ChemWiki - User contributions [en]

Rep:Mod:sk-inorg

2018-05-25T16:40:58Z

Sk716:

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|<ref name=":0"><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf [Accessed 23/05/2018]</nowiki></ref>Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.<ref name=":0" />

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron:
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>Optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>Optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

Compared to an isolectronic molecule of ethane, with a bond energy of around 376.2 kJ/mol,<ref>Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition</ref> this value seems quite weak, despite it having a negative change, meaning that this adduct formation is still an exothermic reaction.

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

<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>Optimised BBr3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BBR3 PP FREQ FINAL.log</uploadedFileContents>
</jmolApplet></jmol>

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

<jmol><jmolApplet>
<title>Optimised benzene molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK C6H6 FREQ 1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

<jmol><jmolApplet>
<title>Optimised borazine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BORAZINE FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 9.PNG|frameless]]
|[[File:Sk - borazine mo 9.PNG|frameless]]
|This is MO 9 for both molecules. In benzene, this has bonding character between the 3 carbon 2s and the 3 hydrogen 1s orbitals in each half of the molecule and antibonding character between the two halves of the molecule. In borazine, only the NH units contribute to this MO, with one NH unit (N's 2s and H's 1s AOs) in a different phase to the 2 other NH units. Benzene's MO is has a C2 rotational axis borazine's doesn't
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Aromaticity can be explained simply using Hückel's rules, where an aromatic molecule fulfils these rules:
* It must be planar,
* Cyclic,
* Have a contiguous array of p orbitals orthogonal to the plane of the ring
* Have 4n+2 electrons in these p orbitals, where ''n'' is an integer

Benzene and borazine both comply with these rules as they're both cyclic and planar, each with 6 electrons in the pz orbitals (each carbon contributes 1 electron in benzene; in borazine, each B contributes no electrons and each N has 2 electrons in the pz orbitals) and MO 17 for both shows the contiguous array of pz orbitals.

It is known that there is a "resonance energy" associated with aromatic compounds, which makes them very stable compounds.<ref>T. M. Krygowski, M. K. CyraÇski, G. Haefelinger, A. R. Katritzky, ''Tetrahedron'' 2000, '''56''', 1783.</ref> In an applied magnetic field, the ring current in aromatic systems creates its own induced magnetic field. The effect of this is that outside the ring, the induced field is in the same direction and the applied field, so hydrogens outside the ring would be deshielded in an NMR spectrometer. The opposite is true inside the ring.

It has been suggested that the sigma framework in aromatic molecules (the p orbitals combining in-phase in the plane of the ring) is an important bonding mode as well, not solely the pz orbitals.<ref>M. Palusiak and T. M.Krygowski, ''Chem. Eur. J.,'' 2007, '''13''', pp. 7996-8006</ref>

Rep:Mod:sk-inorg

2018-05-25T16:39:54Z

Sk716:

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|<ref name=":0"><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf [Accessed 23/05/2018]</nowiki></ref>Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.<ref name=":0" />

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron:
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>Optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>Optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

Compared to an isolectronic molecule of ethane, with a bond energy of around 376.2 kJ/mol,<ref>Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition</ref> this value seems quite weak, despite it having a negative change, meaning that this adduct formation is still an exothermic reaction.

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

<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>Optimised BBr3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BBR3 PP FREQ FINAL.log</uploadedFileContents>
</jmolApplet></jmol>

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

<jmol><jmolApplet>
<title>Optimised benzene molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK C6H6 FREQ 1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

<jmol><jmolApplet>
<title>Optimised borazine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BORAZINE FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 9.PNG|frameless]]
|[[File:Sk - borazine mo 9.PNG|frameless]]
|This is MO 9 for both molecules. In benzene, this has bonding character between the 3 carbon 2s and the 3 hydrogen 1s orbitals in each half of the molecule and antibonding character between the two halves of the molecule. In borazine, only the NH units contribute to this MO, with one NH unit (N's 2s and H's 1s AOs) in a different phase to the 2 other NH units. Benzene's MO is has a C2 rotational axis borazine's doesn't
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Aromaticity can be explained simply using Hückel's rules, where an aromatic molecule fulfils these rules:
* It must be planar,
* Cyclic,
* Have a contiguous array of p orbitals orthogonal to the plane of the ring
* Have 4n+2 electrons in these p orbitals, where ''n'' is an integer

Benzene and borazine both comply with these rules as they're both cyclic and planar, each with 6 electrons in the pz orbitals (each carbon contributes 1 electron in benzene; in borazine, each B contributes no electrons and each N has 2 electrons in the pz orbitals) and MO 17 for both shows the contiguous array of pz orbitals.

It is known that there is a "resonance energy" associated with aromatic compounds, which makes them very stable compounds.<ref>T. M. Krygowski, M. K. CyraÇski, G. Haefelinger, A. R. Katritzky, ''Tetrahedron'' 2000, '''56''', 1783.</ref> In an applied magnetic field, the ring current in aromatic systems creates its own induced magnetic field. The effect of this is that outside the ring, the induced field is in the same direction and the applied field, so hydrogens outside the ring would be deshielded in an NMR spectrometer. The opposite is true inside the ring.

