ChemWiki - User contributions [en]

01217148

2018-05-25T13:45:24Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

'''The optimisation of BH3:'''

[[File:cathy_bh3_opt_1.jpg]]

'''The "item" table for BH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

'''Frequencies tabulated BH3 below:'''

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

'''The optimised BH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''The IR spectral data for optimised BH3 is shown below:'''

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg|The IR spectrum for BH3]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg|Molecular Orbital diagram for BH3 <ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>]]

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

'''The optimisation of NH3:'''

[[File:cathy_nh3_opt_1.jpg]]

'''The "item" table for NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

'''Frequencies tabulated NH3 below:'''

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

'''The optimised NH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

'''The optimisation of NH3BH3:'''

[[File:cathy_bh3nh3_opt_1.jpg]]

'''The "item" table for NH3BH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

'''Frequencies tabulated NH3BH3 below:'''

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

'''The optimised NH3BH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Energy of the Optimised Systems'''

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 Optimisation ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

'''The optimisation of BBr3:'''

[[File:cathy_bbr3_opt.jpg]]

'''The "item" table for BBr3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

'''Frequencies tabulated BBr3 below:'''

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

'''The optimised BBr3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''

[[File:benzene_opt_table.jpg]]

'''The "item" table for benzene:'''

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''The optimised benzene molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]

'''The "item" table for borazine:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]

<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

'''The optimised borazine molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]

[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || MO21-Benzene, MO21-Borazine. Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || MO8-Benzene, MO9-Borazine. Four s orbitals combine to provide relatively deep energy bonding orbital with electron density mainly distributed between the atoms. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || MO14-Benzene, MO15-Borazine. There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with three nodal planes. The orbital is slightly bonding since the electron density lies between the atoms, hence contribute to the bonding between them. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the only MO which spreads electron density over the ring (third MO discussed). For non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of the four factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T13:43:43Z

Ce1116:

===Optimised BH3 Molecule===

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

'''The optimisation of BH3:'''

[[File:cathy_bh3_opt_1.jpg]]

'''The "item" table for BH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

'''Frequencies tabulated BH3 below:'''

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

'''The optimised BH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''The IR spectral data for optimised BH3 is shown below:'''

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg|The IR spectrum for BH3]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg|Molecular Orbital diagram for BH3 <ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>]]

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

'''The optimisation of NH3:'''

[[File:cathy_nh3_opt_1.jpg]]

'''The "item" table for NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

'''Frequencies tabulated NH3 below:'''

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

'''The optimised NH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

'''The optimisation of NH3BH3:'''

[[File:cathy_bh3nh3_opt_1.jpg]]

'''The "item" table for NH3BH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

'''Frequencies tabulated NH3BH3 below:'''

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

'''The optimised NH3BH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Energy of the Optimised Systems'''

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 Optimisation ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

'''The optimisation of BBr3:'''

[[File:cathy_bbr3_opt.jpg]]

'''The "item" table for BBr3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

'''Frequencies tabulated BBr3 below:'''

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

'''The optimised BBr3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''

[[File:benzene_opt_table.jpg]]

'''The "item" table for benzene:'''

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''The optimised benzene molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]

'''The "item" table for borazine:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]

<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

'''The optimised borazine molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]

[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || MO21-Benzene, MO21-Borazine. Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || MO8-Benzene, MO9-Borazine. Four s orbitals combine to provide relatively deep energy bonding orbital with electron density mainly distributed between the atoms. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || MO14-Benzene, MO15-Borazine. There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with three nodal planes. The orbital is slightly bonding since the MOs lie between the atoms, hence contribute to the bonding between them. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the only MO which spreads electron density over the ring (third MO discussed). For non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of the four factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T13:25:12Z

Ce1116:

===Optimised BH3 Molecule===

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

'''The optimisation of BH3:'''

[[File:cathy_bh3_opt_1.jpg]]

'''The "item" table for BH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

'''Frequencies tabulated BH3 below:'''

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

'''The optimised BH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''The IR spectral data for optimised BH3 is shown below:'''

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg|The IR spectrum for BH3]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg|Molecular Orbital diagram for BH3 <ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>]]

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

'''The optimisation of NH3:'''

[[File:cathy_nh3_opt_1.jpg]]

'''The "item" table for NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

'''Frequencies tabulated NH3 below:'''

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

'''The optimised NH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

'''The optimisation of NH3BH3:'''

[[File:cathy_bh3nh3_opt_1.jpg]]

'''The "item" table for NH3BH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

'''Frequencies tabulated NH3BH3 below:'''

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

'''The optimised NH3BH3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Energy of the Optimised Systems'''

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 Optimisation ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

'''The optimisation of BBr3:'''

[[File:cathy_bbr3_opt.jpg]]

'''The "item" table for BBr3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

'''Frequencies tabulated BBr3 below:'''

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

'''The optimised BBr3 molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''

[[File:benzene_opt_table.jpg]]

'''The "item" table for benzene:'''

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''The optimised benzene molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]

'''The "item" table for borazine:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]

<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

'''The optimised borazine molecule:'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]

[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital with electron density mainly distributed between the atoms. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with three nodal planes. The orbital is slightly bonding since the MOs lie between the atoms, hence contribute to the bonding between them. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the only MO which spreads electron density over the ring (third MO discussed). For non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of the four factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T12:57:55Z

Ce1116:

===Optimised BH3 Molecule===

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

'''The optimisation of BH3:'''

[[File:cathy_bh3_opt_1.jpg]]

'''The "item" table for BH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

'''Frequencies tabulated BH3 below:'''

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG|A Gaussview representation of BH3</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital with electron density mainly distributed between the atoms. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with three nodal planes. The orbital is slightly bonding since the MOs lie between the atoms, hence contribute to the bonding between them. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the only MO which spreads electron density over the ring (third MO discussed). For non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of the four factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T12:54:49Z

Ce1116: /* Optimised BH3 Molecule */

===Optimised BH3 Molecule===

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

'''The optimisation of BH3:'''

[[File:cathy_bh3_opt_1.jpg]]

'''The "item" table for BH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital with electron density mainly distributed between the atoms. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with three nodal planes. The orbital is slightly bonding since the MOs lie between the atoms, hence contribute to the bonding between them. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the only MO which spreads electron density over the ring (third MO discussed). For non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of the four factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T12:51:52Z

Ce1116: /* The Concept of Aromaticity */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital with electron density mainly distributed between the atoms. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with three nodal planes. The orbital is slightly bonding since the MOs lie between the atoms, hence contribute to the bonding between them. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the only MO which spreads electron density over the ring (third MO discussed). For non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of the four factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T12:47:23Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital with electron density mainly distributed between the atoms. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with three nodal planes. The orbital is slightly bonding since the MOs lie between the atoms, hence contribute to the bonding between them. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the onlyfor non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T12:43:14Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with three nodal planes. The orbital is slightly bonding since the MOs lie between the atoms, hence contribute to the bonding between them. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the onlyfor non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T12:37:10Z

Ce1116: /* The Concept of Aromaticity */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, not the onlyfor non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T10:53:55Z

Ce1116:

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, for non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

== References ==
<references/>

01217148

2018-05-25T10:53:07Z

Ce1116: /* The Concept of Aromaticity */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, for non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

<references/>

01217148

2018-05-25T10:52:50Z

Ce1116: /* The Concept of Aromaticity */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. The overlap of pz atomic orbitals is a poor description for aromaticity since this purely takes into account the overlap of these orbitals, which is a large factor in compounds such as benzene, however, for non-planar compounds the overlap of these orbitals may not be significant. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T10:47:19Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''

C = -0.239

H = +0.239

'''Charges in Borazine:'''

N = -1.102

B = +0.747

H (bonded to N)= +0.432

H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

File:Charge dist1 ce.jpg

2018-05-25T10:46:17Z

Ce1116:

File:Charge dist ce.jpg

2018-05-25T10:46:03Z

Ce1116:

01217148

2018-05-25T10:45:41Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:charge_dist_ce.jpg]]
[[File:charge_dist1_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''
C = -0.239
H = +0.239

'''Charges in Borazine:'''
N = -1.102
B = +0.747
H (bonded to N)= +0.432
H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T10:42:15Z

Ce1116:

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:borazine_charge_ce.jpg]]
[[File:benzene_charge_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge (see below) and hydrogen atoms have a slight positive charge (see below). This supports the idea that there is a cloud of electrons above and below the plane of the ring.

'''Charges in Benzene:'''
C = -0.239
H = +0.239

'''Charges in Borazine:'''
N = -1.102
B = +0.747
H (bonded to N)= +0.432
H (bonded to B)= +0.747

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T10:31:37Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:borazine_charge_ce.jpg]]
[[File:benzene_charge_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon (2.50) and hydrogen (2.10) atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge and hydrogen atoms have a slight positive charge. This supports the idea that there is a cloud of electrons above and below the plane of the ring.

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T10:29:52Z

Ce1116: /* BBr3 */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:borazine_charge_ce.jpg]]
[[File:benzene_charge_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon and hydrogen atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge and hydrogen atoms have a slight positive charge. This supports the idea that there is a cloud of electrons above and below the plane of the ring.

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T10:29:16Z

Ce1116: /* Optimised BH3 Molecule */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are more diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1' anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:borazine_charge_ce.jpg]]
[[File:benzene_charge_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon and hydrogen atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge and hydrogen atoms have a slight positive charge. This supports the idea that there is a cloud of electrons above and below the plane of the ring.

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T10:28:00Z

Ce1116: /* Optimised NH3BH3 Molecule */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are are diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1| anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.

E(NH3)= -56.55777 a.u.

E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= '''-135.48 kJ/mol'''

The B-N bond is weak. When compared to the energy required to break the bond in hyrodgen (~436kJ/mol) or nitrogen (~945kJ/mol) it is clearly far weaker<ref>Y. R. Luo, ''Comprehensive Handbook of Chemical Bond Energies'', CRC Press, Boca Raton, FL, 2007 </ref>.

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:borazine_charge_ce.jpg]]
[[File:benzene_charge_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon and hydrogen atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge and hydrogen atoms have a slight positive charge. This supports the idea that there is a cloud of electrons above and below the plane of the ring.

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T10:19:04Z

Ce1116:

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are are diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1| anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:borazine_charge_ce.jpg]]
[[File:benzene_charge_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom (3.07) in the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron (2.01) and hydrogen (2.1) atoms with a residual positive charge<ref>E. J. Little and M. M. Jones, ''Journal of Chemical Education'', 1960, '''37''', 231</ref>.

There is only a small electronegativity difference between the carbon and hydrogen atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge and hydrogen atoms have a slight positive charge. This supports the idea that there is a cloud of electrons above and below the plane of the ring.

The charges in each of the molecules adds up to 0. The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T10:03:38Z

Ce1116: /* Optimised BH3 Molecule */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the shape, number of nodes and energy ordering is consistent. The only real difference being that the size of the actual MOs shows that they are are diffuse and larger than represented by the LCAO. This difference increases as the energy of the MOs increases and in the LCAO the contribution from the central B atom seems to be overestimated for the a1| anti-bonding MO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse. However, a little more knowledge is required to allow an appropriate energy ordering of the MOs when a molecular orbital diagram is drawn.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:borazine_charge_ce.jpg]]
[[File:benzene_charge_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom is the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron and hydrogen atoms with a residual positive charge.

There is only a small electronegativity difference between the carbon and hydrogen atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge and hydrogen atoms have a slight positive charge. This supports the idea that there is a cloud of electrons above and below the plane of the ring.

The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T09:56:51Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the only difference being that the actual MOs are more diffuse and larger than represented by the LCAO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

'''Benzene Optimisation'''
[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

'''Borazine Optimisation'''

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

'''Investigating Charge distribution'''

[[File:borazine_charge_ce.jpg]]
[[File:benzene_charge_ce.jpg]]

Borazine is isoelectronic with benzene. The distribution of charge in benzene is far less dramatic than that in borazine. This is represented by the shade difference of the atoms (the more dull/darker the colour, the less charged). The bright green and red boron, nitrogen and hyrdrogen atoms are present due to the large electronegativity difference between these atoms. Nitrogen is the most electronegative atom is the molecule and so most of the negative charge resides on nitrogen atoms, leaving the boron and hydrogen atoms with a residual positive charge.

There is only a small electronegativity difference between the carbon and hydrogen atoms in benzene and so the charge distribution is more evenly distributed around the molecule. The carbon atoms have a slight negative charge and hydrogen atoms have a slight positive charge. This supports the idea that there is a cloud of electrons above and below the plane of the ring.

The more evenly distributed charge in benzene over borazine may provide an explanation as to why benzene is considered more aromatic than benzene.

'''Molecular Orbitals'''
{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || Four s orbitals combine to provide relatively deep energy bonding orbital. There is only one nodal plane and the MOs are anti-symmetric with a centre of inversion.
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || There is a very high symmetry for the MOs (left),which are identical for benzene and borazine with five nodes each present on the ring atoms. Only orbitals from ring atoms are combined for these two MOs.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

File:Cathy mo2 ce.jpg

2018-05-25T09:35:00Z

Ce1116:

01217148

2018-05-25T09:34:43Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the only difference being that the actual MOs are more diffuse and larger than represented by the LCAO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

Borazine is isoelectronic with benzene, however, it is only mildly aromatic.

[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

Borazine Data

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

Charge distribution

[[File:borazine_charge_ce.jpg]]

[[File:benzene_charge_ce.jpg]]

Molecular Orbitals

{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] || Both the benzene and borazine MOs displayed here have the same charge distrubution and size. Three p orbitals are combined in phase and these two combinations are combined out of phase. There are two nodal planes with all ring atoms involved, only two hydrogen atoms involved in this MO.
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:cathy_mo2_ce.jpg]] || s orbitals combine to provide this bonding orbital
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] || These molecular orbitals are anti-bonding, with five nodes for each. Identical MOs for each of these.
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T09:22:49Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the only difference being that the actual MOs are more diffuse and larger than represented by the LCAO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

Borazine is isoelectronic with benzene, however, it is only mildly aromatic.

[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

Borazine Data

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

Charge distribution

[[File:borazine_charge_ce.jpg]]

[[File:benzene_charge_ce.jpg]]

Molecular Orbitals

{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] ||
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:mo3_sketch_ce.jpg]] ||
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] ||
|}

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T09:22:19Z

Ce1116: /* The Concept of Aromaticity */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the only difference being that the actual MOs are more diffuse and larger than represented by the LCAO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

Borazine is isoelectronic with benzene, however, it is only mildly aromatic.

[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

Borazine Data

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

Charge distribution

[[File:borazine_charge_ce.jpg]]

[[File:benzene_charge_ce.jpg]]

Molecular Orbitals

{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] ||
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:mo3_sketch_ce.jpg]] ||
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] ||
|}

[[File:borazine_mo1_ce.jpg]] energy=-0.27591

[[File:benzene_mo1_ce.jpg]] energy=-0.24691

[[File:mo1_sketch_ce.jpg]]

[[File:borazine_mo3_ce.jpg]] energy=-0.83512

[[File:cathy_mo1_ce.jpg]] energy=-0.74004

[[File:mo3_sketch_ce.jpg]]

[[File:borazine_mo4_ce.jpg]] energy=-0.43198

[[File:benzene_mo4_ce.jpg]] energy=-0.43854

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.)<ref>M. Palusiak and T. M. Krygowski,''Chem. Eur. J.'', 2007, '''13''', 7996-8006</ref> so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T09:19:52Z

Ce1116: /* The Concept of Aromaticity */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the only difference being that the actual MOs are more diffuse and larger than represented by the LCAO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

Borazine is isoelectronic with benzene, however, it is only mildly aromatic.

[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

Borazine Data

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

Charge distribution

[[File:borazine_charge_ce.jpg]]

[[File:benzene_charge_ce.jpg]]

Molecular Orbitals

{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] ||
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:mo3_sketch_ce.jpg]] ||
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] ||
|}

[[File:borazine_mo1_ce.jpg]] energy=-0.27591

[[File:benzene_mo1_ce.jpg]] energy=-0.24691

[[File:mo1_sketch_ce.jpg]]

[[File:borazine_mo3_ce.jpg]] energy=-0.83512

[[File:cathy_mo1_ce.jpg]] energy=-0.74004

[[File:mo3_sketch_ce.jpg]]

[[File:borazine_mo4_ce.jpg]] energy=-0.43198

[[File:benzene_mo4_ce.jpg]] energy=-0.43854

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many<ref>Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. von Rague Schleyer, ''Chem. Rev'', 2005, '''105''', 3842-3888</ref>.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.) so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T09:16:10Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the only difference being that the actual MOs are more diffuse and larger than represented by the LCAO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

Borazine is isoelectronic with benzene, however, it is only mildly aromatic.

[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

Borazine Data

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

Charge distribution

[[File:borazine_charge_ce.jpg]]

[[File:benzene_charge_ce.jpg]]

Molecular Orbitals

{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! LCAO !! Description
|-
| [[File:benzene_mo1_ce.jpg]] || [[File:borazine_mo1_ce.jpg]] || [[File:mo1_sketch_ce.jpg]] ||
|-
| [[File:cathy_mo1_ce.jpg]] || [[File:borazine_mo3_ce.jpg]] || [[File:mo3_sketch_ce.jpg]] ||
|-
| [[File:benzene_mo4_ce.jpg]] || [[File:borazine_mo4_ce.jpg]] || [[File:mo4_sketch_ce.jpg]] ||
|}

[[File:borazine_mo1_ce.jpg]] energy=-0.27591

[[File:benzene_mo1_ce.jpg]] energy=-0.24691

[[File:mo1_sketch_ce.jpg]]

[[File:borazine_mo3_ce.jpg]] energy=-0.83512

[[File:cathy_mo1_ce.jpg]] energy=-0.74004

[[File:mo3_sketch_ce.jpg]]

[[File:borazine_mo4_ce.jpg]] energy=-0.43198

[[File:benzene_mo4_ce.jpg]] energy=-0.43854

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.) so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T09:11:18Z

Ce1116: /* Benzene vs Borazine */

===Optimised BH3 Molecule===

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

[[File:cathy_bh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

The frequency file is linked here:[[File:CATHYEAGLE_BH3_FREQ.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -12.3889 -12.3823 -7.7287 0.0008 0.0237 0.4048
Low frequencies --- 1162.9692 1213.1354 1213.1356
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CATHYEAGLE_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

The IR spectral data is shown below:

<pre>
Mode Frequency Intensity Symmetry IR active? Type

1 1163 93 A2" yes out-of-plane bend
2 1213 14 E' slightly in plane bend
3 1213 14 E' slightly in plane bend
4 2583 0 A1' no symmetric stretch
5 2716 126 E' yes asymmetric stretch
6 2716 126 E' yes asymmetric stretch
</pre>

[[File:bh3_spectrum_ce.jpg]]

Vibrational modes 2/3 and 5/6 are degenerate so these only appear as a single peak. The intensity of the 2/3 appears much smaller than the 5/6 peaks, this is due to the stretching frequencies resulting in a larger change in dipole moment therefore higher intensity peak. Mode 4 is IR inactive since there is no change in dipole moment resulting from the symmetric stretch.
[[File:finalmo_ce.jpg]]

<ref>Dr Patricia Hunt, Lecture 4 Tutorial Sheet, Figure 5</ref>

There are no large differences between the real MO diagrams and the LCAO MOs, the only difference being that the actual MOs are more diffuse and larger than represented by the LCAO.
This means that MO theory is extremely useful and sufficiently accurate to give a reasonable approximation as to the shape of the MOs, only the real MOs are just a larger and more diffuse.

===Optimised NH3 Molecule===

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

[[File:cathy_nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000159 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3_OPT_CE_FREQ1.LOG]]

Frequencies tabulated below:

<pre>
Low frequencies --- -0.0050 -0.0014 -0.0009 17.4186 17.4188 19.6420
Low frequencies --- 1089.1064 1693.9379 1693.9379
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3_OPT_CE_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Optimised NH3BH3 Molecule===

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

[[File:cathy_bh3nh3_opt_1.jpg]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000379 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.001716 0.001800 YES
RMS Displacement 0.000619 0.001200 YES
</pre>

The frequency file is linked here: [[File:NH3BH3_OPT_FREQ_CE.LOG]]

<pre>
Low frequencies --- -0.1316 -0.0056 0.0006 2.7940 9.1524 9.1570
Low frequencies --- 263.3683 632.0980 638.7094
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_OPT_FREQ_CE.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532 a.u.
E(NH3)= -56.55777 a.u.
E(NH3BH3)= -83.22469 a.u.

change in energy= E(NH3BH3)-[E(NH3)+E(BH3)]= -0.0516 a.u.= -135.48kJ/mol

The B-N bond is weak. When compared to the energy required to break the bond in nitrogen (~1246kJ/mol) it is clearly far weaker. https://aip.scitation.org/doi/pdf/10.1063/1.1747958

== BBr3 ==
'''B3LYP/6-31G(d,p)LANL2DZ'''

BBr3 identifier:
{{DOI|10042/202467}}

[[File:cathy_bbr3_opt.jpg]]

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

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000037 0.001800 YES
RMS Displacement 0.000018 0.001200 YES
</pre>

The frequency file is linked here: [[File:bbr3_freqanalysis.log]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>bbr3_freqanalysis.log</uploadedFileContents>
</jmolApplet></jmol>

== Benzene vs Borazine ==
'''B3LYP/6-31G(d,p)'''

Borazine is isoelectronic with benzene, however, it is only mildly aromatic.

[[File:benzene_opt_table.jpg]]

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

Link to frequency file of benzene: [[File:BENZENE_OPT_CE_FREQ.LOG]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE_OPT_CE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0054 0.0003
Low frequencies --- 414.1239 414.1239 620.9400
</pre>

Borazine Data

[[File:borazine_opt_table.jpg]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000191 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency file: [[File:borazine_opt_ce_freq.log]]
<pre>
Low frequencies --- -0.0330 -0.0138 -0.0036 2.9275 2.9307 4.0750
Low frequencies --- 289.7198 289.7206 404.4180
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>borazine_opt_ce_freq.log</uploadedFileContents>
</jmolApplet></jmol>

Charge distribution

[[File:borazine_charge_ce.jpg]]

[[File:benzene_charge_ce.jpg]]

Molecular Orbitals

{| class="wikitable" border="1"
|+ Benzene vs Borazine MOs
! Benzene !! Borazine !! Description
|-
| [[File:borazine_mo1_ce.jpg] || cell
|-
| cell || cell
|}

[[File:borazine_mo1_ce.jpg]] energy=-0.27591

[[File:benzene_mo1_ce.jpg]] energy=-0.24691

[[File:mo1_sketch_ce.jpg]]

[[File:borazine_mo3_ce.jpg]] energy=-0.83512

[[File:cathy_mo1_ce.jpg]] energy=-0.74004

[[File:mo3_sketch_ce.jpg]]

[[File:borazine_mo4_ce.jpg]] energy=-0.43198

[[File:benzene_mo4_ce.jpg]] energy=-0.43854

[[File:mo4_sketch_ce.jpg]]

== The Concept of Aromaticity ==

Simply, aromaticity is the delocalisation of eletcrons within a system, resulting in a stabilisation. Beginning with benzene, then extended to other molecules (annulenes, aromatics ommitting benzene and inorganic alternatives), aromaticity does not require the restriction of planarity as was once thought and a compound can actually be three dimensional. Aromaticity has also been linked to the sigma-electron structure by some, since the true reason for the increased stability has eluded many.

There are four major consequences of aromaticity; more stable complexes, lower reactivity to addition (since the original molecule is already extremely stable), bond lengths are generally between the single and double bond length for the non aromatic analogue. Finally, aromatics display magnetic properties due to the network of delocalised electrons present. These four characteristics allow the identification of an aromatic compound, however, many sub-sets of aromaticity have been described (anti-,pseudo-, etc.) so clearly this is only qualitative.

The energy difference between aromatic and non-aromatic analogues can allow an insight into the extent of aromaticity of a complex, however, this is often difficult to measure and calculate and even to attribute any energy difference to the fact that a molecule is aromatic. Overall, aromaticity can be thought of as a combination of these factors (and potentially others e.g. sigma electron structures) and no single factor can be considered in isolation.

01217148

2018-05-25T09:10:02Z

Ce1116: /* Benzene vs Borazine */

File:Cathy mo1 ce.jpg

2018-05-25T09:06:37Z

Ce1116:

01217148

2018-05-25T09:06:20Z

Ce1116: /* Benzene vs Borazine */

01217148

2018-05-25T08:58:01Z

Ce1116:

01217148

2018-05-25T08:55:10Z

Ce1116:

01217148

2018-05-25T08:53:06Z

Ce1116: /* The Concept of Aromaticity */

01217148

2018-05-25T08:45:28Z

Ce1116: /* The Concept of Aromaticity */

01217148

2018-05-25T08:40:15Z

Ce1116:

01217148

2018-05-24T20:14:48Z

Ce1116: /* Headline text */

01217148

2018-05-24T20:14:20Z

Ce1116: /* Optimised NH3BH3 Molecule */

File:Finalmo ce.jpg

2018-05-24T20:08:00Z

Ce1116:

01217148

2018-05-24T20:07:45Z

Ce1116:

File:Mo4 sketch ce.jpg

2018-05-24T19:47:44Z

Ce1116:

File:Benzene mo4 ce.jpg

2018-05-24T19:47:30Z

Ce1116:

File:Borazine mo4 ce.jpg

2018-05-24T19:47:16Z

Ce1116:

01217148

2018-05-24T19:46:58Z

Ce1116:

File:Mo3 sketch ce.jpg

2018-05-24T19:30:24Z

Ce1116:

File:Benzene mo3 ce.jpg

2018-05-24T19:30:09Z

Ce1116:

File:Borazine mo3 ce.jpg

2018-05-24T19:29:55Z

Ce1116: