ChemWiki - User contributions [en]

Rep:Mod:coffee table

2018-05-24T18:55:26Z

Nj916: /* The concept of aromaticity */

=Optimisation of BH3 via Gaussian=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 3-21G then 6-31G then FREQ calculation type of BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.000182 0.001800 YES
RMS Displacement 0.000091 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_bh3_freq.log]]

<pre> Low frequencies --- -0.4072 -0.1962 -0.0054 25.2514 27.2430 27.2460
Low frequencies --- 1163.1897 1213.3128 1213.3155</pre>

Although the low frequencies is out of the range of 12 ± 15 cm-1, the calculation has converged, the geometry and the total energy is correct and I have discussed with the demonstrator who confirmed that it is not outstandingly concerning.

Frequency table

{| class="wikitable" border="1"
! Mode number !! frequency (cm-1) !! Intensity !! Symmetry !! type
|-
| 1 || 1163 || Strong || A1 || Bend
|-
| 2 || 1213 || weak || E || Scissoring
|-
| 3 || 1213 || weak || E || Rocking
|-
| 4 || 2582 || not observed || A1 || Symmetric stretch
|-
| 5 || 2715 || strong || E || Asymmetric stretch
|-
| 6 || 2715 || strong || E || Asymmetric stretch
|}

Predicted IR spectrum

[[File:coffeetable_bh3_ir.png|600px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Molecular Orbitals===

[[File:coffeetable_bh3_mo.png|600px|thumb|none| This figure shows calculated molecular orbitals by gaussview compared to LCAOs using MO theory diagram adapted from tutorial material by Dr P.Hunt<ref>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</ref>. ]]

The diagram above demonstrates that LCAOs using MO theory predicts the nodes between the orbital lobes and the energy levels accurately though does not predict how diffused the orbitals are and the actual extent of how much the AOs overlap each other. Qualitative LCAOs are therefore useful to predict the energy level and the location of the nodes but not the actual shape of the orbitals itself and how diffused they are.

=NH3 analysis=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_nh3_freq.log]]

<pre> Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=NH3BH3=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000117 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000839 0.001800 YES
RMS Displacement 0.000362 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_nh3bh3_freq.log]]

<pre> Low frequencies --- 0.0004 0.0006 0.0013 18.5187 24.9168 40.9948
Low frequencies --- 266.3754 632.3711 639.9574</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3bh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3bh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=B-N Bond strength in NH3BH3=

==Energy Calculation==

To get the association energy of BH3 and NH3, the total energy of the caclulations are substituted into this equation:

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

The calculated total energies are:

BH3= -26.61532 a.u.

NH3= -56.55776 a.u.

NH3BH3= -83.22469 a.u.

Substituting into the equation:

ΔE=-83.22469-[-56.55776-26.61532]= -0.05161 a.u. ≈ -136 kj/mol

The association energy of NH3BH3 is therefore very weak. On average, the C-C bond energy is -347 kj/mol which is a lot higher than that of NH3BH3. To put in perspective, compare with a very weak bond such as F-F which has the association energy of -154 kj/mol<ref>http://butane.chem.uiuc.edu/cyerkes/Chem104ACSpring2009/Genchemref/bondenergies.html</ref>, the association energy is still higher in NH3BH3 which shows how weak it is.

=Psuedo-potential optimisation for BBR3 via B3LYP/6-31G(d,p)LANL2DZ=

===Result summary table===
[[File:coffeetable_bbr3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of BBr3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_bbr3_freq.log]]

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

Vibrational modes and intensities

[[File:coffeetable_bbr3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BBr3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Dspace Link/unique identfier===

{{DOI|10042/202456}}

=Day 2: Analysis of aromaticity=

==Benzene==

===Result summary table===
[[File:coffeetable_benzene_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of benzene ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000087 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000321 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_benzene_freq.log]]

<pre> Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0045 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390</pre>

Vibrational modes and intensities

[[File:coffeetable_benzene_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised benzene</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_benzene_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==

===Result summary table===
[[File:coffeetable_borazine_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000313 0.000450 YES
RMS Force 0.000101 0.000300 YES
Maximum Displacement 0.000511 0.001800 YES
RMS Displacement 0.000151 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_borazine_freq.log]]

<pre> Low frequencies --- -12.2781 -12.1074 -8.6374 -0.0099 -0.0086 0.0754
Low frequencies --- 289.0994 289.1102 403.8930</pre>

Vibrational modes and intensities

[[File:coffeetable_borazine_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised borazine</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_borazine_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Comparison between benzene and borazine==

===Charge distribution===

The charge distribution analysis was performed on both the compounds with these settings:

[[File:coffeetable_colour.png|400px]]

{| class="wikitable" border="1"
! Benzene !! Borazine !! Description
|-
| [[File:coffeetable_benzene_charge.png|300px|thumb|none|C=-0.239 H=0.239]]|| [[File:coffeetable_borazine_charge.png|300px|thumb|none|B=0.747 N=-1.102 H(B)=0.077 H(N)=0.432]] || In benzene, the charge distribution on all the carbons and all the hydrogens have the same values, -0.239 and 0.239 respectively; this is because all the carbons and all the hydrogens are in the same environments. The charge distribution in borazine is however not as uniform; the charges on boron atoms are 0.747, nitrogen atoms are -1.102 and the hydrogen atoms have two values depending on what atom it is bonded to (hence different environments). Nitrogen is electronegative and boron is more electropositive therefore the charge distribution between them is as expected and highly polarised. When hydrogen is bonded to nitrogen, the charge value is 0.432 and for boron hydrogens it is 0.077; this is due to the fact that boron is electron deficient and so pulls the electron density away from the hydrogen that's bonded to it, lowering the value. Comparing the charge distribution difference, in benzene the range is 0.478 while in borazine it's 1.849 which demonstrates how much more polarised borazine is compared to benzene (owing to the large difference in electronegativity between boron and nitrogen). This is the reason for borazine's reactivity and susceptibility to electrophilic attacks.
|}

===Molecular orbitals===

{| class="wikitable" border="1"
! heading !! heading !! Comparison
|-
| [[File:coffeetable_benzene_bonding.png|300px]] || [[File:coffeetable_borazine_bonding.png|300px]] || Both of the MO are formed purely from the overlap of pz orbitals of the heavy atoms. They both are delocalised, have the same phase as the z axis and are both bonding orbitals. The benzene MO is highly symmetrical whilst the borazine MO is less so with the nitrogen atom drawing the electron distribution to it/larger MO contribution due to lower AO energy, demonstrating the polarity of B-N pi bonds.
|-
| [[File:coffeetable_benzene_mild.png|300px]] || [[File:coffeetable_borazine_mildly.png|300px]] || Both of the MO are mildly bonding and are formed from the sigma bonding between the hydrogen sigma orbitals and the sp2 orbitals of the heavy atoms. Both of them have a delocalised orbital in the center of the ring. Benzene MO is highly symmetrical with contribution from all the hydrogen atoms. Borazine MO is less symmetrical and has no contribution from three hydrogen atoms.
|-
| [[File:coffeetable_benzene_anti.png|300px]] || [[File:coffeetable_borazine_anti.png|300px]] || Both of the MO are formed from the hydrogen out of phase sigma AOs with a small contribution from the heavy atoms and are mildly anti-bonding due to the node not being between the bonded atoms. Because they are anti-bonding, the largest contribution is from the higher energy hydrogen AOs. Benzene MO is highly symmetrical whilst the borazine MO has reduced symmetry as the size of the MO is affected by the difference in electronegativity between boron and nitrogen.
|}

===The concept of aromaticity===

Aromatic compounds are especially stable compounds when compared to their related structures and was first observed in benzene. The concept of aromaticity has evolved throughout the years since Kekule's definition on benzene, deducing that any compound related to benzene is aromatic. Another common definition of aromatic compounds are cylic compounds that have delocalised pi electrons, planar and follow Hückel's Rule of 4n+2 electrons. The current definition of aromaticity defines that for any compound to be aromatic, it must follow these criteria:

1) They must be more stable than the acyclic conjugated analogue compound or the saturated cyclic analogue compound. Therefore even if the compound has overlapping pz AOs in a linear conjugated system, it isn't necessarily an aromatic compound. Similarly, some cyclic compounds that have overlapping pz AOs are not stablised, even destablised by the system (anti-aromatic) thus these compounds are not aromatic; overlapping pz AOs is therefore not a good description for aromaticity.

