ChemWiki - User contributions [en]

Kt916

2018-05-10T16:10:29Z

Kt916: /* Aromaticity Discussion */

==Y2 Inorganic Computational Lab==

===EX3 Section===
====BH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_BH3_Summary.png|Thumb|The Summary Table for BH3]]
<pre>

Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES

</pre>

Frequency analysis log file [[File:KT_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.1082 -0.0045 -0.0006 46.3499 46.3501 47.3456
Low frequencies --- 1163.7050 1213.6299 1213.6302
</pre>

<jmol><jmolApplet>
<title>BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrational spectrum for BH3'''
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|92
|A2ˈˈ
|yes
|out-of-plane bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|2580
|0
|A1ˈ
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

[[File:KR_BH3_IR.png|Thumb|The IR spectra for BH3]]

For an stretch to be IR active, it must, after vibration have a change in dipole moment in which the stretch at 2580cm-1, the symmetric stretch does not. The two vibrations corresponding to 1214 and 2713-1, have 2 vibrations that are degenerate, hence they are superimposed on the IR spectra. Hence only 3 peaks are shown on the final spectra, they are 1163, 1214 and 2712 cm-1

'''MO Diagram'''
[[File:KT MO Diagram BH3.png|KT MO Diagram BH3.png]]
Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, accessed on 08/05/2018

The Linear Combination of Atomic orbitals have correctly predicted the phase and the nodes of the real MO's, however the LCAO orbitals do not encompass the whole molecule and are a bit misaligned in regards to the electron densities. The shapes of the MO's are pretty close, they are, however calculated using the IPA (independent Particle approximation) hence to not take into account the V term (The interactions between the electrons) so a slight difference is expected.

====NH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_NH3_Summary.PNG ‎|Thumb|The Summary Table for NH3]]
<pre>

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

</pre>

Frequency analysis log file [[File:KT_NH3_6-31_OPT.LOG]]

<pre>
Low frequencies --- -0.0130 -0.0018 0.0013 7.1034 8.1048 8.1051
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_NH3_6-31_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====NH3BH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_NH3BH3_Summary.PNG ‎|Thumb|The Summary Table for NH3BH3]]
<pre>

Item Value Threshold Converged?
Maximum Force 0.000179 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.001586 0.001800 YES
RMS Displacement 0.000696 0.001200 YES

</pre>

Frequency analysis log file [[File:KT_NH3BH3_6-31_OPT.LOG]]

<pre>
Low frequencies --- -0.0280 -0.0097 -0.0049 10.4098 10.4563 24.2385
Low frequencies --- 265.0508 634.1235 639.9020
</pre>

<jmol><jmolApplet>
<title>NH3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_NH3BH3_6-31_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Energy Calculations====
E(NH3) = -56.55777 Eh = -141394 kJ/mol 
E(BH3) = -26.61532 Eh = -66538 kJ/mol 
E(NH3BH3) = -83.22469 Eh = -208062 kJ/mol 

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 Eh = -129 kJ/mol 

I would say that the bond is around medium strength as expected for a bond with an ionic component. (Electronegativity difference between B and N = 1.0 ). Weaker than a C-C bond (350 KJ/mol) yet stronger than typical Hydrogen bonds (20 KJ/mol).

====BBr3 pseudo-potentials analysis====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p), (B), LanLDZ (Br) (manually specified pseudo-potentials)

[[File:KT_BBR3_Summary.PNG ‎|Thumb|The Summary Table for NH3]]
<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
Predicted change in Energy=-4.301212D-10
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis log file [[File:KT_BBR3_5_FREQ.log]]

'''Dspace link''' {{DOI|10042/202377}}

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

<jmol><jmolApplet>
<title>BBR3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BBR3_5_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Project Section: Aromaticity===
====Borazine====

[[File:KT_BORAZINE_Summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
</pre>

[[File:KT_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -0.0303 -0.0150 -0.0036 3.2025 3.2053 3.7578
Low frequencies --- 289.7201 289.7209 404.4099
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Benzene====