It has been suggested that the sigma framework in aromatic molecules (the p orbitals combining in-phase in the plane of the ring) is an important bonding mode as well, not solely the pz orbitals.<ref>M. Palusiak and T. M.Krygowski, ''Chem. Eur. J.,'' 2007, '''13''', pp. 7996-8006</ref>

Rep:Mod:sk-inorg

2018-05-25T16:34:07Z

Sk716:

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|<ref name=":0"><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf [Accessed 23/05/2018]</nowiki></ref>Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.<ref name=":0" />

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron:
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

Compared to an isolectronic molecule of ethane, with a bond energy of around 376.2 kJ/mol,<ref>Yu-Ran Luo and Jin-Pei Cheng "Bond Dissociation Energies" in CRC Handbook of Chemistry and Physics, 96th Edition</ref> this value seems quite weak, despite it having a negative change, meaning that this adduct formation is still an exothermic reaction.

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 9.PNG|frameless]]
|[[File:Sk - borazine mo 9.PNG|frameless]]
|This is MO 9 for both molecules. In benzene, this has bonding character between the 3 carbon 2s and the 3 hydrogen 1s orbitals in each half of the molecule and antibonding character between the two halves of the molecule. In borazine, only the NH units contribute to this MO, with one NH unit (N's 2s and H's 1s AOs) in a different phase to the 2 other NH units. Benzene's MO is has a C2 rotational axis borazine's doesn't
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Aromaticity can be explained simply using Hückel's rules, where an aromatic molecule fulfils these rules:
* It must be planar,
* Cyclic,
* Have a contiguous array of p orbitals orthogonal to the plane of the ring
* Have 4n+2 electrons in these p orbitals, where ''n'' is an integer

Benzene and borazine both comply with these rules as they're both cyclic and planar, each with 6 electrons in the pz orbitals (each carbon contributes 1 electron in benzene; in borazine, each B contributes no electrons and each N has 2 electrons in the pz orbitals) and MO 17 for both shows the contiguous array of pz orbitals.

It is known that there is a "resonance energy" associated with aromatic compounds, which makes them very stable compounds.<ref>T. M. Krygowski, M. K. CyraÇski, G. Haefelinger, A. R. Katritzky, ''Tetrahedron'' 2000, '''56''', 1783.</ref> In an applied magnetic field, the ring current in aromatic systems creates its own induced magnetic field. The effect of this is that outside the ring, the induced field is in the same direction and the applied field, so hydrogens outside the ring would be deshielded in an NMR spectrometer. The opposite is true inside the ring.

It has been suggested that the sigma framework in aromatic molecules (the p orbitals combining in-phase in the plane of the ring) is an important bonding mode as well, not solely the pz orbitals.<ref>M. Palusiak and T. M.Krygowski, ''Chem. Eur. J.,'' 2007, '''13''', pp. 7996-8006</ref>

Rep:Mod:sk-inorg

2018-05-25T16:27:19Z

Sk716: /* Aromaticity */

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|<ref name=":0"><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf [Accessed 23/05/2018]</nowiki></ref>Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.<ref name=":0" />

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron:
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 9.PNG|frameless]]
|[[File:Sk - borazine mo 9.PNG|frameless]]
|This is MO 9 for both molecules. In benzene, this has bonding character between the 3 carbon 2s and the 3 hydrogen 1s orbitals in each half of the molecule and antibonding character between the two halves of the molecule. In borazine, only the NH units contribute to this MO, with one NH unit (N's 2s and H's 1s AOs) in a different phase to the 2 other NH units. Benzene's MO is has a C2 rotational axis borazine's doesn't
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Aromaticity can be explained simply using Hückel's rules, where an aromatic molecule fulfils these rules:
* It must be planar,
* Cyclic,
* Have a contiguous array of p orbitals orthogonal to the plane of the ring
* Have 4n+2 electrons in these p orbitals, where ''n'' is an integer

Benzene and borazine both comply with these rules as they're both cyclic and planar, each with 6 electrons in the pz orbitals (each carbon contributes 1 electron in benzene; in borazine, each B contributes no electrons and each N has 2 electrons in the pz orbitals) and MO 17 for both shows the contiguous array of pz orbitals.

It is known that there is a "resonance energy" associated with aromatic compounds, which makes them very stable compounds.<ref>T. M. Krygowski, M. K. CyraÇski, G. Haefelinger, A. R. Katritzky, Tetrahedron 2000, 56, 1783.</ref> In an applied magnetic field, the ring current in aromatic systems creates its own induced magnetic field. The effect of this is that outside the ring, the induced field is in the same direction and the applied field, so hydrogens outside the ring would be deshielded in an NMR spectrometer. The opposite is true inside the ring.

It has been suggested that the sigma framework in aromatic molecules (the p orbitals combining in-phase in the plane of the ring) is an important bonding mode as well, not solely the pz orbitals.<ref>M. Palusiak and T. M.Krygowski, ''Chem. Eur. J.,'' 2007, 13, pp. 7996-8006</ref>

Rep:Mod:sk-inorg

2018-05-25T16:16:57Z

Sk716: /* Comparison of benzene and borazine MOs */

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 9.PNG|frameless]]
|[[File:Sk - borazine mo 9.PNG|frameless]]
|This is MO 9 for both molecules. In benzene, this has bonding character between the 3 carbon 2s and the 3 hydrogen 1s orbitals in each half of the molecule and antibonding character between the two halves of the molecule. In borazine, only the NH units contribute to this MO, with one NH unit (N's 2s and H's 1s AOs) in a different phase to the 2 other NH units. Benzene's MO is has a C2 rotational axis borazine's doesn't
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Aromaticity can be explained simply using Hückel's rules (()), where an aromatic molecule fulfils these rules:
* It must be planar,
* Cyclic,
* Have a contiguous array of p orbitals orthogonal to the plane of the ring
* Have 4n+2 electrons in these p orbitals, where ''n'' is an integer

Benzene and borazine both comply with these rules as they're both cyclic and planar, each with 6 electrons in the pz orbitals (each carbon contributes 1 electron in benzene; in borazine, each B contributes no electrons and each N has 2 electrons in the pz orbitals) and MO 17 for both shows the contiguous array of pz orbitals.

It is known that there is a "resonance energy" associated with aromatic compounds, which makes them very stable compounds (()). In an applied magnetic field, the ring current in aromatic systems creates its own induced magnetic field. The effect of this is that outside the ring, the induced field is in the same direction and the applied field, so hydrogens outside the ring would be deshielded in an NMR spectrometer. The opposite is true inside the ring.

It has been suggested that the sigma framework in aromatic molecules (the p orbitals combining in-phase in the plane of the ring) is an important bonding mode as well, not solely the pz orbitals.(())

Rep:Mod:sk-inorg

2018-05-25T16:05:15Z

Sk716: /* Aromaticity */

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 14.PNG|frameless]]
|[[File:Sk - borazine mo 15.PNG|frameless]]
|This is MO 14 for benzene and MO 15 for borazine. These MOs are of the side-on in-phase combination of the 2p orbitals of carbon in benzene or nitrogen and boron in borazine along the σh plane. Both MOs have a C3 rotational axis and appear identical, which could be because of the sum of the contributions by boron and nitrogen equaling that of the carbon atoms in benzene.
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Aromaticity can be explained simply using Hückel's rules (()), where an aromatic molecule fulfils these rules:
* It must be planar,
* Cyclic,
* Have a contiguous array of p orbitals orthogonal to the plane of the ring
* Have 4n+2 electrons in these p orbitals, where ''n'' is an integer

Benzene and borazine both comply with these rules as they're both cyclic and planar, each with 6 electrons in the pz orbitals (each carbon contributes 1 electron in benzene; in borazine, each B contributes no electrons and each N has 2 electrons in the pz orbitals) and MO 17 for both shows the contiguous array of pz orbitals.

It is known that there is a "resonance energy" associated with aromatic compounds, which makes them very stable compounds (()). In an applied magnetic field, the ring current in aromatic systems creates its own induced magnetic field. The effect of this is that outside the ring, the induced field is in the same direction and the applied field, so hydrogens outside the ring would be deshielded in an NMR spectrometer. The opposite is true inside the ring.

It has been suggested that the sigma framework in aromatic molecules (the p orbitals combining in-phase in the plane of the ring) is an important bonding mode as well, not solely the pz orbitals.(())

Rep:Mod:sk-inorg

2018-05-25T16:05:02Z

Sk716: /* Aromaticity */

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 14.PNG|frameless]]
|[[File:Sk - borazine mo 15.PNG|frameless]]
|This is MO 14 for benzene and MO 15 for borazine. These MOs are of the side-on in-phase combination of the 2p orbitals of carbon in benzene or nitrogen and boron in borazine along the σh plane. Both MOs have a C3 rotational axis and appear identical, which could be because of the sum of the contributions by boron and nitrogen equaling that of the carbon atoms in benzene.
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Aromaticity can be explained simply using Hückel's rules (()), where an aromatic molecule fulfils these rules:
* It must be planar,
* Cyclic,
* Have a contiguous array of p orbitals orthogonal to the plane of the ring
* Have 4n+2 electrons in these p orbitals, where ''n'' is an integer

Benzene and borazine both comply with these rules as they're both cyclic and planar, each with 6 electrons in the p<subz orbitals (each carbon contributes 1 electron in benzene; in borazine, each B contributes no electrons and each N has 2 electrons in the pz orbitals) and MO 17 for both shows the contiguous array of pz orbitals.