2) They have bond lengths between the typical bond length values of single and double bonds; this is because the bonds in aromatic/resonance stablised compounds have the bonding molecular orbitals somewhat in between single and double bonds.

3) When subjected to a magnetic field, a pi-electron ring current is induced which in turn induces it's own magnetic field that counters the external magnetic field leading to the higher diamagnetic susceptibility values in 1H NMR spectroscopy for hydrogens that are outside the ring. Linear conjugated compounds do not exhibit this effect.

4) Under go chemical reactions where the pi-electron conjugated structure is conserved (aromatic substitution reactions).

Since aromaticity was first observed with benzene and other planar molecules like naphthalene, classically all aromatic compounds must be planar but following the modern definition, some non-planar compounds such as cyclophanes exhibit aromatic properties. Much of the aromaticity of a compound can be accounted to the cyclic pz overlapping AOs <ref>DOI: 10.1002/chem.200700250</ref>.

{| class="wikitable" border="0"
! !!
|-
||[[File:coffeetable_benzene_bonding.png|400px|thumb|none|This figure shows the delocalised pi MO system formed from the overlapping pz of the carbon atoms. Note the delocalised and diffused MO.]]||[[File:coffeetable_borazine_bonding.png|400px|thumb|none| The delocalised pi bonding MO in borazine analogous to that of benzene]]
|}

Although much of the effects can be accounted to the delocalised pi system, it is debated that other p and s-electron orbitals may play a role in the stability of aromatic compounds. Some compounds exhibit aromatic properties despite the lack of pi-electron structures and the aromaticity is purely due to sigma-electron structures. Examples of these compounds are trihydrogen cations ([H3]+) and PtZnH5- anion that, dubbed to be σ-aromatic <ref>DOI: 10.1021/jz500322n</ref>. The concept of aromaticity thus is still debatable and will likely change to account more observations and phenomena.

=Reference=

Rep:Mod:coffee table

2018-05-24T18:34:57Z

Nj916: /* The concept of aromaticity */

Rep:Mod:coffee table

2018-05-24T18:31:29Z

Nj916: /* The concept of aromaticity */

=Optimisation of BH3 via Gaussian=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 3-21G then 6-31G then FREQ calculation type of BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.000182 0.001800 YES
RMS Displacement 0.000091 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_bh3_freq.log]]

<pre> Low frequencies --- -0.4072 -0.1962 -0.0054 25.2514 27.2430 27.2460
Low frequencies --- 1163.1897 1213.3128 1213.3155</pre>

Although the low frequencies is out of the range of 12 ± 15 cm-1, the calculation has converged, the geometry and the total energy is correct and I have discussed with the demonstrator who confirmed that it is not outstandingly concerning.

Frequency table

{| class="wikitable" border="1"
! Mode number !! frequency (cm-1) !! Intensity !! Symmetry !! type
|-
| 1 || 1163 || Strong || A1 || Bend
|-
| 2 || 1213 || weak || E || Scissoring
|-
| 3 || 1213 || weak || E || Rocking
|-
| 4 || 2582 || not observed || A1 || Symmetric stretch
|-
| 5 || 2715 || strong || E || Asymmetric stretch
|-
| 6 || 2715 || strong || E || Asymmetric stretch
|}

Predicted IR spectrum

[[File:coffeetable_bh3_ir.png|600px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Molecular Orbitals===

[[File:coffeetable_bh3_mo.png|600px|thumb|none| This figure shows calculated molecular orbitals by gaussview compared to LCAOs using MO theory diagram adapted from tutorial material by Dr P.Hunt<ref>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</ref>. ]]

The diagram above demonstrates that LCAOs using MO theory predicts the nodes between the orbital lobes and the energy levels accurately though does not predict how diffused the orbitals are and the actual extent of how much the AOs overlap each other. Qualitative LCAOs are therefore useful to predict the energy level and the location of the nodes but not the actual shape of the orbitals itself and how diffused they are.

=NH3 analysis=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_nh3_freq.log]]

<pre> Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=NH3BH3=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000117 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000839 0.001800 YES
RMS Displacement 0.000362 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_nh3bh3_freq.log]]

<pre> Low frequencies --- 0.0004 0.0006 0.0013 18.5187 24.9168 40.9948
Low frequencies --- 266.3754 632.3711 639.9574</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3bh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3bh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=B-N Bond strength in NH3BH3=

==Energy Calculation==

To get the association energy of BH3 and NH3, the total energy of the caclulations are substituted into this equation:

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

The calculated total energies are:

BH3= -26.61532 a.u.

NH3= -56.55776 a.u.

NH3BH3= -83.22469 a.u.

Substituting into the equation:

ΔE=-83.22469-[-56.55776-26.61532]= -0.05161 a.u. ≈ -136 kj/mol

The association energy of NH3BH3 is therefore very weak. On average, the C-C bond energy is -347 kj/mol which is a lot higher than that of NH3BH3. To put in perspective, compare with a very weak bond such as F-F which has the association energy of -154 kj/mol<ref>http://butane.chem.uiuc.edu/cyerkes/Chem104ACSpring2009/Genchemref/bondenergies.html</ref>, the association energy is still higher in NH3BH3 which shows how weak it is.

=Psuedo-potential optimisation for BBR3 via B3LYP/6-31G(d,p)LANL2DZ=

===Result summary table===
[[File:coffeetable_bbr3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of BBr3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_bbr3_freq.log]]

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

Vibrational modes and intensities

[[File:coffeetable_bbr3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BBr3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Dspace Link/unique identfier===

{{DOI|10042/202456}}

=Day 2: Analysis of aromaticity=

==Benzene==

===Result summary table===
[[File:coffeetable_benzene_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of benzene ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000087 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000321 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_benzene_freq.log]]

<pre> Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0045 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390</pre>

Vibrational modes and intensities

[[File:coffeetable_benzene_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised benzene</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_benzene_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==

===Result summary table===
[[File:coffeetable_borazine_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000313 0.000450 YES
RMS Force 0.000101 0.000300 YES
Maximum Displacement 0.000511 0.001800 YES
RMS Displacement 0.000151 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_borazine_freq.log]]

<pre> Low frequencies --- -12.2781 -12.1074 -8.6374 -0.0099 -0.0086 0.0754
Low frequencies --- 289.0994 289.1102 403.8930</pre>

Vibrational modes and intensities

[[File:coffeetable_borazine_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised borazine</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_borazine_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Comparison between benzene and borazine==