[[File:KT_BENZENE_Summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000084 0.000300 YES
Maximum Displacement 0.000767 0.001800 YES
RMS Displacement 0.000328 0.001200 YES
</pre>

[[File:KT_BENZENE_FREQ.LOG]]

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

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Charge Distributions====
{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_CHARGE.PNG]] || [[File:KT_BORAZINE_CHARGE.PNG]]
|}
For '''Benzene''', the charge distribution for all the Carbon's and Hydrogen's are the same, which is to be expected under the D6H symmetry as all of the C and N are identical to one another. Carbon's Electronegativity is 2.55 while Hydrogen's is 2.20, leading the the electron density in the C-H bond to be drawn to the Carbon, hence -2.39 Db charge and +2.39 Db charge for Carbon and Hydrogen respectively. In addition, there is no dipole moment in the molecule (It all cancels out due to the center of inversion present in the center of the flat ring).

With the introduction of Boron and Nitrogen instead of Carbon in '''Borazine''', there is a reduction in symmetry from C6 to D3H. Looking at the B-N bonds, the more electronegative Nitrogen (3.04) compared to Boron (2.04) means the charges at N are -1.1042 Db and at B are +0.747 Db. In addition even H (electronegativity 2.20) is greater than Boron, leaving hydrogen with a charge of -0.077 Db while the N-H bond Hydrogens are at +0.432 Db. In this case, according to the Jmol images, the Borazine is planar with a center of inversion so there is no net dipole.

====Comparing MOs====
{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_17.PNG]] || [[File:KT_BORAZINE_17.PNG]] || MO17 for both of the aromatic molecules are the lowest totally symmetric in phase π bonding. These are usually the representations of a aromatic molecule when drawing out delocalised pz orbitals. Similar to MO7, the totally symmetric in phase bonding MO for bot complexes, the Benzene MO is very symmetric and delocalized throughout however the Borazine one is a bit skewed, with 3 hydrogen's next to the boron's not contributing.
|-
| [[File:KT_BENZENE_18.PNG]] || [[File:KT_BORAZINE_18.PNG]] || MO 18 on the other hand is a bonding σ orbital with 4 nodal planes. The shape of the MO's are roughly the smae, with the nodes being in roughly the same place, however there is no line of symmetry vertical to the page (σv) for Borazine unlike the highly symmetrical Benzene orbitals. This causes some skewed mismatched orbitals in Borazine consequent of the difference in electronegativityy between N and B. There are more contributions from the negatively charged Hydrogens (B-H bonds) compared to positively charged ones.
|-
| [[File:KT_BENZENE_21.PNG]] || [[File:KT_BORAZINE_21.PNG]] || MO 21 is the HOMO for both of the molecules and unlike MO17, has some anti-bonding character as shown by the 2 nodes, however it is still bonding overall. The π bonding for Benzene again looks identical on both sides of the molecule however in Borazine, the two sides are not equivalent. One consists of 2 B and 1 N and vice versa for the other, leading to a different shape of the 2 B 1 N one being more compact and less like a boomerang shape. In addition, the dis-involvement of some of the H is seen again (as with MO17) in the Borazine.
|}

====Aromaticity Discussion====

{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_7.PNG]] || [[File:KT_BORAZINE_7.PNG]] || MO 7
|-
| [[File:KT_BENZENE_12.PNG]] || [[File:KT_BORAZINE_12.PNG|thumbnail| No contribution to delocalisation]] || MO 12
|}

The basic concepts of aromaticity stems from the delocalisation of π electrons over multiple carbon atoms and is usually represented by the drawing of 6pz p orbitals on a benzene ring. After the computation of the molecules Benzene and Borazine, 3 bonding and 3 anti-bonding π MOs along with many σ MOs were found from the Liunear combination of atomic orbitals. MO 17 (as shown above) pretty much represents the basic picture of aromaticity of p orbital overlap, with 2 lobes above and below the ring giving rise to aromatic traits (Equal bond lengths, Resonance stabilization energies, Pi ring currents). However, it must be noted that there are 2 other π bonding MOs (20 and 21) which also shows the spreading out of electron density across the carbon molecules (albeit with some nodes) though a bit more complex and not as straight forward.