It is known that there is a "resonance energy" associated with aromatic compounds, which makes them very stable compounds (()). In an applied magnetic field, the ring current in aromatic systems creates its own induced magnetic field. The effect of this is that outside the ring, the induced field is in the same direction and the applied field, so hydrogens outside the ring would be deshielded in an NMR spectrometer. The opposite is true inside the ring.

It has been suggested that the sigma framework in aromatic molecules (the p orbitals combining in-phase in the plane of the ring) is an important bonding mode as well, not solely the pz orbitals.(())

Rep:Mod:sk-inorg

2018-05-25T15:43:58Z

Sk716: /* Aromaticity */

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 14.PNG|frameless]]
|[[File:Sk - borazine mo 15.PNG|frameless]]
|This is MO 14 for benzene and MO 15 for borazine. These MOs are of the side-on in-phase combination of the 2p orbitals of carbon in benzene or nitrogen and boron in borazine along the σh plane. Both MOs have a C3 rotational axis and appear identical, which could be because of the sum of the contributions by boron and nitrogen equaling that of the carbon atoms in benzene.
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

It is known that there is a "resonance energy" associated with aromatic compounds, which makes them very stable compounds (()). Aromaticity can be explained simply using Hückel's rules (()), where an aromatic molecule fulfils these rules:
* It must be planar,
* Cyclic,
* Have a contiguous array of p orbitals orthogonal to the plane of the ring
* Have 4n+2 electrons in these p orbitals, where ''n'' is an integer

Benzene and borazine both comply with these rules as they're both cyclic and planar, each with 6 electrons in the p<subz orbitals (each carbon contributes 1 electron in benzene; in borazine, each B contributes no electrons and each N has 2 electrons in the pz orbitals) and MO 17 for both shows the contiguous array of pz orbitals.

Rep:Mod:sk-inorg

2018-05-25T15:23:52Z

Sk716: /* Aromaticity */

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 14.PNG|frameless]]
|[[File:Sk - borazine mo 15.PNG|frameless]]
|This is MO 14 for benzene and MO 15 for borazine. These MOs are of the side-on in-phase combination of the 2p orbitals of carbon in benzene or nitrogen and boron in borazine along the σh plane. Both MOs have a C3 rotational axis and appear identical, which could be because of the sum of the contributions by boron and nitrogen equaling that of the carbon atoms in benzene.
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Aromaticity can be explained simply using Hückel's rules (()), where an aromatic molecule fulfils these rules:

Rep:Mod:sk-inorg

2018-05-25T15:17:47Z

Sk716: /* Revision */

== Day 1 tasks ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 14.PNG|frameless]]
|[[File:Sk - borazine mo 15.PNG|frameless]]
|This is MO 14 for benzene and MO 15 for borazine. These MOs are of the side-on in-phase combination of the 2p orbitals of carbon in benzene or nitrogen and boron in borazine along the σh plane. Both MOs have a C3 rotational axis and appear identical, which could be because of the sum of the contributions by boron and nitrogen equaling that of the carbon atoms in benzene.
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Rep:Mod:sk-inorg

2018-05-25T15:16:18Z

Sk716: /* Comparison of benzene and borazine MOs */

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|-
|[[File:Sk - c6h6 mo 14.PNG|frameless]]
|[[File:Sk - borazine mo 15.PNG|frameless]]
|This is MO 14 for benzene and MO 15 for borazine. These MOs are of the side-on in-phase combination of the 2p orbitals of carbon in benzene or nitrogen and boron in borazine along the σh plane. Both MOs have a C3 rotational axis and appear identical, which could be because of the sum of the contributions by boron and nitrogen equaling that of the carbon atoms in benzene.
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|}

=== Aromaticity ===

Rep:Mod:sk-inorg

2018-05-25T15:10:04Z

Sk716: /* Comparison of benzene and borazine MOs */

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
!
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|
|-
|[[File:Sk - c6h6 mo 14.PNG|frameless]]
|[[File:Sk - borazine mo 15.PNG|frameless]]
|This is MO 14 for benzene and MO 15 for borazine. These MOs are of the side-on in-phase combination of the 2p orbitals of carbon in benzene or nitrogen and boron in borazine along the σh plane. Both MOs have a C3 rotational axis and appear identical, which could be because of the sum of the contributions by boron and nitrogen equaling that of the carbon atoms in benzene.
|
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in borazine is distorted towards the nitrogen atoms, which is caused by the nitrogen atoms having a bigger contribution due to its higher electronegativity than the boron atoms.
|
|}

Rep:Mod:sk-inorg

2018-05-25T15:07:51Z

Sk716:

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment (all of the charges in each molecule add up to 0), although the charge distribution has symmetry corresponding to the point group of the molecule: all of the symmetry operations in benzene's point group (D6h) can be performed on the charge distribution and it will map onto itself and the same is true for borazine's charge distribution using the symmetry operations in the D3h point group. The C-H bonds in benzene are only very slightly polarised, with the carbon atoms being red as it's slightly more electronegative than hydrogen. Borazine's charge distribution is more varied because of the alternating nitrogen/boron pattern in the ring. The nitrogen atoms are bright red because they are the most electronegative atoms present and the boron atoms are bright green as, even though they have a similar electronegativity to the hydrogen atoms, each boron is between two nitrogen atoms, so it will have a more positive charge compared to the hydrogen atoms. The Hydrogen atoms in the NH units have a greater positive charge than the H atoms in the BH units due to being bonded to a more electronegative atom (nitrogen), so more electron density is removed from H than when bonded to B.