===Charge distribution===

The charge distribution analysis was performed on both the compounds with these settings:

[[File:coffeetable_colour.png|400px]]

{| class="wikitable" border="1"
! Benzene !! Borazine !! Description
|-
| [[File:coffeetable_benzene_charge.png|300px|thumb|none|C=-0.239 H=0.239]]|| [[File:coffeetable_borazine_charge.png|300px|thumb|none|B=0.747 N=-1.102 H(B)=0.077 H(N)=0.432]] || In benzene, the charge distribution on all the carbons and all the hydrogens have the same values, -0.239 and 0.239 respectively; this is because all the carbons and all the hydrogens are in the same environments. The charge distribution in borazine is however not as uniform; the charges on boron atoms are 0.747, nitrogen atoms are -1.102 and the hydrogen atoms have two values depending on what atom it is bonded to (hence different environments). Nitrogen is electronegative and boron is more electropositive therefore the charge distribution between them is as expected and highly polarised. When hydrogen is bonded to nitrogen, the charge value is 0.432 and for boron hydrogens it is 0.077; this is due to the fact that boron is electron deficient and so pulls the electron density away from the hydrogen that's bonded to it, lowering the value. Comparing the charge distribution difference, in benzene the range is 0.478 while in borazine it's 1.849 which demonstrates how much more polarised borazine is compared to benzene (owing to the large difference in electronegativity between boron and nitrogen). This is the reason for borazine's reactivity and susceptibility to electrophilic attacks.
|}

===Molecular orbitals===

{| class="wikitable" border="1"
! heading !! heading !! Comparison
|-
| [[File:coffeetable_benzene_bonding.png|300px]] || [[File:coffeetable_borazine_bonding.png|300px]] || Both of the MO are formed purely from the overlap of pz orbitals of the heavy atoms. They both are delocalised, have the same phase as the z axis and are both bonding orbitals. The benzene MO is highly symmetrical whilst the borazine MO is less so with the nitrogen atom drawing the electron distribution to it/larger MO contribution due to lower AO energy, demonstrating the polarity of B-N pi bonds.
|-
| [[File:coffeetable_benzene_mild.png|300px]] || [[File:coffeetable_borazine_mildly.png|300px]] || Both of the MO are mildly bonding and are formed from the sigma bonding between the hydrogen sigma orbitals and the sp2 orbitals of the heavy atoms. Both of them have a delocalised orbital in the center of the ring. Benzene MO is highly symmetrical with contribution from all the hydrogen atoms. Borazine MO is less symmetrical and has no contribution from three hydrogen atoms.
|-
| [[File:coffeetable_benzene_anti.png|300px]] || [[File:coffeetable_borazine_anti.png|300px]] || Both of the MO are formed from the hydrogen out of phase sigma AOs with a small contribution from the heavy atoms and are mildly anti-bonding due to the node not being between the bonded atoms. Because they are anti-bonding, the largest contribution is from the higher energy hydrogen AOs. Benzene MO is highly symmetrical whilst the borazine MO has reduced symmetry as the size of the MO is affected by the difference in electronegativity between boron and nitrogen.
|}

===The concept of aromaticity===

Aromatic compounds are especially stable compounds when compared to their related structures and was first observed in benzene. The concept of aromaticity has evolved throughout the years since Kekule's definition on benzene, deducing that any compound related to benzene is aromatic. Another common definition of aromatic compounds are cylic compounds that have delocalised pi electrons, planar and follow Hückel's Rule of 4n+2 electrons. The current definition of aromaticity defines that for any compound to be aromatic, it must follow these criteria:

1) They must be more stable than the acyclic conjugated analogue compound or the saturated cyclic analogue compound. Therefore even if the compound has overlapping pz AOs in a linear conjugated system, it isn't necessarily an aromatic compound. Similarly, some cyclic compounds that have overlapping pz AOs are not stablised, even destablised by the system (anti-aromatic) thus these compounds are not aromatic; overlapping pz AOs is therefore not a good description for aromaticity.

2) They have bond lengths between the typical bond length values of single and double bonds; this is because the bonds in aromatic/resonance stablised compounds have the bonding molecular orbitals somewhat in between single and double bonds.

3) When subjected to a magnetic field, a pi-electron ring current is induced which in turn induces it's own magnetic field that counters the external magnetic field leading to the higher diamagnetic susceptibility values in 1H NMR spectroscopy for hydrogens that are outside the ring. Linear conjugated compounds do not exhibit this effect.

4) Under go chemical reactions where the pi-electron conjugated structure is conserved (aromatic substitution reactions).

Since aromaticity was first observed with benzene and other planar molecules like naphthalene, classically all aromatic compounds must be planar but following the modern definition, some non-planar compounds such as cyclophanes exhibit aromatic properties. Much of the aromaticity of a compound can be accounted to the cyclic pz overlapping AOs <ref>DOI: 10.1002/chem.200700250</ref>.

[[File:coffeetable_benzene_bonding.png|400px|thumb|none|This figure shows the delocalised pi MO system formed from the overlapping pz of the carbon atoms. Note the delocalised and diffused MO.]] [[File:coffeetable_borazine_bonding.png|400px|thumb|none| The delocalised pi bonding MO in borazine analogous to that of benzene]]

=Reference=

Rep:Mod:coffee table

2018-05-24T18:05:39Z

Nj916: /* The very definition of aromaticity */

=Optimisation of BH3 via Gaussian=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 3-21G then 6-31G then FREQ calculation type of BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.000182 0.001800 YES
RMS Displacement 0.000091 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_bh3_freq.log]]

<pre> Low frequencies --- -0.4072 -0.1962 -0.0054 25.2514 27.2430 27.2460
Low frequencies --- 1163.1897 1213.3128 1213.3155</pre>

Although the low frequencies is out of the range of 12 ± 15 cm-1, the calculation has converged, the geometry and the total energy is correct and I have discussed with the demonstrator who confirmed that it is not outstandingly concerning.

Frequency table

{| class="wikitable" border="1"
! Mode number !! frequency (cm-1) !! Intensity !! Symmetry !! type
|-
| 1 || 1163 || Strong || A1 || Bend
|-
| 2 || 1213 || weak || E || Scissoring
|-
| 3 || 1213 || weak || E || Rocking
|-
| 4 || 2582 || not observed || A1 || Symmetric stretch
|-
| 5 || 2715 || strong || E || Asymmetric stretch
|-
| 6 || 2715 || strong || E || Asymmetric stretch
|}

Predicted IR spectrum

[[File:coffeetable_bh3_ir.png|600px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Molecular Orbitals===

[[File:coffeetable_bh3_mo.png|600px|thumb|none| This figure shows calculated molecular orbitals by gaussview compared to LCAOs using MO theory diagram adapted from tutorial material by Dr P.Hunt<ref>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</ref>. ]]

The diagram above demonstrates that LCAOs using MO theory predicts the nodes between the orbital lobes and the energy levels accurately though does not predict how diffused the orbitals are and the actual extent of how much the AOs overlap each other. Qualitative LCAOs are therefore useful to predict the energy level and the location of the nodes but not the actual shape of the orbitals itself and how diffused they are.

=NH3 analysis=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_nh3_freq.log]]

<pre> Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=NH3BH3=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000117 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000839 0.001800 YES
RMS Displacement 0.000362 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_nh3bh3_freq.log]]

<pre> Low frequencies --- 0.0004 0.0006 0.0013 18.5187 24.9168 40.9948
Low frequencies --- 266.3754 632.3711 639.9574</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3bh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3bh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=B-N Bond strength in NH3BH3=

==Energy Calculation==

To get the association energy of BH3 and NH3, the total energy of the caclulations are substituted into this equation:

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

The calculated total energies are:

BH3= -26.61532 a.u.

NH3= -56.55776 a.u.

NH3BH3= -83.22469 a.u.

Substituting into the equation:

ΔE=-83.22469-[-56.55776-26.61532]= -0.05161 a.u. ≈ -136 kj/mol

The association energy of NH3BH3 is therefore very weak. On average, the C-C bond energy is -347 kj/mol which is a lot higher than that of NH3BH3. To put in perspective, compare with a very weak bond such as F-F which has the association energy of -154 kj/mol<ref>http://butane.chem.uiuc.edu/cyerkes/Chem104ACSpring2009/Genchemref/bondenergies.html</ref>, the association energy is still higher in NH3BH3 which shows how weak it is.

=Psuedo-potential optimisation for BBR3 via B3LYP/6-31G(d,p)LANL2DZ=

===Result summary table===
[[File:coffeetable_bbr3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of BBr3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_bbr3_freq.log]]

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

Vibrational modes and intensities

[[File:coffeetable_bbr3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BBr3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Dspace Link/unique identfier===

{{DOI|10042/202456}}

=Day 2: Analysis of aromaticity=

==Benzene==

===Result summary table===
[[File:coffeetable_benzene_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of benzene ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000087 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000321 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_benzene_freq.log]]

<pre> Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0045 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390</pre>

Vibrational modes and intensities

[[File:coffeetable_benzene_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised benzene</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_benzene_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==

===Result summary table===
[[File:coffeetable_borazine_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000313 0.000450 YES
RMS Force 0.000101 0.000300 YES
Maximum Displacement 0.000511 0.001800 YES
RMS Displacement 0.000151 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_borazine_freq.log]]

<pre> Low frequencies --- -12.2781 -12.1074 -8.6374 -0.0099 -0.0086 0.0754
Low frequencies --- 289.0994 289.1102 403.8930</pre>

Vibrational modes and intensities

[[File:coffeetable_borazine_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised borazine</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_borazine_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Comparison between benzene and borazine==

===Charge distribution===

The charge distribution analysis was performed on both the compounds with these settings:

[[File:coffeetable_colour.png|400px]]

{| class="wikitable" border="1"
! Benzene !! Borazine !! Description
|-
| [[File:coffeetable_benzene_charge.png|300px|thumb|none|C=-0.239 H=0.239]]|| [[File:coffeetable_borazine_charge.png|300px|thumb|none|B=0.747 N=-1.102 H(B)=0.077 H(N)=0.432]] || In benzene, the charge distribution on all the carbons and all the hydrogens have the same values, -0.239 and 0.239 respectively; this is because all the carbons and all the hydrogens are in the same environments. The charge distribution in borazine is however not as uniform; the charges on boron atoms are 0.747, nitrogen atoms are -1.102 and the hydrogen atoms have two values depending on what atom it is bonded to (hence different environments). Nitrogen is electronegative and boron is more electropositive therefore the charge distribution between them is as expected and highly polarised. When hydrogen is bonded to nitrogen, the charge value is 0.432 and for boron hydrogens it is 0.077; this is due to the fact that boron is electron deficient and so pulls the electron density away from the hydrogen that's bonded to it, lowering the value. Comparing the charge distribution difference, in benzene the range is 0.478 while in borazine it's 1.849 which demonstrates how much more polarised borazine is compared to benzene (owing to the large difference in electronegativity between boron and nitrogen). This is the reason for borazine's reactivity and susceptibility to electrophilic attacks.
|}

===Molecular orbitals===

{| class="wikitable" border="1"
! heading !! heading !! Comparison
|-
| [[File:coffeetable_benzene_bonding.png|300px]] || [[File:coffeetable_borazine_bonding.png|300px]] || Both of the MO are formed purely from the overlap of pz orbitals of the heavy atoms. They both are delocalised, have the same phase as the z axis and are both bonding orbitals. The benzene MO is highly symmetrical whilst the borazine MO is less so with the nitrogen atom drawing the electron distribution to it/larger MO contribution due to lower AO energy, demonstrating the polarity of B-N pi bonds.
|-
| [[File:coffeetable_benzene_mild.png|300px]] || [[File:coffeetable_borazine_mildly.png|300px]] || Both of the MO are mildly bonding and are formed from the sigma bonding between the hydrogen sigma orbitals and the sp2 orbitals of the heavy atoms. Both of them have a delocalised orbital in the center of the ring. Benzene MO is highly symmetrical with contribution from all the hydrogen atoms. Borazine MO is less symmetrical and has no contribution from three hydrogen atoms.
|-
| [[File:coffeetable_benzene_anti.png|300px]] || [[File:coffeetable_borazine_anti.png|300px]] || Both of the MO are formed from the hydrogen out of phase sigma AOs with a small contribution from the heavy atoms and are mildly anti-bonding due to the node not being between the bonded atoms. Because they are anti-bonding, the largest contribution is from the higher energy hydrogen AOs. Benzene MO is highly symmetrical whilst the borazine MO has reduced symmetry as the size of the MO is affected by the difference in electronegativity between boron and nitrogen.
|}

===The concept of aromaticity===

Aromatic compounds are especially stable compounds when compared to their related structures and was first observed in benzene. The concept of aromaticity has evolved throughout the years since Kekule's definition on benzene, deducing that any compound related to benzene is aromatic. The current definition of aromaticity defines that for any compound to be aromatic, it must follow these criteria:

1) They must be more stable than the acyclic conjugated analogue compound or the saturated cyclic analogue compound. Therefore even if the compound has overlapping pi AOs in a linear conjugated system, it isn't necessarily an aromatic compound.

2) They have bond lengths between the typical bond length values of single and double bonds; this is because the bonds in aromatic/resonance stablised compounds have the bonding molecular orbitals somewhat in between single and double bonds.

3) When subjected to a magnetic field, a pi-electron ring current is induced which in turn induces it's own magnetic field that counters the external magnetic field leading to the higher diamagnetic susceptibility values in 1H NMR spectroscopy for hydrogens that are outside the ring.

4) Under go chemical reactions where the pi-electron conjugated structure is conserved (aromatic substitution reactions).

=Reference=

Rep:Mod:coffee table

2018-05-24T16:13:41Z

Nj916: /* Molecular orbitals */

=Optimisation of BH3 via Gaussian=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 3-21G then 6-31G then FREQ calculation type of BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.000182 0.001800 YES
RMS Displacement 0.000091 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_bh3_freq.log]]

<pre> Low frequencies --- -0.4072 -0.1962 -0.0054 25.2514 27.2430 27.2460
Low frequencies --- 1163.1897 1213.3128 1213.3155</pre>

Although the low frequencies is out of the range of 12 ± 15 cm-1, the calculation has converged, the geometry and the total energy is correct and I have discussed with the demonstrator who confirmed that it is not outstandingly concerning.

Frequency table

{| class="wikitable" border="1"
! Mode number !! frequency (cm-1) !! Intensity !! Symmetry !! type
|-
| 1 || 1163 || Strong || A1 || Bend
|-
| 2 || 1213 || weak || E || Scissoring
|-
| 3 || 1213 || weak || E || Rocking
|-
| 4 || 2582 || not observed || A1 || Symmetric stretch
|-
| 5 || 2715 || strong || E || Asymmetric stretch
|-
| 6 || 2715 || strong || E || Asymmetric stretch
|}

Predicted IR spectrum

[[File:coffeetable_bh3_ir.png|600px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Molecular Orbitals===

[[File:coffeetable_bh3_mo.png|600px|thumb|none| This figure shows calculated molecular orbitals by gaussview compared to LCAOs using MO theory diagram adapted from tutorial material by Dr P.Hunt<ref>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</ref>. ]]

The diagram above demonstrates that LCAOs using MO theory predicts the nodes between the orbital lobes and the energy levels accurately though does not predict how diffused the orbitals are and the actual extent of how much the AOs overlap each other. Qualitative LCAOs are therefore useful to predict the energy level and the location of the nodes but not the actual shape of the orbitals itself and how diffused they are.

=NH3 analysis=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_nh3_freq.log]]

<pre> Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=NH3BH3=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000117 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000839 0.001800 YES
RMS Displacement 0.000362 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_nh3bh3_freq.log]]

<pre> Low frequencies --- 0.0004 0.0006 0.0013 18.5187 24.9168 40.9948
Low frequencies --- 266.3754 632.3711 639.9574</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3bh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3bh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=B-N Bond strength in NH3BH3=

==Energy Calculation==

To get the association energy of BH3 and NH3, the total energy of the caclulations are substituted into this equation:

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

The calculated total energies are:

BH3= -26.61532 a.u.

NH3= -56.55776 a.u.

NH3BH3= -83.22469 a.u.

Substituting into the equation:

ΔE=-83.22469-[-56.55776-26.61532]= -0.05161 a.u. ≈ -136 kj/mol

The association energy of NH3BH3 is therefore very weak. On average, the C-C bond energy is -347 kj/mol which is a lot higher than that of NH3BH3. To put in perspective, compare with a very weak bond such as F-F which has the association energy of -154 kj/mol<ref>http://butane.chem.uiuc.edu/cyerkes/Chem104ACSpring2009/Genchemref/bondenergies.html</ref>, the association energy is still higher in NH3BH3 which shows how weak it is.

=Psuedo-potential optimisation for BBR3 via B3LYP/6-31G(d,p)LANL2DZ=

===Result summary table===
[[File:coffeetable_bbr3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of BBr3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_bbr3_freq.log]]

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

Vibrational modes and intensities

[[File:coffeetable_bbr3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BBr3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Dspace Link/unique identfier===

{{DOI|10042/202456}}

=Day 2: Analysis of aromaticity=

==Benzene==

===Result summary table===
[[File:coffeetable_benzene_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of benzene ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000087 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000321 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_benzene_freq.log]]

<pre> Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0045 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390</pre>

Vibrational modes and intensities

[[File:coffeetable_benzene_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised benzene</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_benzene_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==

===Result summary table===
[[File:coffeetable_borazine_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000313 0.000450 YES
RMS Force 0.000101 0.000300 YES
Maximum Displacement 0.000511 0.001800 YES
RMS Displacement 0.000151 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_borazine_freq.log]]

<pre> Low frequencies --- -12.2781 -12.1074 -8.6374 -0.0099 -0.0086 0.0754
Low frequencies --- 289.0994 289.1102 403.8930</pre>

Vibrational modes and intensities

[[File:coffeetable_borazine_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised borazine</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_borazine_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Comparison between benzene and borazine==

===Charge distribution===

The charge distribution analysis was performed on both the compounds with these settings:

[[File:coffeetable_colour.png|400px]]

{| class="wikitable" border="1"
! Benzene !! Borazine !! Description
|-
| [[File:coffeetable_benzene_charge.png|300px|thumb|none|C=-0.239 H=0.239]]|| [[File:coffeetable_borazine_charge.png|300px|thumb|none|B=0.747 N=-1.102 H(B)=0.077 H(N)=0.432]] || In benzene, the charge distribution on all the carbons and all the hydrogens have the same values, -0.239 and 0.239 respectively; this is because all the carbons and all the hydrogens are in the same environments. The charge distribution in borazine is however not as uniform; the charges on boron atoms are 0.747, nitrogen atoms are -1.102 and the hydrogen atoms have two values depending on what atom it is bonded to (hence different environments). Nitrogen is electronegative and boron is more electropositive therefore the charge distribution between them is as expected and highly polarised. When hydrogen is bonded to nitrogen, the charge value is 0.432 and for boron hydrogens it is 0.077; this is due to the fact that boron is electron deficient and so pulls the electron density away from the hydrogen that's bonded to it, lowering the value. Comparing the charge distribution difference, in benzene the range is 0.478 while in borazine it's 1.849 which demonstrates how much more polarised borazine is compared to benzene (owing to the large difference in electronegativity between boron and nitrogen). This is the reason for borazine's reactivity and susceptibility to electrophilic attacks.
|}

===Molecular orbitals===

{| class="wikitable" border="1"
! heading !! heading !! Comparison
|-
| [[File:coffeetable_benzene_bonding.png|300px]] || [[File:coffeetable_borazine_bonding.png|300px]] || Both of the MO are formed purely from the overlap of pz orbitals of the heavy atoms. They both are delocalised, have the same phase as the z axis and are both bonding orbitals. The benzene MO is highly symmetrical whilst the borazine MO is less so with the nitrogen atom drawing the electron distribution to it/larger MO contribution due to lower AO energy, demonstrating the polarity of B-N pi bonds.
|-
| [[File:coffeetable_benzene_mild.png|300px]] || [[File:coffeetable_borazine_mildly.png|300px]] || Both of the MO are mildly bonding and are formed from the sigma bonding between the hydrogen sigma orbitals and the sp2 orbitals of the heavy atoms. Both of them have a delocalised orbital in the center of the ring. Benzene MO is highly symmetrical with contribution from all the hydrogen atoms. Borazine MO is less symmetrical and has no contribution from three hydrogen atoms.
|-
| [[File:coffeetable_benzene_anti.png|300px]] || [[File:coffeetable_borazine_anti.png|300px]] || Both of the MO are formed from the hydrogen out of phase sigma AOs with a small contribution from the heavy atoms and are mildly anti-bonding due to the node not being between the bonded atoms. Because they are anti-bonding, the largest contribution is from the higher energy hydrogen AOs. Benzene MO is highly symmetrical whilst the borazine MO has reduced symmetry as the size of the MO is affected by the difference in electronegativity between boron and nitrogen.
|}

===The very definition of aromaticity===

Say something about the aromaticity of both compounds

=Reference=

Rep:Mod:coffee table

2018-05-24T15:57:11Z

Nj916: /* Molecular orbitals */

=Optimisation of BH3 via Gaussian=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 3-21G then 6-31G then FREQ calculation type of BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.000182 0.001800 YES
RMS Displacement 0.000091 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_bh3_freq.log]]

<pre> Low frequencies --- -0.4072 -0.1962 -0.0054 25.2514 27.2430 27.2460
Low frequencies --- 1163.1897 1213.3128 1213.3155</pre>

Although the low frequencies is out of the range of 12 ± 15 cm-1, the calculation has converged, the geometry and the total energy is correct and I have discussed with the demonstrator who confirmed that it is not outstandingly concerning.

Frequency table

{| class="wikitable" border="1"
! Mode number !! frequency (cm-1) !! Intensity !! Symmetry !! type
|-
| 1 || 1163 || Strong || A1 || Bend
|-
| 2 || 1213 || weak || E || Scissoring
|-
| 3 || 1213 || weak || E || Rocking
|-
| 4 || 2582 || not observed || A1 || Symmetric stretch
|-
| 5 || 2715 || strong || E || Asymmetric stretch
|-
| 6 || 2715 || strong || E || Asymmetric stretch
|}

Predicted IR spectrum

[[File:coffeetable_bh3_ir.png|600px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Molecular Orbitals===

[[File:coffeetable_bh3_mo.png|600px|thumb|none| This figure shows calculated molecular orbitals by gaussview compared to LCAOs using MO theory diagram adapted from tutorial material by Dr P.Hunt<ref>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</ref>. ]]

The diagram above demonstrates that LCAOs using MO theory predicts the nodes between the orbital lobes and the energy levels accurately though does not predict how diffused the orbitals are and the actual extent of how much the AOs overlap each other. Qualitative LCAOs are therefore useful to predict the energy level and the location of the nodes but not the actual shape of the orbitals itself and how diffused they are.

=NH3 analysis=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_nh3_freq.log]]

<pre> Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=NH3BH3=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000117 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000839 0.001800 YES
RMS Displacement 0.000362 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_nh3bh3_freq.log]]

<pre> Low frequencies --- 0.0004 0.0006 0.0013 18.5187 24.9168 40.9948
Low frequencies --- 266.3754 632.3711 639.9574</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3bh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3bh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=B-N Bond strength in NH3BH3=

==Energy Calculation==

To get the association energy of BH3 and NH3, the total energy of the caclulations are substituted into this equation:

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

The calculated total energies are:

BH3= -26.61532 a.u.

NH3= -56.55776 a.u.

NH3BH3= -83.22469 a.u.

Substituting into the equation:

ΔE=-83.22469-[-56.55776-26.61532]= -0.05161 a.u. ≈ -136 kj/mol

The association energy of NH3BH3 is therefore very weak. On average, the C-C bond energy is -347 kj/mol which is a lot higher than that of NH3BH3. To put in perspective, compare with a very weak bond such as F-F which has the association energy of -154 kj/mol<ref>http://butane.chem.uiuc.edu/cyerkes/Chem104ACSpring2009/Genchemref/bondenergies.html</ref>, the association energy is still higher in NH3BH3 which shows how weak it is.

=Psuedo-potential optimisation for BBR3 via B3LYP/6-31G(d,p)LANL2DZ=

===Result summary table===
[[File:coffeetable_bbr3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of BBr3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_bbr3_freq.log]]

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

Vibrational modes and intensities

[[File:coffeetable_bbr3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BBr3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Dspace Link/unique identfier===

{{DOI|10042/202456}}

=Day 2: Analysis of aromaticity=

==Benzene==

===Result summary table===
[[File:coffeetable_benzene_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of benzene ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000087 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000321 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_benzene_freq.log]]

<pre> Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0045 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390</pre>

Vibrational modes and intensities

[[File:coffeetable_benzene_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised benzene</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_benzene_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==

===Result summary table===
[[File:coffeetable_borazine_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000313 0.000450 YES
RMS Force 0.000101 0.000300 YES
Maximum Displacement 0.000511 0.001800 YES
RMS Displacement 0.000151 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_borazine_freq.log]]

<pre> Low frequencies --- -12.2781 -12.1074 -8.6374 -0.0099 -0.0086 0.0754
Low frequencies --- 289.0994 289.1102 403.8930</pre>

Vibrational modes and intensities

[[File:coffeetable_borazine_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised borazine</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_borazine_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Comparison between benzene and borazine==

===Charge distribution===

The charge distribution analysis was performed on both the compounds with these settings:

[[File:coffeetable_colour.png|400px]]

{| class="wikitable" border="1"
! Benzene !! Borazine !! Description
|-
| [[File:coffeetable_benzene_charge.png|300px|thumb|none|C=-0.239 H=0.239]]|| [[File:coffeetable_borazine_charge.png|300px|thumb|none|B=0.747 N=-1.102 H(B)=0.077 H(N)=0.432]] || In benzene, the charge distribution on all the carbons and all the hydrogens have the same values, -0.239 and 0.239 respectively; this is because all the carbons and all the hydrogens are in the same environments. The charge distribution in borazine is however not as uniform; the charges on boron atoms are 0.747, nitrogen atoms are -1.102 and the hydrogen atoms have two values depending on what atom it is bonded to (hence different environments). Nitrogen is electronegative and boron is more electropositive therefore the charge distribution between them is as expected and highly polarised. When hydrogen is bonded to nitrogen, the charge value is 0.432 and for boron hydrogens it is 0.077; this is due to the fact that boron is electron deficient and so pulls the electron density away from the hydrogen that's bonded to it, lowering the value. Comparing the charge distribution difference, in benzene the range is 0.478 while in borazine it's 1.849 which demonstrates how much more polarised borazine is compared to benzene (owing to the large difference in electronegativity between boron and nitrogen). This is the reason for borazine's reactivity and susceptibility to electrophilic attacks.
|}

===Molecular orbitals===

{| class="wikitable" border="1"
! heading !! heading !! Comparison
|-
| [[File:coffeetable_benzene_bonding.png|300px]] || [[File:coffeetable_borazine_bonding.png|300px]] || Both of the MO is formed purely from the overlap of pz orbitals of the heavy atoms. They both are delocalised, have the same phase as the z axis and are both bonding orbitals. The benzene MO is highly symmetrical whilst the borazine MO is less so with the nitrogen atom drawing the electron distribution to it/larger MO contribution due to lower AO energy, demonstrating the polarity of B-N pi bonds.
|-
| [[File:coffeetable_benzene_mild.png|300px]] || [[File:coffeetable_borazine_mildly.png|300px]] || Both of the MO are mildly bonding and are formed from the sigma bonding between the hydrogen sigma orbitals and the sp2 orbitals of the heavy atoms. Both of them have a delocalised orbital in the center of the ring. Benzene MO is highly symmetrical with contribution from all the hydrogen atoms. Borazine MO is less symmetrical and has no contribution from three hydrogen atoms.
|-
| [[File:coffeetable_benzene_anti.png|300px]] || [[File:coffeetable_borazine_anti.png|300px]] || cell
|}

===The very definition of aromaticity===

Say something about the aromaticity of both compounds

=Reference=

Rep:Mod:coffee table

2018-05-24T15:36:55Z

Nj916: /* Molecular orbitals */

=Optimisation of BH3 via Gaussian=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 3-21G then 6-31G then FREQ calculation type of BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.000182 0.001800 YES
RMS Displacement 0.000091 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_bh3_freq.log]]

<pre> Low frequencies --- -0.4072 -0.1962 -0.0054 25.2514 27.2430 27.2460
Low frequencies --- 1163.1897 1213.3128 1213.3155</pre>

Although the low frequencies is out of the range of 12 ± 15 cm-1, the calculation has converged, the geometry and the total energy is correct and I have discussed with the demonstrator who confirmed that it is not outstandingly concerning.

Frequency table

{| class="wikitable" border="1"
! Mode number !! frequency (cm-1) !! Intensity !! Symmetry !! type
|-
| 1 || 1163 || Strong || A1 || Bend
|-
| 2 || 1213 || weak || E || Scissoring
|-
| 3 || 1213 || weak || E || Rocking
|-
| 4 || 2582 || not observed || A1 || Symmetric stretch
|-
| 5 || 2715 || strong || E || Asymmetric stretch
|-
| 6 || 2715 || strong || E || Asymmetric stretch
|}

Predicted IR spectrum

[[File:coffeetable_bh3_ir.png|600px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Molecular Orbitals===

[[File:coffeetable_bh3_mo.png|600px|thumb|none| This figure shows calculated molecular orbitals by gaussview compared to LCAOs using MO theory diagram adapted from tutorial material by Dr P.Hunt<ref>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</ref>. ]]

The diagram above demonstrates that LCAOs using MO theory predicts the nodes between the orbital lobes and the energy levels accurately though does not predict how diffused the orbitals are and the actual extent of how much the AOs overlap each other. Qualitative LCAOs are therefore useful to predict the energy level and the location of the nodes but not the actual shape of the orbitals itself and how diffused they are.

=NH3 analysis=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_nh3_freq.log]]

<pre> Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=NH3BH3=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000117 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000839 0.001800 YES
RMS Displacement 0.000362 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_nh3bh3_freq.log]]

<pre> Low frequencies --- 0.0004 0.0006 0.0013 18.5187 24.9168 40.9948
Low frequencies --- 266.3754 632.3711 639.9574</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3bh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3bh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=B-N Bond strength in NH3BH3=

==Energy Calculation==

To get the association energy of BH3 and NH3, the total energy of the caclulations are substituted into this equation:

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

The calculated total energies are:

BH3= -26.61532 a.u.

NH3= -56.55776 a.u.

NH3BH3= -83.22469 a.u.

Substituting into the equation:

ΔE=-83.22469-[-56.55776-26.61532]= -0.05161 a.u. ≈ -136 kj/mol

The association energy of NH3BH3 is therefore very weak. On average, the C-C bond energy is -347 kj/mol which is a lot higher than that of NH3BH3. To put in perspective, compare with a very weak bond such as F-F which has the association energy of -154 kj/mol<ref>http://butane.chem.uiuc.edu/cyerkes/Chem104ACSpring2009/Genchemref/bondenergies.html</ref>, the association energy is still higher in NH3BH3 which shows how weak it is.

=Psuedo-potential optimisation for BBR3 via B3LYP/6-31G(d,p)LANL2DZ=

===Result summary table===
[[File:coffeetable_bbr3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of BBr3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_bbr3_freq.log]]

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

Vibrational modes and intensities

[[File:coffeetable_bbr3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BBr3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Dspace Link/unique identfier===

{{DOI|10042/202456}}

=Day 2: Analysis of aromaticity=

==Benzene==

===Result summary table===
[[File:coffeetable_benzene_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of benzene ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000087 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000321 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_benzene_freq.log]]

<pre> Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0045 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390</pre>

Vibrational modes and intensities

[[File:coffeetable_benzene_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised benzene</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_benzene_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==

===Result summary table===
[[File:coffeetable_borazine_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000313 0.000450 YES
RMS Force 0.000101 0.000300 YES
Maximum Displacement 0.000511 0.001800 YES
RMS Displacement 0.000151 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_borazine_freq.log]]

<pre> Low frequencies --- -12.2781 -12.1074 -8.6374 -0.0099 -0.0086 0.0754
Low frequencies --- 289.0994 289.1102 403.8930</pre>

Vibrational modes and intensities

[[File:coffeetable_borazine_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised borazine</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_borazine_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Comparison between benzene and borazine==

===Charge distribution===

The charge distribution analysis was performed on both the compounds with these settings:

[[File:coffeetable_colour.png|400px]]

{| class="wikitable" border="1"
! Benzene !! Borazine !! Description
|-
| [[File:coffeetable_benzene_charge.png|300px|thumb|none|C=-0.239 H=0.239]]|| [[File:coffeetable_borazine_charge.png|300px|thumb|none|B=0.747 N=-1.102 H(B)=0.077 H(N)=0.432]] || In benzene, the charge distribution on all the carbons and all the hydrogens have the same values, -0.239 and 0.239 respectively; this is because all the carbons and all the hydrogens are in the same environments. The charge distribution in borazine is however not as uniform; the charges on boron atoms are 0.747, nitrogen atoms are -1.102 and the hydrogen atoms have two values depending on what atom it is bonded to (hence different environments). Nitrogen is electronegative and boron is more electropositive therefore the charge distribution between them is as expected and highly polarised. When hydrogen is bonded to nitrogen, the charge value is 0.432 and for boron hydrogens it is 0.077; this is due to the fact that boron is electron deficient and so pulls the electron density away from the hydrogen that's bonded to it, lowering the value. Comparing the charge distribution difference, in benzene the range is 0.478 while in borazine it's 1.849 which demonstrates how much more polarised borazine is compared to benzene (owing to the large difference in electronegativity between boron and nitrogen). This is the reason for borazine's reactivity and susceptibility to electrophilic attacks.
|}

===Molecular orbitals===

{| class="wikitable" border="1"
! heading !! heading !! Comparison
|-
| [[File:coffeetable_benzene_bonding.png|300px]] || [[File:coffeetable_borazine_bonding.png|300px]] || Both of the MO is formed purely from the overlap of pz orbitals of the heavy atoms. They both are delocalised, have the same phase as the z axis and are both bonding orbitals. The benzene MO is highly symmetrical whilst the borazine MO is less so with the nitrogen atom drawing the electron distribution to it/larger MO contribution due to lower AO energy, demonstrating the polarity of B-N pi bonds.
|-
| [[File:coffeetable_benzene_mild.png|300px]] || [[File:coffeetable_borazine_mildly.png|300px]] || cell
|-
| [[File:coffeetable_benzene_anti.png|300px]] || [[File:coffeetable_borazine_anti.png|300px]] || cell
|}

===The very definition of aromaticity===

Say something about the aromaticity of both compounds

=Reference=

Rep:Mod:coffee table

2018-05-24T15:20:46Z

Nj916: /* Molecular orbitals */

=Optimisation of BH3 via Gaussian=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 3-21G then 6-31G then FREQ calculation type of BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.000182 0.001800 YES
RMS Displacement 0.000091 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_bh3_freq.log]]

<pre> Low frequencies --- -0.4072 -0.1962 -0.0054 25.2514 27.2430 27.2460
Low frequencies --- 1163.1897 1213.3128 1213.3155</pre>

Although the low frequencies is out of the range of 12 ± 15 cm-1, the calculation has converged, the geometry and the total energy is correct and I have discussed with the demonstrator who confirmed that it is not outstandingly concerning.

Frequency table

{| class="wikitable" border="1"
! Mode number !! frequency (cm-1) !! Intensity !! Symmetry !! type
|-
| 1 || 1163 || Strong || A1 || Bend
|-
| 2 || 1213 || weak || E || Scissoring
|-
| 3 || 1213 || weak || E || Rocking
|-
| 4 || 2582 || not observed || A1 || Symmetric stretch
|-
| 5 || 2715 || strong || E || Asymmetric stretch
|-
| 6 || 2715 || strong || E || Asymmetric stretch
|}

Predicted IR spectrum

[[File:coffeetable_bh3_ir.png|600px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Molecular Orbitals===

[[File:coffeetable_bh3_mo.png|600px|thumb|none| This figure shows calculated molecular orbitals by gaussview compared to LCAOs using MO theory diagram adapted from tutorial material by Dr P.Hunt<ref>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</ref>. ]]

The diagram above demonstrates that LCAOs using MO theory predicts the nodes between the orbital lobes and the energy levels accurately though does not predict how diffused the orbitals are and the actual extent of how much the AOs overlap each other. Qualitative LCAOs are therefore useful to predict the energy level and the location of the nodes but not the actual shape of the orbitals itself and how diffused they are.

=NH3 analysis=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_nh3_freq.log]]

<pre> Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=NH3BH3=

==B3LYP/6-31G level==

===Result summary table===
[[File:coffeetable_nh3bh3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000117 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000839 0.001800 YES
RMS Displacement 0.000362 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_nh3bh3_freq.log]]

<pre> Low frequencies --- 0.0004 0.0006 0.0013 18.5187 24.9168 40.9948
Low frequencies --- 266.3754 632.3711 639.9574</pre>

Vibrational modes and intensities

[[File:coffeetable_nh3bh3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

[[File:coffeetable_nh3bh3_ir.png|500px]]

===3D model===

<jmol><jmolApplet>
<title>Optimised NH3BH3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_nh3bh3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

=B-N Bond strength in NH3BH3=

==Energy Calculation==

To get the association energy of BH3 and NH3, the total energy of the caclulations are substituted into this equation:

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

The calculated total energies are:

BH3= -26.61532 a.u.

NH3= -56.55776 a.u.

NH3BH3= -83.22469 a.u.

Substituting into the equation:

ΔE=-83.22469-[-56.55776-26.61532]= -0.05161 a.u. ≈ -136 kj/mol

The association energy of NH3BH3 is therefore very weak. On average, the C-C bond energy is -347 kj/mol which is a lot higher than that of NH3BH3. To put in perspective, compare with a very weak bond such as F-F which has the association energy of -154 kj/mol<ref>http://butane.chem.uiuc.edu/cyerkes/Chem104ACSpring2009/Genchemref/bondenergies.html</ref>, the association energy is still higher in NH3BH3 which shows how weak it is.

=Psuedo-potential optimisation for BBR3 via B3LYP/6-31G(d,p)LANL2DZ=

===Result summary table===
[[File:coffeetable_bbr3_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of BBr3 ]]

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

===Frequency analysis===

Log file

[[File:coffeetable_bbr3_freq.log]]

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

Vibrational modes and intensities

[[File:coffeetable_bbr3_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised BBr3</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

===Dspace Link/unique identfier===

{{DOI|10042/202456}}

=Day 2: Analysis of aromaticity=

==Benzene==

===Result summary table===
[[File:coffeetable_benzene_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of benzene ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000087 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000321 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_benzene_freq.log]]

<pre> Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0045 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390</pre>

Vibrational modes and intensities

[[File:coffeetable_benzene_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised benzene</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_benzene_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==

===Result summary table===
[[File:coffeetable_borazine_rtable.png|500px|thumb|none|The result summary table after optimisation via 6-31G then FREQ calculation type of NH3BH3 ]]

===Convergance===
<pre> Item Value Threshold Converged?
Maximum Force 0.000313 0.000450 YES
RMS Force 0.000101 0.000300 YES
Maximum Displacement 0.000511 0.001800 YES
RMS Displacement 0.000151 0.001200 YES</pre>

===Frequency analysis===

Log file

[[File:coffeetable_borazine_freq.log]]

<pre> Low frequencies --- -12.2781 -12.1074 -8.6374 -0.0099 -0.0086 0.0754
Low frequencies --- 289.0994 289.1102 403.8930</pre>

Vibrational modes and intensities

[[File:coffeetable_borazine_vib.png|500px|thumb|none| Figure showing vibrational modes and the intensities]]

===3D model===

<jmol><jmolApplet>
<title>Optimised borazine</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>coffeetable_borazine_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Comparison between benzene and borazine==

===Charge distribution===

The charge distribution analysis was performed on both the compounds with these settings:

[[File:coffeetable_colour.png|400px]]

{| class="wikitable" border="1"
! Benzene !! Borazine !! Description
|-
| [[File:coffeetable_benzene_charge.png|300px|thumb|none|C=-0.239 H=0.239]]|| [[File:coffeetable_borazine_charge.png|300px|thumb|none|B=0.747 N=-1.102 H(B)=0.077 H(N)=0.432]] || In benzene, the charge distribution on all the carbons and all the hydrogens have the same values, -0.239 and 0.239 respectively; this is because all the carbons and all the hydrogens are in the same environments. The charge distribution in borazine is however not as uniform; the charges on boron atoms are 0.747, nitrogen atoms are -1.102 and the hydrogen atoms have two values depending on what atom it is bonded to (hence different environments). Nitrogen is electronegative and boron is more electropositive therefore the charge distribution between them is as expected and highly polarised. When hydrogen is bonded to nitrogen, the charge value is 0.432 and for boron hydrogens it is 0.077; this is due to the fact that boron is electron deficient and so pulls the electron density away from the hydrogen that's bonded to it, lowering the value. Comparing the charge distribution difference, in benzene the range is 0.478 while in borazine it's 1.849 which demonstrates how much more polarised borazine is compared to benzene (owing to the large difference in electronegativity between boron and nitrogen). This is the reason for borazine's reactivity and susceptibility to electrophilic attacks.
|}

===Molecular orbitals===

{| class="wikitable" border="1"
! heading !! heading !! Comparison
|-
| [[File:coffeetable_benzene_bonding.png|300px]] || [[File:coffeetable_borazine_bonding.png|300px]] || cell
|-
| [[File:coffeetable_benzene_mild.png|300px]] || [[File:coffeetable_borazine_mildly.png|300px]] || cell
|-
| [[File:coffeetable_benzene_anti.png|300px]] || [[File:coffeetable_borazine_anti.png|300px]] || cell
|}

===The very definition of aromaticity===

Say something about the aromaticity of both compounds

=Reference=

File:Coffeetable borazine mildly.png

2018-05-24T15:19:37Z

Nj916:

File:Coffeetable borazine bonding.png

2018-05-24T15:19:21Z

Nj916:

File:Coffeetable borazine anti.png

2018-05-24T15:19:01Z

Nj916:

File:Coffeetable benzene mild.png

2018-05-24T15:18:49Z

Nj916:

File:Coffeetable benzene bonding.png

2018-05-24T15:18:30Z

Nj916:

File:Coffeetable benzene anti.png

2018-05-24T15:18:21Z

Nj916:

Rep:Mod:coffee table

2018-05-24T14:49:58Z

Nj916: /* Comparison between benzene and borazine */

Rep:Mod:coffee table

2018-05-24T14:39:12Z

Nj916: /* Comparison between benzene and borazine */

Rep:Mod:coffee table

2018-05-24T14:37:46Z

Nj916: /* Comparison between benzene and borazine */

Rep:Mod:coffee table

2018-05-24T14:32:06Z

Nj916: /* Charge distribution */

Rep:Mod:coffee table

2018-05-24T14:31:47Z

Nj916: /* Charge distribution */

File:Coffeetable colour.png

2018-05-24T14:06:44Z

Nj916:

Rep:Mod:coffee table

2018-05-24T14:01:02Z

Nj916: /* Charge distribution */

Rep:Mod:coffee table

2018-05-24T14:00:39Z

Nj916: /* Charge distribution */

File:Coffeetable borazine charge.png

2018-05-24T13:59:36Z

Nj916:

File:Coffeetable benzene charge.png

2018-05-24T13:59:21Z

Nj916:

Rep:Mod:coffee table

2018-05-24T13:51:21Z