The concept of overlapping pz AOs does not give the whole story of aromaticity. This is due to 2 reasons. One being the fact that the other 2 bonding π bonding MOs were not included in the basic explanation of aromaticity. The other, is due to ignoring the σ orbital contributions to aromticity at all. Literature states that the role of σ-electron structure may be of importance as well and it is the vital to explain the more detailed picture of aromaticity. Computational analysis of MOs via LCAO shpws 2 σ orbitals for Benzene (7 and 12) which contribute to the spreading out of electron density across the carbon bonds. In Borazine, however only has 1 (MO 7), therefore the σ framework actually can be used to explain why Borazine is less aromatic than benzene (Lower resonance stabilization energy) and also why Borazine is generally more reactive.

Kt916

2018-05-10T16:09:48Z

Kt916: /* Aromaticity Discussion */

==Y2 Inorganic Computational Lab==

===EX3 Section===
====BH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_BH3_Summary.png|Thumb|The Summary Table for BH3]]
<pre>

Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES

</pre>

Frequency analysis log file [[File:KT_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.1082 -0.0045 -0.0006 46.3499 46.3501 47.3456
Low frequencies --- 1163.7050 1213.6299 1213.6302
</pre>

<jmol><jmolApplet>
<title>BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrational spectrum for BH3'''
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|92
|A2ˈˈ
|yes
|out-of-plane bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|2580
|0
|A1ˈ
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

[[File:KR_BH3_IR.png|Thumb|The IR spectra for BH3]]

For an stretch to be IR active, it must, after vibration have a change in dipole moment in which the stretch at 2580cm-1, the symmetric stretch does not. The two vibrations corresponding to 1214 and 2713-1, have 2 vibrations that are degenerate, hence they are superimposed on the IR spectra. Hence only 3 peaks are shown on the final spectra, they are 1163, 1214 and 2712 cm-1

'''MO Diagram'''
[[File:KT MO Diagram BH3.png|KT MO Diagram BH3.png]]
Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, accessed on 08/05/2018

The Linear Combination of Atomic orbitals have correctly predicted the phase and the nodes of the real MO's, however the LCAO orbitals do not encompass the whole molecule and are a bit misaligned in regards to the electron densities. The shapes of the MO's are pretty close, they are, however calculated using the IPA (independent Particle approximation) hence to not take into account the V term (The interactions between the electrons) so a slight difference is expected.

====NH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_NH3_Summary.PNG ‎|Thumb|The Summary Table for NH3]]
<pre>

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

</pre>

Frequency analysis log file [[File:KT_NH3_6-31_OPT.LOG]]

<pre>
Low frequencies --- -0.0130 -0.0018 0.0013 7.1034 8.1048 8.1051
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_NH3_6-31_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====NH3BH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_NH3BH3_Summary.PNG ‎|Thumb|The Summary Table for NH3BH3]]
<pre>

Item Value Threshold Converged?
Maximum Force 0.000179 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.001586 0.001800 YES
RMS Displacement 0.000696 0.001200 YES

</pre>

Frequency analysis log file [[File:KT_NH3BH3_6-31_OPT.LOG]]

<pre>
Low frequencies --- -0.0280 -0.0097 -0.0049 10.4098 10.4563 24.2385
Low frequencies --- 265.0508 634.1235 639.9020
</pre>

<jmol><jmolApplet>
<title>NH3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_NH3BH3_6-31_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Energy Calculations====
E(NH3) = -56.55777 Eh = -141394 kJ/mol 
E(BH3) = -26.61532 Eh = -66538 kJ/mol 
E(NH3BH3) = -83.22469 Eh = -208062 kJ/mol 

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 Eh = -129 kJ/mol 

I would say that the bond is around medium strength as expected for a bond with an ionic component. (Electronegativity difference between B and N = 1.0 ). Weaker than a C-C bond (350 KJ/mol) yet stronger than typical Hydrogen bonds (20 KJ/mol).

====BBr3 pseudo-potentials analysis====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p), (B), LanLDZ (Br) (manually specified pseudo-potentials)

[[File:KT_BBR3_Summary.PNG ‎|Thumb|The Summary Table for NH3]]
<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
Predicted change in Energy=-4.301212D-10
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis log file [[File:KT_BBR3_5_FREQ.log]]

'''Dspace link''' {{DOI|10042/202377}}

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

<jmol><jmolApplet>
<title>BBR3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BBR3_5_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Project Section: Aromaticity===
====Borazine====

[[File:KT_BORAZINE_Summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
</pre>

[[File:KT_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -0.0303 -0.0150 -0.0036 3.2025 3.2053 3.7578
Low frequencies --- 289.7201 289.7209 404.4099
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Benzene====

[[File:KT_BENZENE_Summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000084 0.000300 YES
Maximum Displacement 0.000767 0.001800 YES
RMS Displacement 0.000328 0.001200 YES
</pre>

[[File:KT_BENZENE_FREQ.LOG]]

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

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Charge Distributions====
{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_CHARGE.PNG]] || [[File:KT_BORAZINE_CHARGE.PNG]]
|}
For '''Benzene''', the charge distribution for all the Carbon's and Hydrogen's are the same, which is to be expected under the D6H symmetry as all of the C and N are identical to one another. Carbon's Electronegativity is 2.55 while Hydrogen's is 2.20, leading the the electron density in the C-H bond to be drawn to the Carbon, hence -2.39 Db charge and +2.39 Db charge for Carbon and Hydrogen respectively. In addition, there is no dipole moment in the molecule (It all cancels out due to the center of inversion present in the center of the flat ring).

With the introduction of Boron and Nitrogen instead of Carbon in '''Borazine''', there is a reduction in symmetry from C6 to D3H. Looking at the B-N bonds, the more electronegative Nitrogen (3.04) compared to Boron (2.04) means the charges at N are -1.1042 Db and at B are +0.747 Db. In addition even H (electronegativity 2.20) is greater than Boron, leaving hydrogen with a charge of -0.077 Db while the N-H bond Hydrogens are at +0.432 Db. In this case, according to the Jmol images, the Borazine is planar with a center of inversion so there is no net dipole.

====Comparing MOs====
{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_17.PNG]] || [[File:KT_BORAZINE_17.PNG]] || MO17 for both of the aromatic molecules are the lowest totally symmetric in phase π bonding. These are usually the representations of a aromatic molecule when drawing out delocalised pz orbitals. Similar to MO7, the totally symmetric in phase bonding MO for bot complexes, the Benzene MO is very symmetric and delocalized throughout however the Borazine one is a bit skewed, with 3 hydrogen's next to the boron's not contributing.
|-
| [[File:KT_BENZENE_18.PNG]] || [[File:KT_BORAZINE_18.PNG]] || MO 18 on the other hand is a bonding σ orbital with 4 nodal planes. The shape of the MO's are roughly the smae, with the nodes being in roughly the same place, however there is no line of symmetry vertical to the page (σv) for Borazine unlike the highly symmetrical Benzene orbitals. This causes some skewed mismatched orbitals in Borazine consequent of the difference in electronegativityy between N and B. There are more contributions from the negatively charged Hydrogens (B-H bonds) compared to positively charged ones.
|-
| [[File:KT_BENZENE_21.PNG]] || [[File:KT_BORAZINE_21.PNG]] || MO 21 is the HOMO for both of the molecules and unlike MO17, has some anti-bonding character as shown by the 2 nodes, however it is still bonding overall. The π bonding for Benzene again looks identical on both sides of the molecule however in Borazine, the two sides are not equivalent. One consists of 2 B and 1 N and vice versa for the other, leading to a different shape of the 2 B 1 N one being more compact and less like a boomerang shape. In addition, the dis-involvement of some of the H is seen again (as with MO17) in the Borazine.
|}