=== Comparison of benzene and borazine MOs ===
In the following discussion, the z-axis is taken to be the principal axis of each molecule.
{| class="wikitable"
!Benzene
!Borazine
!Comparison
!
|-
|[[File:Sk - c6h6 mo 17.PNG|frameless]]
|[[File:Sk - borazine mo 17.PNG|frameless]]
|This is MO 17 of both molecules, which corresponds to the 2pz orbitals of carbon combining in-phase in benzene and the 2pz orbitals of boron and nitrogen combining in-phase in borazine. This MO for both molecules are very similar because they're symmetric, although the MO for borazine has a C3 axis (and not the C6 present in benzene) due to the greater contribution from nitrogen due to its greater electronegativity. There is a nodal plane between the lobes - along the σh plane.
|
|-
|[[File:Sk - c6h6 mo 14.PNG|frameless]]
|[[File:Sk - borazine mo 15.PNG|frameless]]
|This is MO 14 for benzene and MO 15 for borazine. These MOs are of the side-on in-phase combination of the 2p orbitals of carbon in benzene or nitrogen and boron in borazine along the σh plane. Both MOs have a C3 rotational axis and appear identical, which could be because of the sum of the contributions by boron and nitrogen equaling that of the carbon atoms in benzene.
|
|-
|[[File:Sk - c6h6 mo 20 (homo).PNG|frameless]]
|[[File:Sk - borazine mo 20 (homo).PNG|frameless]]
|This is the MO 20 (the HOMO) for both molecules, which is the in-phase combination of 2 pairs of 2 adjacent 2pz orbitals. In both molecules, there is no contribution from the two atoms on opposite sides of the ring. It is evident that the MO in
|
|}

Rep:Mod:sk-inorg

2018-05-25T14:37:24Z

Sk716:

Rep:Mod:sk-inorg

2018-05-25T14:03:25Z

Sk716:

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK BH3 FREQ.LOG| BH3 frequency log file]].
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Vibrational mode
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|1213
|14
|E'
|Very slightly
|Symmetric bend
|-
|2583
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

[[File:Sk - ir spectrum.PNG|frameless|563x563px]]

Only three peaks are visible in the IR spectrum (instead of the 6 present in the table given above). The vibration at 2583 cm-1 is not present because this frequency is for the symmetric stretch vibrational mode, which doesn't change the dipole moment of the molecule whereas the other vibrations do. A change in dipole moment is needed for a vibration to be IR active as one of the selection rules for this spectroscopy is Δμ ≠ 0, where Δμ is the change in dipole moment. There is also 2-fold degeneracy present for the vibration at the wavenumbers of 1213 and 2716 cm-1, removing two possible peaks and this means only one peak will be present at these frequencies.

==== Molecular orbital diagram ====
[[File:Sk_-_bh3_MO_diagram.png|thumb|Molecular orbital diagram of BH3, with the computed MOs (calculated using the Gaussian software) shown alongside the LCAO MOs]]
The molecular orbital diagram of BH3 is given with the computed molecular orbitals alongside the predicted LCAOs molecular orbitals.(())

The 1s orbital of boron (of 1a1' symmetry) was ignored in the diagram as it is too deep in energy to combine with any other hydrogen orbitals. Due to hydrogen being more electronegative than boron (()):
* The highest energy orbitals of boron, the 2p orbitals, are placed higher up in the diagram than the halfway point of the H3 fragment orbitals
* The bonding orbitals have a larger contribution from the H3 FOs and a smaller contribution from the boron AOs (and vice versa for the antibonding orbitals)
In general, the computed MOs agreed with the predicted ones as the shapes where very similar, showing that qualitative MO theory is useful as it uses relatively simple principles to predict the shapes of the actual MOs, with quite good accuracy; however, there is one significant slight discrepancy: there was a greater contribution from the 1s hydrogen orbitals in the antibonding MOs, especially in the 3a1' MO, where it was predicted that the boron 2s orbital would have a greater contribution due to boron being more electronegative than hydrogen. This shows that qualitative MO theory is not completely accurate as this difference suggests that merely using the electronegativities of boron and hydrogen to create the MOs won't always lead to the correct shapes.

<nowiki>=</nowiki>=

=== NH3 ===
NH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3 FREQ.LOG| NH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

=== NH3BH3 ===
NH3BH3 was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (C3v);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[Media:SK NH3BH3 FREQ.LOG| NH3BH3 frequency log file]].

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

==== Association energy of NH3BH3 ====
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
NH3 was optimised using the RB3LYP method and the GEN basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation ({{DOI|10042/202460}}), which shows that the optimisation is fully completed;
* The low frequencies obtained from the BBr3 frequency file: {{DOI|10042/202461}}
[[File:Sk - bbr3 pp opt final.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>

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

<nowiki>=</nowiki>=

== Aromaticity project ==

=== Benzene ===
Benzene was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D6h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK C6H6 FREQ 1.LOG|C6H6 frequency log file]].

[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
Borazine was optimised using the B3LYP method and the 6-31G(d,p) basis set. Below is:
* The summary window, which shows the correct molecular symmetry (D3h);
* The item table in the log file obtained after the optimisation, which shows that the optimisation is fully completed;
* The low frequencies obtained from the [[:File:SK BORAZINE FREQ.LOG|Borazine frequency log file]].

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

=== NBO charge analysis ===
The table below shows the results from the NBO charge analysis of benzene and borazine. In the images below, a colour scale of -1.10 (red) to +1.10 (green) was used and black corresponded to a charge of 0. The charges of each atom in the molecule given below the corresponding image.
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Sk - c6h6 charge dist.PNG|frameless]]
|[[File:Sk - borazine charge dist.PNG|frameless]]
|-
|C = -0.24
|N = -1.10
|-
|H = 0.24
|H in NH unit = 0.43
|-
|
|B = 0.75
|-
|
|H in BH unit = -0.08
|}

Being symmetric, both molecules have no dipole moment. As a whole, the atoms in benzene are closer to black than the ones in borazine, which shows that the C-C aren't polarized and the C-H bonds are only very slightly polarised, which the H atoms

Rep:Mod:sk-inorg

2018-05-25T13:27:19Z

Sk716:

Rep:Mod:sk-inorg

2018-05-25T13:26:14Z

Sk716:

Rep:Mod:sk-inorg

2018-05-25T13:24:22Z

Sk716:

File:SK NH3 FREQ.LOG

2018-05-25T12:52:56Z

Sk716:

Rep:Mod:sk-inorg

2018-05-25T12:49:55Z

Sk716: /* Molecular orbital diagram */

Rep:Mod:sk-inorg

2018-05-25T12:08:57Z

Sk716:

Rep:Mod:sk-inorg

2018-05-25T12:03:20Z

Sk716:

File:Sk - bh3 MO diagram.png

2018-05-25T12:03:11Z

Sk716: Sk716 uploaded a new version of File:Sk - bh3 MO diagram.png

File:Sk - ir spectrum.PNG

2018-05-25T11:06:08Z

Sk716:

Rep:Mod:sk-inorg

2018-05-24T22:16:39Z

Sk716:

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
Spectrum!!

==== Molecular orbital diagram ====
[[File:Sk - bh3 MO diagram.png|frameless]]

<nowiki>=</nowiki>=

=== NH3 ===

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

Upload freq file, for jmol as well!!

==

=== NH3BH3 ===
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

=== Association energy of NH3BH3 ===
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -2.3055 -0.0029 -0.0018 0.0774 0.7534 0.7534
Low frequencies --- 155.9402 155.9405 267.6894
</pre>

{{DOI|10042/202460}}, {{DOI|10042/202461}}

==

== Aromaticity project ==

=== Benzene ===
[[File:Sk - c6h6 opt 1.PNG|frameless]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===

[[File:Sk - borazine opt.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T22:15:21Z

Sk716:

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
Spectrum!!

==== Molecular orbital diagram ====
[[File:Sk - bh3 MO diagram.png|frameless]]

<nowiki>=</nowiki>=

=== NH3 ===

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

Upload freq file, for jmol as well!!

==

=== NH3BH3 ===
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

=== Association energy of NH3BH3 ===
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -2.3055 -0.0029 -0.0018 0.0774 0.7534 0.7534
Low frequencies --- 155.9402 155.9405 267.6894
</pre>

{{DOI|10042/202460}}, {{DOI|10042/202461}}

==

== Aromaticity project ==

=== Benzene ===
[[File:Sk - c6h6 opt 1.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
[[File:Sk - borazine opt.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.</pre>The frequency log file is located here: .<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T22:08:52Z

Sk716:

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.</pre>
<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

==== Vibrational modes ====
Spectrum!!

==== Molecular orbital diagram ====
[[File:Sk - bh3 MO diagram.png|frameless]]

<nowiki>=</nowiki>=

=== NH3 ===

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

Upload freq file, for jmol as well!!

==

=== NH3BH3 ===
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

=== Association energy of NH3BH3 ===
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

==

== Aromaticity project ==

=== Benzene ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T22:07:10Z

Sk716:

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.</pre>

==== Vibrational modes ====
Spectrum!!

==== Molecular orbital diagram ====
[[File:Sk - bh3 MO diagram.png|frameless]]

<nowiki>=</nowiki>=

=== NH3 ===

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

Upload freq file, for jmol as well!!

==

=== NH3BH3 ===
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

=== Association energy of NH3BH3 ===
E(NH3) = -56.55777 a.u.

E(BH3) = -26.61532 a.u.

E(NH3BH3) = -83.22468 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159 a.u. = -135 kJ/mol

=== BBr3 ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

==

== Aromaticity project ==

=== Benzene ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T21:22:04Z

Sk716:

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.</pre>

==== Vibrational modes ====
Spectrum!!

==== Molecular orbital diagram ====
[[File:Sk - bh3 MO diagram.png|frameless]]

<nowiki>=</nowiki>=

=== NH3 ===

==== Optimisation & Frequency analysis ====
[[File:Sk - nh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

Upload freq file, for jmol as well!!

==

=== NH3BH3 ===
[[File:Sk - nh3bh3 opt 621g.PNG|frameless]]<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

=== Association energy of NH3BH3 ===
E(NH3) = -56.55776873

E(BH3) =

ΔE

=== BBr3 ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

==

== Aromaticity project ==

=== Benzene ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

=== Borazine ===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T20:44:12Z

Sk716:

== Revision ==

=== BH3 ===

==== Optimisation & frequency analysis ====
[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0058 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0007 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9935 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

[[File:Sk - bh3 MO diagram.png|frameless]]

==

NH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

NH3BH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,7) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,7) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,8) 1.21 -DE/DX = -0.0001 !
! R5 R(5,8) 1.21 -DE/DX = -0.0001 !
! R6 R(6,8) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8684 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8684 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0301 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8684 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0301 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0301 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8746 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8746 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5965 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8746 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5965 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.5965 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -60.0 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 60.0 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 180.0 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0 -DE/DX = 0.0 !
! D8 D(3,7,8,5) 180.0 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

BBr3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

==

C6H6

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

Borazine

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T20:41:00Z

Sk716:

BH3

[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0058 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0007 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9935 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

[[File:Sk - bh3 MO diagram.png|frameless]]

==

NH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

==

NH3BH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,7) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,7) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,8) 1.21 -DE/DX = -0.0001 !
! R5 R(5,8) 1.21 -DE/DX = -0.0001 !
! R6 R(6,8) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8684 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8684 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0301 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8684 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0301 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0301 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8746 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8746 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5965 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8746 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5965 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.5965 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -60.0 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 60.0 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 180.0 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0 -DE/DX = 0.0 !
! D8 D(3,7,8,5) 180.0 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

==

BBr3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

==

C6H6

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

==

Borazine

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

==

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T20:25:20Z

Sk716:

BH3

[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0058 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0007 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9935 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

[[File:Sk - bh3 MO diagram.png|frameless]]

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>Optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3 OPT 631G.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3BH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,7) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,7) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,8) 1.21 -DE/DX = -0.0001 !
! R5 R(5,8) 1.21 -DE/DX = -0.0001 !
! R6 R(6,8) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8684 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8684 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0301 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8684 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0301 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0301 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8746 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8746 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5965 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8746 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5965 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.5965 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -60.0 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 60.0 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 180.0 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0 -DE/DX = 0.0 !
! D8 D(3,7,8,5) 180.0 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>Optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

BBr3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

<jmol><jmolApplet>
<title>Optimised BBr3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BBR3 PP FREQ FINAL.log</uploadedFileContents>
</jmolApplet></jmol>

C6H6

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

<jmol><jmolApplet>
<title>Optimised C6H6 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK C6H6 FREQ 1.LOG</uploadedFileContents>
</jmolApplet></jmol>

Borazine

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

<jmol><jmolApplet>
<title>Optimised borazine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BORAZINE FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T20:24:16Z

Sk716:

BH3

[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0058 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0007 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9935 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

[[File:Sk - bh3 MO diagram.png|frameless]]

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>Optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3 OPT 631G.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3BH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,7) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,7) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,8) 1.21 -DE/DX = -0.0001 !
! R5 R(5,8) 1.21 -DE/DX = -0.0001 !
! R6 R(6,8) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8684 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8684 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0301 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8684 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0301 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0301 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8746 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8746 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5965 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8746 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5965 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.5965 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -60.0 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 60.0 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 180.0 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0 -DE/DX = 0.0 !
! D8 D(3,7,8,5) 180.0 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>Optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

BBr3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

<jmol><jmolApplet>
<title>Optimised BBr3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BBR3 PP FREQ FINAL.LOG</uploadedFileContents>
</jmolApplet></jmol>

C6H6

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

<jmol><jmolApplet>
<title>Optimised C6H6 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK C6H6 FREQ 1.LOG</uploadedFileContents>
</jmolApplet></jmol>

Borazine

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

<jmol><jmolApplet>
<title>Optimised borazine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BBR3 PP FREQ FINAL.log</uploadedFileContents>
</jmolApplet></jmol>

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T20:22:45Z

Sk716:

BH3

[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0058 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0007 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9935 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

[[File:Sk - bh3 MO diagram.png|frameless]]

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>Optimised NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3 OPT 631G.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3BH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,7) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,7) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,8) 1.21 -DE/DX = -0.0001 !
! R5 R(5,8) 1.21 -DE/DX = -0.0001 !
! R6 R(6,8) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8684 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8684 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0301 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8684 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0301 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0301 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8746 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8746 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5965 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8746 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5965 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.5965 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -60.0 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 60.0 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 180.0 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0 -DE/DX = 0.0 !
! D8 D(3,7,8,5) 180.0 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>Optimised NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

BBr3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

<jmol><jmolApplet>
<title>Optimised BBr3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BBR3 PP FREQ FINAL.LOG</uploadedFileContents>
</jmolApplet></jmol>

C6H6

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

<jmol><jmolApplet>
<title>Optimised C6H6 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK C6H6 FREQ 1.LOG</uploadedFileContents>
</jmolApplet></jmol>

Borazine

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

<jmol><jmolApplet>
<title>Optimised borazine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BORAZINE FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T18:27:04Z

Sk716:

BH3

[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0058 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0007 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9935 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

[[File:Sk - bh3 MO diagram.png|frameless]]

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3BH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,7) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,7) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,8) 1.21 -DE/DX = -0.0001 !
! R5 R(5,8) 1.21 -DE/DX = -0.0001 !
! R6 R(6,8) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8684 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8684 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0301 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8684 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0301 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0301 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8746 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8746 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5965 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8746 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5965 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.5965 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -60.0 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 60.0 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 180.0 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0 -DE/DX = 0.0 !
! D8 D(3,7,8,5) 180.0 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

BBr3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

C6H6

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK C6H6 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Borazine

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

Rep:Mod:sk-inorg

2018-05-24T18:25:03Z

Sk716:

BH3

[[File:Sk - bh3 opt 621g sym.PNG|frameless]]

<pre>
Low frequencies --- -12.3492 -12.3425 -7.6649 -0.0008 0.0239 0.4061

Low frequencies --- 1162.9695 1213.1356 1213.1358
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128858D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0058 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0007 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9935 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

[[File:Sk - bh3 MO diagram.png|frameless]]

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843984D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

NH3BH3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.655851D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,7) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,7) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,8) 1.21 -DE/DX = -0.0001 !
! R5 R(5,8) 1.21 -DE/DX = -0.0001 !
! R6 R(6,8) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8684 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8684 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0301 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8684 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0301 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0301 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8746 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8746 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5965 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8746 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5965 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.5965 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -60.0 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 60.0 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 180.0 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0 -DE/DX = 0.0 !
! D8 D(3,7,8,5) 180.0 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

<pre>
Low frequencies --- -0.0251 -0.0033 -0.0008 17.1236 17.1258 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK NH3BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

BBr3

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.085774D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

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

{{DOI|10042/202460}}, {{DOI|10042/202461}}

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BBR3 FREQ FINAL.LOG</uploadedFileContents>
</jmolApplet></jmol>

C6H6

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-4.437902D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -17.2053 -14.9372 -14.9372 -0.0055 -0.0055 -0.0007
Low frequencies --- 414.1053 414.1053 620.9426
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK C6H6 FREQ .LOG</uploadedFileContents>
</jmolApplet></jmol>

Borazine

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
Predicted change in Energy=-9.233282D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0105 -0.0090 -0.0035 2.8223 2.8805 4.1465
Low frequencies --- 289.7095 289.7101 404.4118
</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SK BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Comparison

Benzene - C:-0.239 ; H:0.239
Borazine - NH:-1.102, 0.432; BH:0.747, -0.077

File:Sk - c6h6 opt 1.PNG

2018-05-24T15:45:00Z

Sk716:

File:Sk - borazine opt.PNG

2018-05-24T15:44:51Z

Sk716:

File:SK C6H6 FREQ 1.LOG

2018-05-24T15:44:34Z

Sk716:

File:SK BORAZINE FREQ.LOG

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Sk716:

File:Sk - c6h6 mo 20 (homo).PNG

2018-05-24T15:43:53Z

Sk716:

File:Sk - borazine mo 20 (homo).PNG

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File:Sk - c6h6 mo 9.PNG

2018-05-24T15:43:32Z

Sk716:

File:Sk - borazine mo 9.PNG

2018-05-24T15:43:23Z

Sk716:

File:Sk - c6h6 mo 14.PNG

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Sk716:

File:Sk - borazine mo 15.PNG

2018-05-24T15:43:05Z

Sk716:

File:Sk - c6h6 mo 17.PNG

2018-05-24T15:42:56Z

Sk716:

File:Sk - borazine mo 17.PNG

2018-05-24T15:42:47Z

Sk716:

File:Sk - c6h6 charge dist.PNG

2018-05-24T15:42:38Z

Sk716:

File:Sk - borazine charge dist.PNG

2018-05-24T15:42:29Z

Sk716: