p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals empty. Both molecules therefore obey the 4n + 2 π electron rule (n=1) and are aromatic. As discussed early, borazine is less aromatic then benzene.&lt;br /&gt;
&lt;br /&gt;
However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3. It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723818</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723818"/>
		<updated>2018-05-18T16:29:23Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3. It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723816</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723816"/>
		<updated>2018-05-18T16:29:02Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723812</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723812"/>
		<updated>2018-05-18T16:28:50Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723805</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723805"/>
		<updated>2018-05-18T16:28:06Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723789</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723789"/>
		<updated>2018-05-18T16:26:05Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital (MO17) in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine (MO17) spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon.]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules and are based upon maximising the pi interaction between parallel p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals of the same phase, which allows delocalisation to occur. This is shown in MO17 opposite. &lt;br /&gt;
&lt;br /&gt;
However, the rules fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t fully and explicitly describe what makes a molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723715</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723715"/>
		<updated>2018-05-18T16:18:05Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* Charge Distribution (NBO charge analysis) */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. This distribution follows the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry of borazine. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723698</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723698"/>
		<updated>2018-05-18T16:16:43Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* Charge Distribution (NBO charge analysis) */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723697</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723697"/>
		<updated>2018-05-18T16:16:33Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* Charge Distribution (NBO charge analysis) */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
Pauling electronegativities: B(2.04); H(2.20); C(2.55); N(3.04)&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723521</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723521"/>
		<updated>2018-05-18T15:57:16Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* Charge Distribution */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution (NBO charge analysis)===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723507</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723507"/>
		<updated>2018-05-18T15:55:31Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* Charge Distribution */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723505</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723505"/>
		<updated>2018-05-18T15:55:17Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* Charge Distribution */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723480</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723480"/>
		<updated>2018-05-18T15:53:02Z</updated>

		<summary type="html">&lt;p&gt;Asp216: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
It is interesting to see how the core MOs of borazine reflect the D&amp;lt;sub&amp;gt;3h&amp;lt;/sub&amp;gt; symmetry fragment s orbitals. The nitrogen based core orbitals are considerably lower in energy than the boron s fragment orbitals. Further to this, these boron MOs are more diffused than the nitrogen MOs.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &#039;&#039;Organic chemistry&#039;&#039;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. &#039;&#039;Inorganica Chimica Acta&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. &#039;&#039;Chemistry - A European Journal&#039;&#039; &#039;&#039;&#039;2007&#039;&#039;&#039;, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723313</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723313"/>
		<updated>2018-05-18T15:32:07Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. Inorganica Chimica Acta 2007, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. Chemistry - A European Journal 2007, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723311</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723311"/>
		<updated>2018-05-18T15:31:55Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Borazine aromaticity&amp;quot;&amp;gt;Shen, W.; Li, M.; Li, Y.; Wang, S. Inorganica Chimica Acta 2007, 360 (2), 619–624.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. Chemistry - A European Journal 2007, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723306</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723306"/>
		<updated>2018-05-18T15:31:15Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* Charge Distribution */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. These differences electronegativity lead to a lower aromaticity in borazine than in benzene, as electron density is focused more on the nitrogen atoms (more negative charge), reducing the delocalisation of the electrons.&amp;lt;ref name=&amp;quot;borazine aromaticity&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. Chemistry - A European Journal 2007, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723254</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723254"/>
		<updated>2018-05-18T15:23:51Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the energy difference in the hydrogenation of cyclohexene cyclohexadiene and benzene. The energy for benzene is lower than expected by the trend of the other two. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. Chemistry - A European Journal 2007, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723231</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723231"/>
		<updated>2018-05-18T15:20:57Z</updated>

		<summary type="html">&lt;p&gt;Asp216: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;/&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. Chemistry - A European Journal 2007, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723226</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723226"/>
		<updated>2018-05-18T15:20:44Z</updated>

		<summary type="html">&lt;p&gt;Asp216: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Aromatic&amp;quot;&amp;gt;Palusiak, M.; Krygowski, T. M. Chemistry - A European Journal 2007, 13 (28), 7996–8006.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723184</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723184"/>
		<updated>2018-05-18T15:17:23Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is failed to be accounted for in the simple considerations of aromaticity and Hückel theory.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723174</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723174"/>
		<updated>2018-05-18T15:16:01Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron, nitrogen and some hydrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is not accounted for in the simple considerations of aromaticity.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723169</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723169"/>
		<updated>2018-05-18T15:15:28Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding, with bonding regions between the ring atoms and hydrogens but nodes between the ring atoms themselves lead to antibonding character. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is not accounted for in the simple considerations of aromaticity.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723151</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723151"/>
		<updated>2018-05-18T15:14:15Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is not accounted for in the simple considerations of aromaticity.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723147</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723147"/>
		<updated>2018-05-18T15:13:48Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate π* LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate π HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These σ orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is not accounted for in the simple considerations of aromaticity.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723136</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723136"/>
		<updated>2018-05-18T15:12:26Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between. This has been shown in the examples opposite where all the bonds within the ring are the same length.&lt;br /&gt;
&lt;br /&gt;
By considerations of the real MOs of aromatic molecules, it can be seen that aromaticity does not solely arise from delocalisation of π electrons from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. The MOs opposite show how in benzene and borazine there is also electron density spread across the molecule in σ MOs, not arising from p&amp;lt;sub&amp;gt;z&amp;lt;/sub&amp;gt; orbitals. This is not accounted for in the simple considerations of aromaticity.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723065</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723065"/>
		<updated>2018-05-18T15:04:25Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene. The resonance also produces bonds in the ring that aren&#039;t defined single or double bonds, but somewhere in between&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
[[User:Asp216|Asp216]] ([[User talk:Asp216|talk]]) 16:04, 18 May 2018 (BST)&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723045</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723045"/>
		<updated>2018-05-18T15:01:53Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
[[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]]&lt;br /&gt;
[[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723039</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=723039"/>
		<updated>2018-05-18T15:01:05Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|A π bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]][[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]][[File:Asp216_benzene_aromatic_sigma.png|thumb|A σ bonding molecular orbital in benzene which shows a region of electron density spread over the carbon. ]][[File:Asp216_borazine_aromatic_sigma.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_aromatic_sigma.png&amp;diff=723016</id>
		<title>File:Asp216 borazine aromatic sigma.png</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_aromatic_sigma.png&amp;diff=723016"/>
		<updated>2018-05-18T14:59:14Z</updated>

		<summary type="html">&lt;p&gt;Asp216: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_benzene_aromatic_sigma.png&amp;diff=723012</id>
		<title>File:Asp216 benzene aromatic sigma.png</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_benzene_aromatic_sigma.png&amp;diff=723012"/>
		<updated>2018-05-18T14:58:50Z</updated>

		<summary type="html">&lt;p&gt;Asp216: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722970</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722970"/>
		<updated>2018-05-18T14:54:22Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|Bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]][[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine spread over the boron and nitrogen atoms.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722961</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722961"/>
		<updated>2018-05-18T14:53:48Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb|Bonding molecular orbital in benzene which shows a region of electron density spread over the carbon atoms above and below the plane of the ring. ]][[File:Asp216_borazine_aromatic.png|thumb|The same can be seen in borazine.]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722949</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722949"/>
		<updated>2018-05-18T14:51:52Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb]][[File:Asp216_borazine_aromatic.png|thumb]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
The delocalisation of electrons allows resonance within the ring. This resonance is found to have a stabilising effect, lowering the energy of the aromatic molecule. For example the difference in energy needed to hydrogenate cyclohexadiene to benzene is less than that of cyclohexene to cyclohexadiene.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722905</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722905"/>
		<updated>2018-05-18T14:45:22Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb]][[File:Asp216_borazine_aromatic.png|thumb]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings. It is clear that this approach doesn&#039;t accurately describe what makes the molecule aromatic. Better considerations of aromaticity are based upon:&lt;br /&gt;
*resonance stabilisation energies&lt;br /&gt;
*bond lengths of ring atoms between their single and double bond lengths &lt;br /&gt;
*considerations of the MOs involved in delocalisation&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722869</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722869"/>
		<updated>2018-05-18T14:41:04Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb]][[File:Asp216_borazine_aromatic.png|thumb]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722829</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722829"/>
		<updated>2018-05-18T14:37:17Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb]][[File:Asp216_borazine_aromatic.png|thumb]]&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
These rules work well for many simple aromatic molecules, but fail to account for more complex aromatic fused rings.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722788</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722788"/>
		<updated>2018-05-18T14:32:26Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb]][[File:Asp216_borazine_aromatic.png|thumb]]&lt;br /&gt;
&lt;br /&gt;
According to Hückel&#039;s rules, cyclic molecules can be classified as aromatic if they:&lt;br /&gt;
# They contain 4n + 2 π electrons &lt;br /&gt;
# From a contiguous ring of parallel p orbitals&lt;br /&gt;
# which are coplanar.&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_benzene_aromatic.png&amp;diff=722496</id>
		<title>File:Asp216 benzene aromatic.png</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_benzene_aromatic.png&amp;diff=722496"/>
		<updated>2018-05-18T14:07:00Z</updated>

		<summary type="html">&lt;p&gt;Asp216: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_aromatic.png&amp;diff=722488</id>
		<title>File:Asp216 borazine aromatic.png</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_aromatic.png&amp;diff=722488"/>
		<updated>2018-05-18T14:06:32Z</updated>

		<summary type="html">&lt;p&gt;Asp216: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722487</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722487"/>
		<updated>2018-05-18T14:06:17Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_aromatic.png|thumb]][[File:Asp216_borazine_aromatic.png|thumb]]&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_mo17.png&amp;diff=722458</id>
		<title>File:Asp216 borazine mo17.png</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_mo17.png&amp;diff=722458"/>
		<updated>2018-05-18T14:03:07Z</updated>

		<summary type="html">&lt;p&gt;Asp216: Asp216 uploaded a new version of File:Asp216 borazine mo17.png&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_mo17.png&amp;diff=722456</id>
		<title>File:Asp216 borazine mo17.png</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_mo17.png&amp;diff=722456"/>
		<updated>2018-05-18T14:02:47Z</updated>

		<summary type="html">&lt;p&gt;Asp216: Asp216 uploaded a new version of File:Asp216 borazine mo17.png&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_mo17.png&amp;diff=722448</id>
		<title>File:Asp216 borazine mo17.png</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_mo17.png&amp;diff=722448"/>
		<updated>2018-05-18T14:01:52Z</updated>

		<summary type="html">&lt;p&gt;Asp216: Asp216 uploaded a new version of File:Asp216 borazine mo17.png&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722434</id>
		<title>Rep:Mod:asp216 Y2</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:asp216_Y2&amp;diff=722434"/>
		<updated>2018-05-18T14:00:13Z</updated>

		<summary type="html">&lt;p&gt;Asp216: /* MOs */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==EX&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; section==&lt;br /&gt;
&lt;br /&gt;
===BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BH3_FREQ.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Item                     Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000190     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000095     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000747     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000374     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BH3_FREQ.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---   -0.2260   -0.1036   -0.0055   48.0278   49.0875   49.0880&lt;br /&gt;
Low frequencies --- 1163.7224 1213.6715 1213.6741&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1164 || 92 || A&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;&amp;quot; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1214 || 14 || E&#039; || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 2580 || 0 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; || No || Symmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|-&lt;br /&gt;
| 2713 || 126 || E&#039; || Yes || Asymmetric Stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
For borane, there are 6 vibrational modes but only 3 peaks are visible in the IR spectrum. The symmetric stretch (ν = 2580 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) is not IR active as the stretch has no change in dipole moment. The two asymmetrics stretches are degenerate (have the same energy) as they vibrate at the same frequency and therefore the peaks overlap to form one. This is also true for the 2 bends (ν = 1214 cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;MOs&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
There is little difference between the LCAO and calulated MOs. However, the calculated MOs better show the distribution of electron density across the molecule. It can also be seen that the unoccupied real MOs are more diffuse the occupied MOs, which cannot be realised from the LCAO MOs. This suggests that qualitative MO theory (LCAOs) is useful and reliable for occupied MOs, but less accurate for predicting unoccupied MOs.&lt;br /&gt;
&lt;br /&gt;
For the antibonding MOs it can be seen how electron density is directed away from the B–H bond.&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bh3_mo.png|thumb|centre|MO diagram of BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; showing LCAO MOs and calculated MOs]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item             Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000086     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000034     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000315     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000106     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
Low frequencies ---  -30.2921  -30.2783   -0.0039    0.0080    0.0336    3.6335&lt;br /&gt;
Low frequencies --- 1088.7748 1694.0376 1694.0379&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
!wavenumber (cm&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) !! Intensity (arbitrary units) !! symmetry !! IR active? !! type&lt;br /&gt;
|-&lt;br /&gt;
| 1089 || 146 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || Yes || Bend (out of plane)&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 1694 || 14 || E || slightly || Bend&lt;br /&gt;
|-&lt;br /&gt;
| 3462 || 1 || A&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; || No || Symmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|-&lt;br /&gt;
| 3591 || 0 || E || No || Asymmetric stretch&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3_ir_spectrum.png]]&lt;br /&gt;
&lt;br /&gt;
===NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised ammonia borane molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_NH3BH3_FREQ_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_nh3bh3_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000237     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000052     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.001353     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000365     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_NH3BH3_FREQ_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.1948   -0.0607   -0.0067   10.8243   16.5775   16.5866&lt;br /&gt;
 Low frequencies ---  263.0568  631.4015  638.8808&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Energy Calculation====&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -56.55776861 a.u.&lt;br /&gt;
&lt;br /&gt;
E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -26.61532342 a.u.&lt;br /&gt;
&lt;br /&gt;
E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)= -83.22469012 a.u.&lt;br /&gt;
&lt;br /&gt;
ΔE=E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)-[E(NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)+E(BH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;)]&lt;br /&gt;
&lt;br /&gt;
ΔE= -83.22469012 - (-56.55776861 + -26.61532342)&lt;br /&gt;
&lt;br /&gt;
ΔE= -0.05159809 a.u. = -135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dative bond between B and N in ammonia borane is relatively weak (dissociation energy = 135 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;), as it is less than that of a covalent C–C bond (350 kJmol&amp;lt;sup&amp;gt;-1&amp;lt;/sup&amp;gt;) in isoelectronic ethane. &amp;lt;ref name=&amp;quot;Organic&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===BBr&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borone tribromide molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BBR3_FREQ_GEN2.log&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;B3LYP/6-31G(d,p)LANL2DZ level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_bbr3_summary2.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000019     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000010     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000090     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000045     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BBR3_FREQ_GEN2.log| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
{{DOI|10042/202414}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -0.0126   -0.0064   -0.0046    2.6412    2.6412    4.9503&lt;br /&gt;
 Low frequencies ---  155.9599  155.9619  267.6868&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Project Section==&lt;br /&gt;
&lt;br /&gt;
===Benzene===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised benzene molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BENZENE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000198     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000087     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000757     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000321     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BENZENE_FREQ2_631G_DP.LOG| Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---   -2.1456   -2.1456   -0.0088   -0.0042   -0.0041   10.4835&lt;br /&gt;
 Low frequencies ---  413.9768  413.9768  621.1390&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Borazine===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;jmol&amp;gt;&amp;lt;jmolApplet&amp;gt;&lt;br /&gt;
  &amp;lt;title&amp;gt;Optimised borazine molecule&amp;lt;/title&amp;gt;&lt;br /&gt;
  &amp;lt;color&amp;gt;black&amp;lt;/color&amp;gt;&lt;br /&gt;
  &amp;lt;size&amp;gt;200&amp;lt;/size&amp;gt;&lt;br /&gt;
  &amp;lt;uploadedFileContents&amp;gt;ASP216_BORAZINE_FREQ2_631G_DP.LOG&amp;lt;/uploadedFileContents&amp;gt;&lt;br /&gt;
&amp;lt;/jmolApplet&amp;gt;&amp;lt;/jmol&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;RB3LYP/6-31G(d,p) level&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_borazine_summary.PNG]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
         Item               Value     Threshold  Converged?&lt;br /&gt;
 Maximum Force            0.000016     0.000450     YES&lt;br /&gt;
 RMS     Force            0.000005     0.000300     YES&lt;br /&gt;
 Maximum Displacement     0.000025     0.001800     YES&lt;br /&gt;
 RMS     Displacement     0.000008     0.001200     YES&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Media:ASP216_BORAZINE_FREQ2_631G_DP.LOG | Download optimised .log file here]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Frequencies&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
 Low frequencies ---  -13.6679  -13.4715  -10.3782   -0.0099    0.0321    0.0716&lt;br /&gt;
 Low frequencies ---  289.1330  289.1422  404.0164&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Charge Distribution===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! !! Benzene !! Borazine&lt;br /&gt;
|-&lt;br /&gt;
|  || [[File:Asp216_benzene_charge.png|thumb|upright=1.5]] ||&lt;br /&gt;
 [[File:Asp216_borazine_charge.png|thumb|upright=1.5]]&lt;br /&gt;
|-&lt;br /&gt;
| &#039;&#039;&#039;Charges on atom /e&#039;&#039;&#039; || C: -0.239, H: 0.239 || N: -1.102, B: 0.747, H(–N): 0.432, H(–B): -0.077&lt;br /&gt;
|}&lt;br /&gt;
The above colour scheme ranges from red at a charge of -1.102 and green at 1.102.&lt;br /&gt;
&lt;br /&gt;
The distribution of charge in each molecule reflects that molecule&#039;s symmetry. In benzene, the D&amp;lt;sub&amp;gt;6h&amp;lt;/sub&amp;gt; symmetry shows all carbon atoms have the same charge. This indicates the covalent nature of the C–C bonds in the ring, as the electron density is evenly spread across the C atoms with no polarised C–C bonds. Conversely, in borazine the nitrogen and boron ring atoms differ in their charge due to the fact that nitrogen is electronegative and boron is electropositive. The B–N bond is polarised and therefore has some ionic character. &lt;br /&gt;
&lt;br /&gt;
There are different degrees of polarisation between the B–H and N–H bonds, with the N–H bond being more polarised. The greater ionic character shortens (1.097 Å) and strengthens the N–H bond more than the B–H bond (1.195 Å).&lt;br /&gt;
&lt;br /&gt;
Both molecules have not overall charge, as the sum of charges of each atom are zero.&lt;br /&gt;
&lt;br /&gt;
* quote eneg values and scale used to measure values&lt;br /&gt;
&lt;br /&gt;
===MOs===&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; border=1&lt;br /&gt;
! Benzene !! Borazine !! Comment&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo22.png|thumb]] || [[File:Asp216_borazine_mo22.png|thumb]] || MO22 is one of the degenerate LUMO orbitals. This orbital shows some bonding character across two of the C–C/N–B bonds, but is ultimately destabilised by nodes across four of the C–C/N–B bonds leading to overall antibonding character. The benzene MO has e&amp;lt;sub&amp;gt;2u&amp;lt;/sub&amp;gt; symmetry and the borazine MO has e&amp;quot; symmetry.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo21.png|thumb]] || [[File:Asp216_borazine_mo21.png|thumb]] || MO21 is one of the degenerate HOMO orbital. This is overall bonding with the lobes spread over ring atoms, but a few nodes along C–C/N–B bonds indicating antibonding character which destabilise the bonding character. In benzene it has e&amp;lt;sub&amp;gt;1g&amp;lt;/sub&amp;gt; symmetry and for borazine it has e&amp;quot; symmetry. In borazine there is a larger contribution to the MO from the nitrogen atoms, evidenced by larger lobes over these atoms. N atoms are more electronegative than B and so its p orbitals are lower in energy, and are therefore closer in energy to the bonding MOs, giving them a larger contribution.&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Asp216_benzene_mo13.png|thumb]] || [[File:Asp216_borazine_mo16.png|thumb]] || The MO13 of benzene has b&amp;lt;sub&amp;gt;1u&amp;lt;/sub&amp;gt; symmetry and the MO16 of borazine e&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;&#039; symmetry. These orbitals show only contribution from the sigma fragment orbitals of the H atoms, and are overall non-bonding. There is an equal contribution from each H atom in benzene but, the contributions are larger for H bonded to N and smaller for H bonded to B in borazine.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Aromaticity&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[File:Asp216_benzene_mo17.png|thumb]][[File:Asp216_borazine_mo17.png|thumb]]&lt;br /&gt;
&lt;br /&gt;
*discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.&lt;br /&gt;
*how do the real MOs relate to the common (very basic) conceptions of aromaticity? you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.&lt;br /&gt;
&lt;br /&gt;
extra interesting: core orbitals of borazine for boron and nitrogen atoms show the same symmetry as BH3.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;references&amp;gt;&lt;br /&gt;
&amp;lt;ref name=&amp;quot;Organic&amp;quot;&amp;gt;Clayden, J.; Greeves, N.; Warren, S. G. &amp;lt;i&amp;gt;Organic chemistry&amp;lt;/i&amp;gt;; Oxford University Press: Oxford, 2012.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;/references&amp;gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
	<entry>
		<id>https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_mo17.png&amp;diff=722427</id>
		<title>File:Asp216 borazine mo17.png</title>
		<link rel="alternate" type="text/html" href="https://chemwiki.ch.ic.ac.uk/index.php?title=File:Asp216_borazine_mo17.png&amp;diff=722427"/>
		<updated>2018-05-18T13:58:49Z</updated>

		<summary type="html">&lt;p&gt;Asp216: Asp216 uploaded a new version of File:Asp216 borazine mo17.png&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Asp216</name></author>
	</entry>
</feed>