====Aromaticity Discussion====

{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_7.PNG]] || [[File:KT_BORAZINE_7.PNG]] || MO 7
|-
| [[File:KT_BENZENE_12.PNG]] || [[File:KT_BORAZINE_12.PNG|thumbnail| No contribution to delocalisation]] || MO 12
|}

The basic concepts of aromaticity stems from the delocalisation of π electrons over multiple carbon atoms and is usually represented by the drawing of 6pz p orbitals on a benzene ring. After the computation of the molecules Benzene and Borazine, 3 bonding and 3 anti-bonding π MOs along with many σ MOs were found from the Liunear combination of atomic orbitals. MO 17 (as shown above) pretty much represents the basic picture of aromaticity of p orbital overlap, with 2 lobes above and below the ring giving rise to aromatic traits (Equal bond lengths, Resonance stabilization energies, Pi ring currents). However, it must be noted that there are 2 other π bonding MOs (20 and 21) which also shows the spreading out of electron density across the carbon molecules (albeit with some nodes) though a bit more complex and not as straight forward.

The concept of overlapping pz AOs does not give the whole story of aromaticity. This is due to 2 reasons. One being the fact that the other 2 bonding π bonding MOs were not included in the basic explanation of aromaticity. The other, is due to ignoring the σ orbital contributions to aromticity at all. Literature states that the role of σ-electron structure may be of importance as well and it is the vital to explain the more detailed picture of aromaticity. In addition σ electrons are actually more well known to delocalise compared to π electrons, so the equal bond lengths are also owed to the σ framework. Computational analysis of MOs via LCAO shpws 2 σ orbitals for Benzene (7 and 12) which contribute to the spreading out of electron density across the carbon bonds. In Borazine, however only has 1 (MO 7), therefore the σ framework actually can be used to explain why Borazine is less aromatic than benzene (Lower resonance stabilization energy) and also why Borazine is generally more reactive.

Kt916

2018-05-10T16:09:17Z

Kt916: /* Aromaticity Discussion */

==Y2 Inorganic Computational Lab==

===EX3 Section===
====BH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_BH3_Summary.png|Thumb|The Summary Table for BH3]]
<pre>

Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES

</pre>

Frequency analysis log file [[File:KT_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.1082 -0.0045 -0.0006 46.3499 46.3501 47.3456
Low frequencies --- 1163.7050 1213.6299 1213.6302
</pre>

<jmol><jmolApplet>
<title>BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrational spectrum for BH3'''
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|92
|A2ˈˈ
|yes
|out-of-plane bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|2580
|0
|A1ˈ
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

[[File:KR_BH3_IR.png|Thumb|The IR spectra for BH3]]

For an stretch to be IR active, it must, after vibration have a change in dipole moment in which the stretch at 2580cm-1, the symmetric stretch does not. The two vibrations corresponding to 1214 and 2713-1, have 2 vibrations that are degenerate, hence they are superimposed on the IR spectra. Hence only 3 peaks are shown on the final spectra, they are 1163, 1214 and 2712 cm-1

'''MO Diagram'''
[[File:KT MO Diagram BH3.png|KT MO Diagram BH3.png]]
Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, accessed on 08/05/2018

The Linear Combination of Atomic orbitals have correctly predicted the phase and the nodes of the real MO's, however the LCAO orbitals do not encompass the whole molecule and are a bit misaligned in regards to the electron densities. The shapes of the MO's are pretty close, they are, however calculated using the IPA (independent Particle approximation) hence to not take into account the V term (The interactions between the electrons) so a slight difference is expected.

====NH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_NH3_Summary.PNG ‎|Thumb|The Summary Table for NH3]]
<pre>

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

</pre>

Frequency analysis log file [[File:KT_NH3_6-31_OPT.LOG]]

<pre>
Low frequencies --- -0.0130 -0.0018 0.0013 7.1034 8.1048 8.1051
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_NH3_6-31_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====NH3BH3====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p)

[[File:KT_NH3BH3_Summary.PNG ‎|Thumb|The Summary Table for NH3BH3]]
<pre>

Item Value Threshold Converged?
Maximum Force 0.000179 0.000450 YES
RMS Force 0.000097 0.000300 YES
Maximum Displacement 0.001586 0.001800 YES
RMS Displacement 0.000696 0.001200 YES

</pre>

Frequency analysis log file [[File:KT_NH3BH3_6-31_OPT.LOG]]

<pre>
Low frequencies --- -0.0280 -0.0097 -0.0049 10.4098 10.4563 24.2385
Low frequencies --- 265.0508 634.1235 639.9020
</pre>

<jmol><jmolApplet>
<title>NH3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_NH3BH3_6-31_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Energy Calculations====
E(NH3) = -56.55777 Eh = -141394 kJ/mol 
E(BH3) = -26.61532 Eh = -66538 kJ/mol 
E(NH3BH3) = -83.22469 Eh = -208062 kJ/mol 

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 Eh = -129 kJ/mol 

I would say that the bond is around medium strength as expected for a bond with an ionic component. (Electronegativity difference between B and N = 1.0 ). Weaker than a C-C bond (350 KJ/mol) yet stronger than typical Hydrogen bonds (20 KJ/mol).

====BBr3 pseudo-potentials analysis====

'''Method''': RB3LYP
'''Basis Set''': 6-31G(d.p), (B), LanLDZ (Br) (manually specified pseudo-potentials)

[[File:KT_BBR3_Summary.PNG ‎|Thumb|The Summary Table for NH3]]
<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
Predicted change in Energy=-4.301212D-10
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis log file [[File:KT_BBR3_5_FREQ.log]]

'''Dspace link''' {{DOI|10042/202377}}

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

<jmol><jmolApplet>
<title>BBR3Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BBR3_5_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Project Section: Aromaticity===
====Borazine====

[[File:KT_BORAZINE_Summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000061 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
</pre>

[[File:KT_BORAZINE_FREQ.LOG]]

<pre>
Low frequencies --- -0.0303 -0.0150 -0.0036 3.2025 3.2053 3.7578
Low frequencies --- 289.7201 289.7209 404.4099
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Benzene====

[[File:KT_BENZENE_Summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000084 0.000300 YES
Maximum Displacement 0.000767 0.001800 YES
RMS Displacement 0.000328 0.001200 YES
</pre>

[[File:KT_BENZENE_FREQ.LOG]]

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

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>KT_BENZENE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Charge Distributions====
{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_CHARGE.PNG]] || [[File:KT_BORAZINE_CHARGE.PNG]]
|}
For '''Benzene''', the charge distribution for all the Carbon's and Hydrogen's are the same, which is to be expected under the D6H symmetry as all of the C and N are identical to one another. Carbon's Electronegativity is 2.55 while Hydrogen's is 2.20, leading the the electron density in the C-H bond to be drawn to the Carbon, hence -2.39 Db charge and +2.39 Db charge for Carbon and Hydrogen respectively. In addition, there is no dipole moment in the molecule (It all cancels out due to the center of inversion present in the center of the flat ring).

With the introduction of Boron and Nitrogen instead of Carbon in '''Borazine''', there is a reduction in symmetry from C6 to D3H. Looking at the B-N bonds, the more electronegative Nitrogen (3.04) compared to Boron (2.04) means the charges at N are -1.1042 Db and at B are +0.747 Db. In addition even H (electronegativity 2.20) is greater than Boron, leaving hydrogen with a charge of -0.077 Db while the N-H bond Hydrogens are at +0.432 Db. In this case, according to the Jmol images, the Borazine is planar with a center of inversion so there is no net dipole.

====Comparing MOs====
{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_17.PNG]] || [[File:KT_BORAZINE_17.PNG]] || MO17 for both of the aromatic molecules are the lowest totally symmetric in phase π bonding. These are usually the representations of a aromatic molecule when drawing out delocalised pz orbitals. Similar to MO7, the totally symmetric in phase bonding MO for bot complexes, the Benzene MO is very symmetric and delocalized throughout however the Borazine one is a bit skewed, with 3 hydrogen's next to the boron's not contributing.
|-
| [[File:KT_BENZENE_18.PNG]] || [[File:KT_BORAZINE_18.PNG]] || MO 18 on the other hand is a bonding σ orbital with 4 nodal planes. The shape of the MO's are roughly the smae, with the nodes being in roughly the same place, however there is no line of symmetry vertical to the page (σv) for Borazine unlike the highly symmetrical Benzene orbitals. This causes some skewed mismatched orbitals in Borazine consequent of the difference in electronegativityy between N and B. There are more contributions from the negatively charged Hydrogens (B-H bonds) compared to positively charged ones.
|-
| [[File:KT_BENZENE_21.PNG]] || [[File:KT_BORAZINE_21.PNG]] || MO 21 is the HOMO for both of the molecules and unlike MO17, has some anti-bonding character as shown by the 2 nodes, however it is still bonding overall. The π bonding for Benzene again looks identical on both sides of the molecule however in Borazine, the two sides are not equivalent. One consists of 2 B and 1 N and vice versa for the other, leading to a different shape of the 2 B 1 N one being more compact and less like a boomerang shape. In addition, the dis-involvement of some of the H is seen again (as with MO17) in the Borazine.
|}

====Aromaticity Discussion====

{| class="wikitable" border="1"
! Benzene
! Borazine
|-
| [[File:KT_BENZENE_7.PNG]] || [[File:KT_BORAZINE_7.PNG]]
|-
| [[File:KT_BENZENE_12.PNG]] || [[File:KT_BORAZINE_12.PNG|thumbnail| No contribution to delocalisation]]
|}

The basic concepts of aromaticity stems from the delocalisation of π electrons over multiple carbon atoms and is usually represented by the drawing of 6pz p orbitals on a benzene ring. After the computation of the molecules Benzene and Borazine, 3 bonding and 3 anti-bonding π MOs along with many σ MOs were found from the Liunear combination of atomic orbitals. MO 17 (as shown above) pretty much represents the basic picture of aromaticity of p orbital overlap, with 2 lobes above and below the ring giving rise to aromatic traits (Equal bond lengths, Resonance stabilization energies, Pi ring currents). However, it must be noted that there are 2 other π bonding MOs (20 and 21) which also shows the spreading out of electron density across the carbon molecules (albeit with some nodes) though a bit more complex and not as straight forward.

The concept of overlapping pz AOs does not give the whole story of aromaticity. This is due to 2 reasons. One being the fact that the other 2 bonding π bonding MOs were not included in the basic explanation of aromaticity. The other, is due to ignoring the σ orbital contributions to aromticity at all. Literature states that the role of σ-electron structure may be of importance as well and it is the vital to explain the more detailed picture of aromaticity. In addition σ electrons are actually more well known to delocalise compared to π electrons, so the equal bond lengths are also owed to the σ framework. Computational analysis of MOs via LCAO shpws 2 σ orbitals for Benzene (7 and 12) which contribute to the spreading out of electron density across the carbon bonds. In Borazine, however only has 1 (MO 7), therefore the σ framework actually can be used to explain why Borazine is less aromatic than benzene (Lower resonance stabilization energy) and also why Borazine is generally more reactive.

File:KT BORAZINE 12.PNG

2018-05-10T16:08:43Z

Kt916:

2018-05-10T15:07:42Z

Kt916: /* Comparing MOs */

Kt916