ChemWiki - User contributions [en]

Rep:Mod:XYZ2025

2013-02-08T16:10:46Z

Avc110: /* Conclusion */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 47: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 48: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 48 and 49, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 50: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 51: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 52: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 51 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 54: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 55: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 54) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 55) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 56: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 57: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 58: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 56. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 57 and 58, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 59: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 59. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

== '''Conclusion''' ==

Computational chemistry is a very important tool because it allows us to carry out calculations that would otherwise be too time-consuming and complicated to solve. Calculations can be solved in a series of steps using Gaussview, which uses a series of approximations to solve the important Schrodinger equation.

Rep:Mod:XYZ2025

2013-02-08T16:10:10Z

Avc110: /* Conclusion */

Rep:Mod:XYZ2025

2013-02-08T16:05:42Z

Avc110: /* Analysis of charge distribution */

Rep:Mod:XYZ2025

2013-02-08T16:04:47Z

Avc110: /* NBO analysis */

Rep:Mod:XYZ2025

2013-02-08T16:04:24Z

Avc110: /* Population analysis */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 47: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 48: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 48 and 49, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 50: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 51: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 52: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 51 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 54: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 55: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 54) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 55) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 56: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 57: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 58: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 56. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 57 and 58, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 59: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 59. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:54:37Z

Avc110: /* Frequency analysis */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 47: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 48: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 48 and 49, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 50: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 51: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 52: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 51 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 54: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 55: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 54) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 55) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 56: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 57: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 58: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 56. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 57 and 58, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 59: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 59. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:54:17Z

Avc110: /* Optimisation - high level basis set */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 47: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 48: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 48 and 49, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 50: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 51: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 52: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 51 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 54: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 55: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 54) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 55) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 56: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 57: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 58: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 56. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 57 and 58, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:53:41Z

Avc110: /* Optimisation - low level basis set */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 47: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 48: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 48 and 49, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 50: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 51: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 52: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 51 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 54: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 55: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 54) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 55) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 50: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 51: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 52: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 51 and 52, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:53:03Z

Avc110: /* NBO analysis */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 47: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 48: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 48 and 49, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 50: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 51: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 52: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 51 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 47: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 48: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 48) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 49) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 50: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 51: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 52: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 51 and 52, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:52:36Z

Avc110: /* Frequency analysis */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 47: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 48: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 48 and 49, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 50: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 21: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 47: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 48: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 48) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 49) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 50: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 51: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 52: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 51 and 52, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:52:13Z

Avc110: /* Optimisation - high level basis set */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 47: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 48: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 48 and 49, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 46: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 46. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 21: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 47: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 48: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 48) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 49) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 50: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 51: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 52: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 51 and 52, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:51:35Z

Avc110: /* Pyridinium */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

 
=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 43: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 44: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 45: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 43. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 44 and 45, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 46: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 46. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 21: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 

=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 47: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 48: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 48) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 49) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 50: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 51: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 52: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 51 and 52, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:51:15Z

Avc110: /* Optimisation - low level basis set */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 44: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 45: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 46: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 44. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 45) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 46) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 43: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 44: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 45: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 43. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 44 and 45, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 46: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 46. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 21: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 
=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 47: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 48: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 48) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 49) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 50: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 51: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 52: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 51 and 52, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:50:45Z

Avc110: /* NBO analysis */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 42: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 43: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 42 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 40: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 41: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 42: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 40. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 41) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 42) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 43: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 44: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 45: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 43. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 44 and 45, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 46: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 46. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 21: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 
=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 47: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 48: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 48) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 49) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 50: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 51: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 52: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 51 and 52, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.

Rep:Mod:XYZ2025

2013-02-08T15:50:21Z

Avc110: /* Frequency analysis */

== '''Week 1: Understanding Computational Chemistry''' ==

===BH3===

==== Optimisation - low level basis set ====
[[File:BH3 AVC.png‎‎‎|thumb|left|Figure 1: Gaussview image of optimised BH3 molecule (3-21G).]]
[[File:BH3 total energy.png|thumb|left|Figure 2: Total energy of optimised BH3 molecule (3-21G).]]
[[File:BH3 rmsgradient.png|thumb|left|Figure 3: Gradient of optimised BH3 molecule (3-21G).]]
A molecule of BH3 was created and optimised in Gaussview, a program which uses different approximations to solve the Schrodinger equation. A low level basis set (3-21G) was first employed to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BH3_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 1. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 1 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 AVC.mol</uploadedFileContents>
<text>Molecule 1</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.46226347 a.u.
|-
| RMS Gradient Norm || 0.00020667 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 10.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19349 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees</table>
|}
The total energy curve (Figure 2) shows the program moving along the potential energy surface (PES) of the BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 3) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000415 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001614 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071259D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0006 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9987 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Optimisation - high level basis set====
[[File:BH3 631G AVC.png‎‎‎|thumb|left|Figure 4: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G totalenergy.png‎‎‎|thumb|left|Figure 5: Total energy of optimised BH3 molecule (6-31G(d,p)).]]
[[File:BH3 631G rmsgradient.png|thumb|left|Figure 6: Gradient of optimised BH3 molecule (6-31G(d,p)).]]

Following the successful optimisation of the BH3 molecule with a low level basis set, a new optimisation was carried out using a higher level basis set. The output log file is linked [[Media:BH3_631G_AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 4. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 2 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 631G AVC.mol</uploadedFileContents>
<text>Molecule 2</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised BH3 molecule are both linear and are shown in Figures 5 and 6, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|BH3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000237 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 6.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 119.999 degrees
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000018 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.321559D-10
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) 120.0005 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0005 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.999 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad</pre>

==== Frequency analysis ====

[[File:BH3 FREQ AVC.png‎‎‎|thumb|left|Figure 7: Gaussview image of optimised BH3 molecule (6-31G(d,p)).]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 7. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 3 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 3</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ BH3 Frequency
|-
! colspan="3" style="text-align: center;"|BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -26.61532374 a.u.
|-
| RMS Gradient Norm || 0.00000242 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C2V
|-
| Calculation Time|| 8.0 seconds
|-
| Optimised B-H Bond Distance|| 1.19232 Angstrom
|-
| Optimised H-B-H Bond Angle|| 120.001 degrees
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.384885D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -18.7412 0.0007 0.0007 0.0008 12.4957 12.6461
Low frequencies --- 1162.9784 1213.1790 1213.2325
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for BH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of BH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1213.18 || 14.0573 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1213.23 || 14.0607 || E'
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'
|}

The infrared spectrum of BH3, obtained from frequency analysis, is shown below in Figure 8.

[[File:BH3 FREQ INFRARED.png‎‎‎|650px|thumb|center|Figure 8: Infrared spectrum of BH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as a single peak.

==== Population analysis ====

The molecular orbitals of BH3 were obtained using the fully optimised molecule (6-31G). The output log file is linked [[Media:BH3 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23263. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:MO diagram.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals, but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

=== TlBr3 ===

==== Optimisation ====
[[File:TLBR3 AVC.png‎‎‎|thumb|left|Figure 9: Gaussview image of optimised TlBr3 molecule.]]
[[File:TLBR3 totalenergy AVC.png|thumb|left|Figure 10: Total energy of optimised TlBr3 molecule.]]
[[File:TLBR3 rmsgradient AVC.png|thumb|left|Figure 11: Gradient of optimised TlBr3 molecule.]]
The optimisation of TlBr3 was carried out on the HPC using pseudo-potentials.

The output log file is linked to [[Media:TLBR3 AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23012. A Gaussview image of the optimised molecule is shown in Figure 9. The total energy and gradient curves of the TlBr3 molecule are shown in Figures 10 and 11, respectively.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 4 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 AVC.mol</uploadedFileContents>
<text>Molecule 4</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ TlBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|TLBR3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000090 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 48.8 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The observed Tl-Br bond length is slightly longer than the literature value of 2.5122 Angstrom.<ref name="TlBr" />
<references> 
<ref name="TlBr">J. Glaser and G. Johansson. ''Acta. Chem. Scand. A.'' 1982, '''36''': 125-135.</ref>
</references>

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084065D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -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>

==== Frequency analysis ====

[[File:TLBR3 FREQ AVC.png‎‎‎|thumb|left|Figure 12: Gaussview image of optimised TlBr3 molecule.]]

Frequency analysis was carried out on the fully optimised TlBr3 structure to confirm the minimum energy structures. The output log file is linked [[Media:TLBR3 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23204. A Gaussview image of the molecule is shown in Figure 12. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 5 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>TLBR3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 5</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ TlBr3 Frequency
|-
! colspan="3" style="text-align: center;"|TLBR3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || LANL2DZ
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -91.21812851 a.u.
|-
| RMS Gradient Norm || 0.00000088 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| D3H
|-
| Calculation Time|| 28.2 seconds
|-
| Optimised Tl-Br Bond Distance|| 2.65095 Angstrom
|-
| Optimised Br-Tl-Br Bond Angle|| 120.000 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

The lowest "real" normal mode is -3.4213cm-1 and the highest is 3.9367cm-1.

The infrared spectrum of TlBr3, obtained from frequency analysis, is shown below in Figure 13.

[[File:TLBR3 FREQ AVC IR.jpg‎‎‎|650px|thumb|center|Figure 13: Infrared spectrum of TlBr3 molecule.]]

As with the BH3 molecule, the infrared spectrum only shows four peaks, whereas six distinct peaks are expected for the six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one single peak.

=== BBr3 ===

==== Optimisation ====
[[File:BBR3 631G AVC.png|thumb|left|Figure 14: Gaussview image of optimised BBr3 molecule.]]

A molecule of BBr3 was created from the fully optimised BH3 (6-31G(d,p)) molecule. It was then optimised, with the calculation being carried out on the HPC using psuedo-potentials. The output log file is linked to [[Media:BBR3 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23205. A Gaussview image of the optimised molecule is shown in Figure 14.

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 6 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BBR3 631G AVC.mol</uploadedFileContents>
<text>Molecule 6</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ BBr3 Optimisation
|-
! colspan="3" style="text-align: center;"|BBR3_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || Gen
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -64.43645277 a.u.
|-
| RMS Gradient Norm || 0.00000383 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| CS
|-
| Calculation Time|| 40.5 seconds
|-
| Optimised B-Br Bond Distance|| 1.93397 Angstrom
|-
| Optimised Br-B-Br Bond Angle|| 119.996 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful.

<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=-4.079985D-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) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9955 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Analysis of bond distance - BH3, BBr3 and TlBr3 ===

The table below shows the bond distances for the three molecules that have been optimised so far:

{|class="wikitable" border="1"
|+ Comparison of bond distances
! Molecule !! Bond distance (Angstrom)
|-
| BH3 || 1.19232
|-
| BBr3 || 1.93397
|-
| TlBr3 || 2.65095
|}

As observed in BH3 and BBr3, changing the ligand has a large effect on bond length, and the larger the ligand, the longer the bond length. H and Br are similar because both atoms require one more electron to complete their valence electron shells. The difference between H and Br is that Br is a highly electronegative atom whereas H is not. Br is a much more electron-rich atom, which means it will undergo stronger electronic repulsion and result in a longer bond length.

As observed in BBr3 and TlBr3, changing the central element has a profound effect on the bond length. Both B and Tl are in Group 13 of the Periodic table, which means they have 3 electrons in their outer shell. The difference between them is that Tl is a very large, heavy atom whereas B is very light. The larger the central atom, the greater the repulsion and the longer the bond length.

A bond can be described as a mutual attraction between two atoms, resulting in the formation of a molecule. The type of attraction can be distinguished by the organisation of valence electrons (i.e. covalent, ionic or metallic bonds).

In some structures, Gaussview does not draw bonds as expected. This is because the distance between the atoms exceeds a predefined value and, since bonds are used as a structural convenience for visualisation, they are not drawn in Gaussview.

=== Analysis of vibrations - BH3 and TlBr3 ===

The table in section 1.1.4 describes the six different vibrations of BH3. Using the frequency analysis in section 1.2.2, the different vibrations of TlBr3 were explored and compared to BH3, as shown in the table below:

{| class="wikitable" border="1"
|+ Vibrations of BH3
|-
! rowspan="2" | '''No.'''
! colspan="5" style="text-align: center;"|'''BH3''' || colspan="5" style="text-align: center;"|'''TlBr3'''
|-
!| Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group || Vibration || Description || Frequency (cm-1)|| Intensity || Symmetry of Point Group
|-
| 1 ||[[Media:BH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down together, and the B atom moves up and down in the opposite direction. || 1162.98 || 92.5514 ||A2 || [[Media:TLBR3 vibration 1 avc.gif|View animation 1]] || Two Br atoms move in the plane towards and away from each other, and this pushes the Tl and remaining Br atom further away and then back to the original position. || 46.43 || 3.6867 || E'
|-
| 2 || [[Media:BH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom further away and then back to the original position. || 1213.18 || 14.0573 || E'|| [[Media:TLBR3 vibration 2 avc.gif|View animation 2]] || Two Br atoms move in the plane towards and away from each other, whilst the other Br atom vibrates left and right independently.|| 46.43 || 3.6867 || E'
|-
| 3 || [[Media:BH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently.|| 1213.23 || 14.0607 || E'||[[Media:TLBR3 vibration 3 avc.gif|View animation 3]]|| The three Br atoms move up and down together, and the Tl atom moves up and down in the opposite direction. || 52.14 || 5.8466 || A2
|-
| 4 || [[Media:BH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the B atom, which remains stationary. || 2582.26 || 0.0000 || A1'||[[Media:TLBR3 vibration 4 avc.gif|View animation 4]]|| The three Br atoms move simultaneously along the bond towards the Tl atom, which remains stationary. || 165.27 || 0.0000 || A1'
|-
| 5 || [[Media:BH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 2715.41 || 126.3292 || E' || [[Media:TLBR3 vibration 5 avc.gif|View animation 5]]|| Two Br atoms move in and out along the bond towards the Tl atom, in a non-concerted manner. The other Br remains stationary.|| 210.69 || 25.4830 || E'
|-
| 6 || [[Media:BH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the B, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The B atom remains stationary. || 2715.45 || 126.3228 || E'|| [[Media:TLBR3 vibration 6 avc.gif|View animation 6]]|| Two Br atoms move unanimously in and out along the bond towards the Tl, whilst the other Br moves with the same motion but not simultaneously with the 2 other Br atoms. The Tl atom remains stationary. || 210.69 || 25.4797 || E'
|}

There is a large difference between the frequencies of BH3 and TlBr3. The Br atom has a higher moment of inertia because the molecule is larger and heavier. This results in fewer vibrations and a lower frequency for TlBr3. This also means that TlBr3 is less susceptible to changing vibrations than BH3 and therefore the range of frequencies is much smaller.

There has been a reordering of modes in the first three vibrations, because they are different for both BH3 and TlBr3. However, vibrations 3-6 are the same for both molecules.

The infrared spectra for BH3 and TlBr3 are similar because some of the vibrations overlap, resulting in only some distinct peaks. Also, there is a large difference in frequency between the lowest two peaks, representing the A2 and E' modes, and the highest peaks, representing the A1' and E' modes. The reason for this is strong repulsion between atoms in the molecules, which increases the energy and therefore the frequency of vibrations.

When carrying out optimisation and frequency analysis for a molecule, the same method and basis set must be employed. This is because frequency analysis is carried out on fully optimised molecules to confirm the successful structure, and provide spectral data for the molecule. Use of a different method or basis set will result in incorrect findings.

The purpose of carrying out frequency analysis is to further confirm successful optimisation of a molecule, because frequency analysis is essentially the second derivative of the potential energy surface. Also, it produces infrared spectra and Raman modes, which can be compared to experimental results and analysed for better understanding.

The "low frequencies" represent the motions of the center of mass of the molecule. Since every molecule has 3N-6 vibrational frequencies, the frequencies listed show the "-6" values.

=== NH3 ===

==== Optimisation ====
[[File:NH3 AVC.png|thumb|left|Figure 15: Gaussview image of optimised NH3 molecule.]]
[[File:NH3 totalenergy AVC.png|thumb|left|Figure 16: Total energy of optimised NH3 molecule.]]
[[File:NH3 rmsgradient AVC.png|thumb|left|Figure 17: Gradient of optimised NH3 molecule.]]

A molecule of NH3 was created and optimised in Gaussview. Since the molecule is so small, it was only necessary to use the high level basis set, 6-31G(d,p). The output log file of this optimisation is linked [[Media:NH3 AVC.LOG‎‎| here]] and a Gaussview image of the optimised molecule is shown in Figure 15. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 7 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 AVC.mol</uploadedFileContents>
<text>Molecule 7</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003472 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 0.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.714 degrees</table>
|}
The total energy curve (Figure 16) shows the program moving along the potential energy surface (PES) of the NH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 17) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000630 0.001800 YES
RMS Displacement 0.000369 0.001200 YES
Predicted change in Energy=-5.618230D-08
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) 1.0179 -DE/DX = 0.0001 !
! A1 A(2,1,3) 105.7109 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7143 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7134 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8004 -DE/DX = -0.0001 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis====
[[File:NH3 FREQUENCY AVC.png‎‎‎|thumb|left|Figure 18: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3 FREQUENCY AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 18. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 8 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3 FREQUENCY AVC.mol</uploadedFileContents>
<text>Molecule 8</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -56.55776852 a.u.
|-
| RMS Gradient Norm || 0.00003463 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 1.8480 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 9.0 seconds
|-
| Optimised N-H Bond Distance|| 1.01798 Angstrom
|-
| Optimised H-N-H Bond Angle|| 105.713 degrees
|}
The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000035 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000288 0.001200 YES
Predicted change in Energy=-5.731720D-08
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -35.2863 -15.3544 -0.0012 0.0008 0.0012 8.2630
Low frequencies --- 1090.9042 1694.1849 1694.2501
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Animating vibrations ====

Using the completed frequency analysis for NH3, the vibrations of the molecule were explored in Gaussview. The six distinct vibrations of NH3 are summarised in the table below:

{| class="wikitable" border="1"
|+ Vibrations of NH3
! No. !! Vibration !! Description !! Frequency (cm-1)!! Intensity !! Symmetry of Point Group
|-
| 1 ||[[Media:NH3 vibration 1 avc.gif|View animation 1]]|| The three H atoms move up and down, and the N atom moves up and down in the opposite direction. || 1090.90 || 145.0149 ||A2
|-
| 2 || [[Media:NH3 vibration 2 avc.gif|View animation 2]] || Two H atoms move in the plane towards and away from each other, and this pushes the B and remaining H atom away and back to the original position. || 1694.18 || 13.5212 || E'
|-
| 3 || [[Media:NH3 vibration 3 avc.gif|View animation 3]] || Two H atoms move in the plane towards and away from each other, whilst the other H atom vibrates left and right independently. || 1694.25 || 13.5214 || E'
|-
| 4 || [[Media:NH3 vibration 4 avc.gif|View animation 4]] || The three H atoms move simultaneously along the bond towards the N atom, which remains stationary. || 3461.25 || 1.0716 || A1'
|-
| 5 || [[Media:NH3 vibration 5 avc.gif|View animation 5]] || Two H atoms move in and out along the bond towards the B atom, in a non-concerted manner. The other H remains stationary.|| 3589.33 || 0.2820 || E'
|-
| 6 || [[Media:NH3 vibration 6 avc.gif|View animation 6]] || Two H atoms move unanimously in and out along the bond towards the N, whilst the other H moves with the same motion but not simultaneously with the 2 other H atoms. The N atom remains stationary. || 3589.60 || 0.2810 || E'
|}

The infrared spectrum of NH3, obtained from frequency analysis, is shown below in Figure 19.

[[File:NH3 AVC IR.png‎‎‎|650px|thumb|center|Figure 19: Infrared spectrum of NH3 molecule.]]

The infrared spectrum only shows four peaks, whereas six distinct peaks are expected since there are six different vibrations. The reason for this is that some peaks have similar frequencies, which are superimposed and therefore appear overlapped as one peak.

==== Population analysis ====

The molecular orbitals of NH3 were obtained using the fully optimised molecule (6-31G(d,p)). The output log file is linked to [[Media:NH3 NBO AVC.LOG| here]]. An MO diagram of the trigonal planar molecule was created in ChemDraw. The LCAOs for each energy level were included, as well as a snap-shot of the "real" MOs obtained in Gaussview. The completed MO diagram is shown below:

[[File:NH3 modiagram AVC.png‎‎‎|500px|center]]

The "real" computed MOs are very similar to the LCAOs. However, the unoccupied orbitals are more diffuse than the occupied orbitals and this can result in unexpected shapes. It can therefore be proposed that qualitative MO theory is accurate for occupied and low-energy unoccupied orbitals , but becomes less useful for higher energy unoccupied orbitals because they are more diffuse.

==== NBO analysis ====
[[File:NH3 NBO CHARGED AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged NH3 molecule.]]
[[File:NH3 NBO CHARGED numbers AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged NH3 molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of NH3. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of NH3 is -1.125 to +1.125. As shown in Figure 21, the N has a charge of -1.125 and each H has a charge of +0.375.

 
 
 
 

 

=== NH3BH3 ===

==== Optimisation ====
[[File:NH3BH3 AVC.png|thumb|left|Figure 22: Gaussview image of optimised NH3BH3 molecule.]]
[[File:NH3BH3 totalenergy AVC.png|thumb|left|Figure 23: Total energy of optimised NH3BH3 molecule.]]
[[File:NH3BH3 rmsgradient AVC.png|thumb|left|Figure 24: Gradient of optimised NH3BH3 molecule.]]

A molecule of NH3BH3 was created and optimised in Gaussview, ensuring the same basis set and method was used. The output log file of this optimisation is linked [[Media:NH3BH3 AVC.LOG| here]] and a Gaussview image of the optimised molecule is shown in Figure 22. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 9 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 AVC.mol</uploadedFileContents>
<text>Molecule 9</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ NH3BH3 Optimisation
|-
! colspan="3" style="text-align: center;"|NH3BH3_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005935 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 58.0 seconds</table>
|}
The total energy curve (Figure 23) shows the program moving along the potential energy surface (PES) of the NH3BH3 molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 24) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000508 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
Predicted change in Energy=-1.611643D-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) 107.873 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.873 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0212 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8692 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0298 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0297 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.8796 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.8796 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(5,8,6) 113.8728 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.591 -DE/DX = 0.0 !
! A12 A(6,8,7) 104.591 -DE/DX = 0.0 !
! D1 D(1,7,8,4) 179.9998 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9967 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9963 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0005 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.003 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.996 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0001 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9964 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0034 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:NH3BH3 FREQ AVC.png|thumb|left|Figure 25: Gaussview image of optimised NH3 molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked [[Media:NH3BH3 FREQ AVC.LOG| here]] and the Gaussview image of the molecule is shown in Figure 25. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 10 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NH3BH3 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 10</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ NH3BH3 Frequency
|-
! colspan="3" style="text-align: center;"|NH3BH3_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -83.22469032 a.u.
|-
| RMS Gradient Norm || 0.00005943 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 5.5648 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 44.0 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000582 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
Predicted change in Energy=-1.716440D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -0.0011 0.0006 0.0009 18.5424 23.7766 41.0416
Low frequencies --- 266.2888 632.2327 639.8262
</pre>

The better the method employed, the closer to zero these frequencies will be. Ideally, these should be within plus/minus 15 cm-1.

==== Association energies ====

The total energies of the molecules, obtained from frequency analysis, are:

E(NH3) = -56.55776852 a.u. 
E(BH3) = -26.61532374 a.u. 
E(NH3BH3) = -83.22469032 a.u. 

The energy difference is given by:

ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -83.22469032 - [-56.55776852 + -26.61532374] 
ΔE = -0.05159826 a.u. = -135.471 kJ/mol

This number is the association energy for combining a molecule of NH3 with a molecule of BH3. It is also the dissociation energy. The literature value for the dissociation energy was found to be -98.3250 kJ/mol (-0.03745 a.u.), which is of the same order of magnitude as the obtained value.<ref name="NH3BH3" />
<references> 
<ref name="NH3BH3">J. S. Binkley and L. R. Thorne. ''J. Chem. Phys''. 79, '''6''': 2932-2940. </ref>
</references>

== '''Week 2: Investigating Aromaticity Project''' ==

=== Benzene ===

==== Optimisation - low level basis set ====
[[File:Benzene 321g avc.png|thumb|left|Figure 26: Gaussview image of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G totalenergy AVC.png|thumb|left|Figure 27: Total energy of optimised benzene molecule (3-21G).]]
[[File:BENZENE 321G rmsgradient AVC.png|thumb|left|Figure 28: Gradient of optimised benzene molecule (3-21G).]]

A molecule of benzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BENZENE 321G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23254. A Gaussview image of the optimised molecule is shown in Figure 26. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 11 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 321G AVC.mol</uploadedFileContents>
<text>Molecule 11</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|benzene_321g_avc
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -230.97576955 a.u.
|-
| RMS Gradient Norm || 0.00011167 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 56.0 seconds</table>
|}
The total energy curve (Figure 27) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 28) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000216 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000267 0.001200 YES
Predicted change in Energy=-4.465157D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3974 -DE/DX = 0.0 !
! R2 R(1,6) 1.3971 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0838 -DE/DX = 0.0002 !
! R4 R(2,3) 1.3971 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0838 -DE/DX = 0.0002 !
! R6 R(3,4) 1.3973 -DE/DX = 0.0 !
! R7 R(3,9) 1.0838 -DE/DX = 0.0002 !
! R8 R(4,5) 1.3971 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0838 -DE/DX = 0.0002 !
! R10 R(5,6) 1.3973 -DE/DX = 0.0 !
! R11 R(5,11) 1.0838 -DE/DX = 0.0002 !
! R12 R(6,12) 1.0838 -DE/DX = 0.0002 !
! A1 A(2,1,6) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9999 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.002 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9952 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0027 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9997 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0093 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9909 -DE/DX = 0.0 !
! A10 A(3,4,5) 119.9979 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9871 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.015 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0025 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0084 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9891 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9995 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0058 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9947 -DE/DX = 0.0 !
! D1 D(6,1,2,3) -0.0094 -DE/DX = 0.0 !
! D2 D(6,1,2,8) 180.0028 -DE/DX = 0.0 !
! D3 D(7,1,2,3) -180.0118 -DE/DX = 0.0 !
! D4 D(7,1,2,8) 0.0004 -DE/DX = 0.0 !
! D5 D(2,1,6,5) -0.0054 -DE/DX = 0.0 !
! D6 D(2,1,6,12) 180.0048 -DE/DX = 0.0 !
! D7 D(7,1,6,5) -180.003 -DE/DX = 0.0 !
! D8 D(7,1,6,12) 0.0072 -DE/DX = 0.0 !
! D9 D(1,2,3,4) 0.0171 -DE/DX = 0.0 !
! D10 D(1,2,3,9) 180.0093 -DE/DX = 0.0 !
! D11 D(8,2,3,4) 180.0049 -DE/DX = 0.0 !
! D12 D(8,2,3,9) -0.003 -DE/DX = 0.0 !
! D13 D(2,3,4,5) -0.01 -DE/DX = 0.0 !
! D14 D(2,3,4,10) -180.0081 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9978 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0003 -DE/DX = 0.0 !
! D17 D(3,4,5,6) -0.0048 -DE/DX = 0.0 !
! D18 D(3,4,5,11) 180.0075 -DE/DX = 0.0 !
! D19 D(10,4,5,6) -180.0067 -DE/DX = 0.0 !
! D20 D(10,4,5,11) 0.0056 -DE/DX = 0.0 !
! D21 D(4,5,6,1) 0.0125 -DE/DX = 0.0 !
! D22 D(4,5,6,12) 180.0023 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 180.0002 -DE/DX = 0.0 !
! D24 D(11,5,6,12) -0.01 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:BENZENE 631G AVC.png|thumb|left|Figure 29: Gaussview image of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G totalenergy AVC.png|thumb|left|Figure 30: Total energy of optimised benzene molecule (6-31G(d,p)).]]
[[File:BENZENE 631G rmsgradient AVC.png|thumb|left|Figure 31: Gradient of optimised benzene molecule (6-31G(d,p)).]]

Following successful optimisation with a low level basis set, a high level basis set, 6-31G(d,p), was then used to fully optimise the molecule of benzene. The output log file of this optimisation is linked [[Media:BENZENE 631G AVC.LOG| here]] and the link to the D-space file is http://dx.doi.org/10042/23255. A Gaussview image of the optimised molecule is shown in Figure 29. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 12 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE 631G AVC.mol</uploadedFileContents>
<text>Molecule 12</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Benzene Optimisation
|-
! colspan="3" style="text-align: center;"|BENZENE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003385 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 6.0 seconds</table>
|}
The total energy curve (Figure 30) shows the program moving along the potential energy surface (PES) of the benzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 31) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000049 0.001200 YES
Predicted change in Energy=-2.212772D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3963 -DE/DX = 0.0 !
! R2 R(1,6) 1.3962 -DE/DX = 0.0001 !
! R3 R(1,7) 1.0864 -DE/DX = 0.0 !
! R4 R(2,3) 1.3962 -DE/DX = 0.0001 !
! R5 R(2,8) 1.0864 -DE/DX = 0.0 !
! R6 R(3,4) 1.3963 -DE/DX = 0.0 !
! R7 R(3,9) 1.0864 -DE/DX = 0.0 !
! R8 R(4,5) 1.3962 -DE/DX = 0.0001 !
! R9 R(4,10) 1.0864 -DE/DX = 0.0 !
! R10 R(5,6) 1.3963 -DE/DX = 0.0 !
! R11 R(5,11) 1.0864 -DE/DX = 0.0 !
! R12 R(6,12) 1.0864 -DE/DX = 0.0 !
! A1 A(2,1,6) 120.0009 -DE/DX = 0.0 !
! A2 A(2,1,7) 119.9975 -DE/DX = 0.0 !
! A3 A(6,1,7) 120.0017 -DE/DX = 0.0 !
! A4 A(1,2,3) 120.0012 -DE/DX = 0.0 !
! A5 A(1,2,8) 119.9967 -DE/DX = 0.0 !
! A6 A(3,2,8) 120.0021 -DE/DX = 0.0 !
! A7 A(2,3,4) 119.9979 -DE/DX = 0.0 !
! A8 A(2,3,9) 120.0052 -DE/DX = 0.0 !
! A9 A(4,3,9) 119.9969 -DE/DX = 0.0 !
! A10 A(3,4,5) 120.0008 -DE/DX = 0.0 !
! A11 A(3,4,10) 119.9941 -DE/DX = 0.0 !
! A12 A(5,4,10) 120.0051 -DE/DX = 0.0 !
! A13 A(4,5,6) 120.0012 -DE/DX = 0.0 !
! A14 A(4,5,11) 120.0039 -DE/DX = 0.0 !
! A15 A(6,5,11) 119.9948 -DE/DX = 0.0 !
! A16 A(1,6,5) 119.9979 -DE/DX = 0.0 !
! A17 A(1,6,12) 120.0044 -DE/DX = 0.0 !
! A18 A(5,6,12) 119.9976 -DE/DX = 0.0 !
! D1 D(6,1,2,3) 0.0034 -DE/DX = 0.0 !
! D2 D(6,1,2,8) -180.0015 -DE/DX = 0.0 !
! D3 D(7,1,2,3) 180.0033 -DE/DX = 0.0 !
! D4 D(7,1,2,8) -0.0017 -DE/DX = 0.0 !
! D5 D(2,1,6,5) 0.0015 -DE/DX = 0.0 !
! D6 D(2,1,6,12) -180.0007 -DE/DX = 0.0 !
! D7 D(7,1,6,5) 180.0016 -DE/DX = 0.0 !
! D8 D(7,1,6,12) -0.0005 -DE/DX = 0.0 !
! D9 D(1,2,3,4) -0.006 -DE/DX = 0.0 !
! D10 D(1,2,3,9) -180.0022 -DE/DX = 0.0 !
! D11 D(8,2,3,4) -180.0011 -DE/DX = 0.0 !
! D12 D(8,2,3,9) 0.0027 -DE/DX = 0.0 !
! D13 D(2,3,4,5) 0.0037 -DE/DX = 0.0 !
! D14 D(2,3,4,10) 180.0024 -DE/DX = 0.0 !
! D15 D(9,3,4,5) 179.9999 -DE/DX = 0.0 !
! D16 D(9,3,4,10) -0.0014 -DE/DX = 0.0 !
! D17 D(3,4,5,6) 0.0012 -DE/DX = 0.0 !
! D18 D(3,4,5,11) -180.0014 -DE/DX = 0.0 !
! D19 D(10,4,5,6) 180.0025 -DE/DX = 0.0 !
! D20 D(10,4,5,11) -0.0001 -DE/DX = 0.0 !
! D21 D(4,5,6,1) -0.0038 -DE/DX = 0.0 !
! D22 D(4,5,6,12) -180.0017 -DE/DX = 0.0 !
! D23 D(11,5,6,1) 179.9988 -DE/DX = 0.0 !
! D24 D(11,5,6,12) 0.001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BENZENE FREQ AVC.png‎‎‎|thumb|left|Figure 32: Gaussview image of optimised benzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BENZENE FREQUENCY AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23253. The Gaussview image of the molecule is shown in Figure 32. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 13 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BENZENE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 13</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Benzene Frequency
|-
! colspan="3" style="text-align: center;"|BENZENE_FREQUENCY_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -232.25821232 a.u.
|-
| RMS Gradient Norm || 0.00003384 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 35.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000124 0.001800 YES
RMS Displacement 0.000064 0.001200 YES
Predicted change in Energy=-2.546715D-08
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -5.1642 -0.0010 -0.0009 -0.0005 13.0466 16.7439
Low frequencies --- 414.1402 414.9607 621.1690
</pre>

==== Population analysis ====

MO analysis was carried out on the optimised benzene molecule. The output log file is linked [[Media:BENZENE POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23264.

==== NBO analysis ====
[[File:BENZENE NBO colour AVC.png‎‎‎|thumb|left|Figure 33: Gaussview image of charged benzene molecule.]]
[[File:BENZENE NBO number AVC.png‎‎‎|thumb|right|Figure 34: Gaussview image of charged benzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of benzene, using the output log from from the population analysis. Figure 33 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of benzene is -0.239 to +0.239. As shown in Figure 34, the C atoms have a charge of -0.239 and each H has a charge of +0.239.

 
 
 
 

 

=== Boratabenzene ===

==== Optimisation - low level basis set ====
[[File:BC5H6 321G AVC.png|thumb|left|Figure 35: Gaussview image of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 totalenergy AVC.png|thumb|left|Figure 36: Total energy of optimised boratabenzene molecule (3-21G).]]
[[File:BC5H6 rmsgradient AVC.png|thumb|left|Figure 37: Gradient of optimised boratabenzene molecule (3-21G).]]

A molecule of boratabenzene was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked [[Media:BC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23250. A Gaussview image of the optimised molecule is shown in Figure 35. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 14 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 14</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -217.81414734 a.u.
|-
| RMS Gradient Norm || 0.00004211 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.2275 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 37.2 seconds</table>
|}
The total energy curve (Figure 36) shows the program moving along the potential energy surface (PES) of the boratabenzene molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 37) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000282 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-4.181592D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4054 -DE/DX = 0.0 !
! R2 R(1,5) 1.4053 -DE/DX = 0.0 !
! R3 R(1,6) 1.0896 -DE/DX = 0.0 !
! R4 R(2,3) 1.4017 -DE/DX = -0.0001 !
! R5 R(2,7) 1.0948 -DE/DX = 0.0 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0 !
! R7 R(3,12) 1.5149 -DE/DX = 0.0001 !
! R8 R(4,5) 1.4018 -DE/DX = -0.0001 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0 !
! R10 R(4,12) 1.5149 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0948 -DE/DX = 0.0 !
! R12 R(9,12) 1.2183 -DE/DX = 0.0 !
! A1 A(2,1,5) 120.5537 -DE/DX = 0.0 !
! A2 A(2,1,6) 119.7217 -DE/DX = 0.0 !
! A3 A(5,1,6) 119.7246 -DE/DX = 0.0 !
! A4 A(1,2,3) 122.1916 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.6592 -DE/DX = 0.0 !
! A6 A(3,2,7) 120.1492 -DE/DX = 0.0 !
! A7 A(2,3,8) 116.3905 -DE/DX = 0.0 !
! A8 A(2,3,12) 119.8052 -DE/DX = 0.0 !
! A9 A(8,3,12) 123.8042 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.3798 -DE/DX = 0.0 !
! A11 A(5,4,12) 119.8002 -DE/DX = 0.0 !
! A12 A(10,4,12) 123.82 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.195 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.6458 -DE/DX = 0.0 !
! A15 A(4,5,11) 120.1592 -DE/DX = 0.0 !
! A16 A(3,12,4) 115.4543 -DE/DX = 0.0 !
! A17 A(3,12,9) 122.2759 -DE/DX = 0.0 !
! A18 A(4,12,9) 122.2698 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0032 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9998 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.002 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.001 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0009 -DE/DX = 0.0 !
! D6 D(2,1,5,11) 180.0018 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9997 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0025 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0033 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9997 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0013 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -180.0011 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0005 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0003 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -179.9999 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0008 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.001 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 180.0001 -DE/DX = 0.0 !
! D21 D(5,4,12,3) -0.0008 -DE/DX = 0.0 !
! D22 D(5,4,12,9) -180.001 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0002 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BC5H6 631G AVC.png|thumb|left|Figure 38: Gaussview image of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 39: Total energy of optimised boratabenzene molecule (6-31G(d,p)).]]
[[File:BC5H6 631G rmsgradient AVC.png|thumb|left|Figure 40: Gradient of optimised boratabenzene molecule (6-31G(d,p)).]]

Following the successful optimisation of the boratabenzene molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked [[Media:BC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23251. A Gaussview image of the optimised molecule is shown in Figure 38. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 15 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 15</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised boratabenzene molecule are both linear and are shown in Figures 39 and 40, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Boratabenzene Optimisation
|-
! colspan="3" style="text-align: center;"|BC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019085 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 59.4 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000235 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.001778 0.001800 YES
RMS Displacement 0.000515 0.001200 YES
Predicted change in Energy=-1.134863D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4048 -DE/DX = 0.0002 !
! R2 R(1,5) 1.4048 -DE/DX = 0.0002 !
! R3 R(1,6) 1.0915 -DE/DX = 0.0 !
! R4 R(2,3) 1.3989 -DE/DX = 0.0 !
! R5 R(2,7) 1.0968 -DE/DX = 0.0001 !
! R6 R(3,8) 1.0965 -DE/DX = 0.0002 !
! R7 R(3,12) 1.5139 -DE/DX = 0.0001 !
! R8 R(4,5) 1.399 -DE/DX = 0.0 !
! R9 R(4,10) 1.0965 -DE/DX = 0.0002 !
! R10 R(4,12) 1.5138 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0968 -DE/DX = 0.0001 !
! R12 R(9,12) 1.2188 -DE/DX = -0.0001 !
! A1 A(2,1,5) 120.4786 -DE/DX = -0.0002 !
! A2 A(2,1,6) 119.7577 -DE/DX = 0.0001 !
! A3 A(5,1,6) 119.7637 -DE/DX = 0.0001 !
! A4 A(1,2,3) 122.162 -DE/DX = 0.0 !
! A5 A(1,2,7) 117.5047 -DE/DX = -0.0001 !
! A6 A(3,2,7) 120.3334 -DE/DX = 0.0001 !
! A7 A(2,3,8) 116.0906 -DE/DX = -0.0002 !
! A8 A(2,3,12) 120.0008 -DE/DX = 0.0002 !
! A9 A(8,3,12) 123.9087 -DE/DX = 0.0 !
! A10 A(5,4,10) 116.0795 -DE/DX = -0.0002 !
! A11 A(5,4,12) 119.9982 -DE/DX = 0.0002 !
! A12 A(10,4,12) 123.9223 -DE/DX = 0.0 !
! A13 A(1,5,4) 122.1622 -DE/DX = 0.0 !
! A14 A(1,5,11) 117.4953 -DE/DX = -0.0001 !
! A15 A(4,5,11) 120.3425 -DE/DX = 0.0001 !
! A16 A(3,12,4) 115.1982 -DE/DX = -0.0002 !
! A17 A(3,12,9) 122.4036 -DE/DX = 0.0001 !
! A18 A(4,12,9) 122.3982 -DE/DX = 0.0001 !
! D1 D(5,1,2,3) 0.0012 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 179.9996 -DE/DX = 0.0 !
! D3 D(6,1,2,3) 180.0012 -DE/DX = 0.0 !
! D4 D(6,1,2,7) -0.0004 -DE/DX = 0.0 !
! D5 D(2,1,5,4) -0.0002 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -180.0006 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 179.9998 -DE/DX = 0.0 !
! D8 D(6,1,5,11) -0.0006 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0013 -DE/DX = 0.0 !
! D10 D(1,2,3,12) -0.0012 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0003 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9995 -DE/DX = 0.0 !
! D13 D(2,3,12,4) 0.0003 -DE/DX = 0.0 !
! D14 D(2,3,12,9) 180.0005 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 180.0004 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0006 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) 0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0006 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0003 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 180.0004 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9999 -DE/DX = 0.0 !
! D24 D(10,4,12,9) -0.0001 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:BC5H6 FREQ AVC.png|thumb|left|Figure 41: Gaussview image of optimised boratabenzene molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23252. A Gaussview image of the molecule is shown in Figure 41. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 16 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 16</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Boratabenzene Frequency
|-
! colspan="3" style="text-align: center;"|BC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || -1
|-
| Spin || Singlet
|-
| Total energy || -219.02052430 a.u.
|-
| RMS Gradient Norm || 0.00019093 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 8.1137 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.2 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000448 0.000450 YES
RMS Force 0.000191 0.000300 YES
Maximum Displacement 0.002063 0.001800 NO
RMS Displacement 0.000710 0.001200 YES
Predicted change in Energy=-1.290820D-06
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -17.4214 -3.4426 -0.0008 -0.0005 0.0002 10.4928
Low frequencies --- 370.7426 404.4178 565.0823

</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised boratabenzene molecule. The output log file is linked [[Media:BC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23265.

==== NBO analysis ====
[[File:BC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged boratabenzene molecule.]]
[[File:BC5H6 NBO number AVC.png‎‎‎|thumb|right|Figure 21: Gaussview image of charged boratabenzene molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of boratabenzene. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of boratabenzene is -0.588 to +0.588.

 
 
 
 

 

=== Pyridinium ===

==== Optimisation - low level basis set ====
[[File:NC5H3 321G AVC.png|thumb|left|Figure 40: Gaussview image of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G totalenergy AVC.png|thumb|left|Figure 41: Total energy of optimised pyridinium molecule (3-21G).]]
[[File:NC5H3 321G rmsgradient AVC.png|thumb|left|Figure 42: Gradient of optimised pyridinium molecule (3-21G).]]

A molecule of pyridinium was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:NC5H6 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23245. A Gaussview image of the optimised molecule is shown in Figure 40. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 17 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 321G AVC.mol</uploadedFileContents>
<text>Molecule 17</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -247.29354287 a.u.
|-
| RMS Gradient Norm || 0.00019627 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.7154 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 2.7 seconds</table>
|}
The total energy curve (Figure 41) shows the program moving along the potential energy surface (PES) of the pyridinium molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 42) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000409 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.001776 0.001800 YES
RMS Displacement 0.000676 0.001200 YES
Predicted change in Energy=-1.671961D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.4004 -DE/DX = 0.0 !
! R2 R(1,5) 1.4002 -DE/DX = 0.0 !
! R3 R(1,6) 1.0828 -DE/DX = 0.0001 !
! R4 R(2,3) 1.3844 -DE/DX = -0.0004 !
! R5 R(2,7) 1.0812 -DE/DX = -0.0001 !
! R6 R(3,8) 1.0808 -DE/DX = 0.0 !
! R7 R(3,12) 1.3602 -DE/DX = 0.0001 !
! R8 R(4,5) 1.3845 -DE/DX = -0.0004 !
! R9 R(4,10) 1.0808 -DE/DX = 0.0 !
! R10 R(4,12) 1.3601 -DE/DX = 0.0002 !
! R11 R(5,11) 1.0812 -DE/DX = -0.0001 !
! R12 R(9,12) 1.0232 -DE/DX = 0.0003 !
! A1 A(2,1,5) 119.8465 -DE/DX = 0.0003 !
! A2 A(2,1,6) 120.077 -DE/DX = -0.0001 !
! A3 A(5,1,6) 120.0765 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.2863 -DE/DX = -0.0001 !
! A5 A(1,2,7) 121.3043 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4094 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.0766 -DE/DX = 0.0002 !
! A8 A(2,3,12) 119.5212 -DE/DX = -0.0002 !
! A9 A(8,3,12) 117.4022 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.0644 -DE/DX = 0.0002 !
! A11 A(5,4,12) 119.5191 -DE/DX = -0.0002 !
! A12 A(10,4,12) 117.4165 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.2896 -DE/DX = -0.0001 !
! A14 A(1,5,11) 121.3065 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.4039 -DE/DX = 0.0001 !
! A16 A(3,12,4) 122.5373 -DE/DX = 0.0003 !
! A17 A(3,12,9) 118.7255 -DE/DX = -0.0001 !
! A18 A(4,12,9) 118.7371 -DE/DX = -0.0001 !
! D1 D(5,1,2,3) -0.001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) -179.9987 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0018 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0006 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0004 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9983 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0012 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0024 -DE/DX = 0.0 !
! D9 D(1,2,3,8) 180.0018 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0013 -DE/DX = 0.0 !
! D11 D(7,2,3,8) -0.0005 -DE/DX = 0.0 !
! D12 D(7,2,3,12) 179.999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0011 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) -180.0016 -DE/DX = 0.0 !
! D16 D(8,3,12,9) -0.0004 -DE/DX = 0.0 !
! D17 D(10,4,5,1) -180.0014 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0027 -DE/DX = 0.0 !
! D19 D(12,4,5,1) -0.0002 -DE/DX = 0.0 !
! D20 D(12,4,5,11) -180.0014 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0006 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9993 -DE/DX = 0.0 !
! D23 D(10,4,12,3) 180.0017 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Optimisation - high level basis set ====
[[File:NC5H6 631G AVC.png|thumb|left|Figure 43: Gaussview image of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G totalenergy AVC.png‎‎‎|thumb|left|Figure 44: Total energy of optimised pyridinium molecule (6-31G(d,p)).]]
[[File:NC5H6 631G rmsgradient AVC.png|thumb|left|Figure 45: Gradient of optimised pyridinium molecule (6-31G(d,p)).]]

Following the successful optimisation of the pyridinium molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:NC5H6 631G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23248. A Gaussview image of the optimised molecule is shown in Figure 43. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 18 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 631G AVC.mol</uploadedFileContents>
<text>Molecule 18</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised pyridinium molecule are shown in Figures 44 and 45, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Pyridinium Optimisation
|-
! colspan="3" style="text-align: center;"|NC5H6_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004950 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 3 minutes 0.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000861 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.449365D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3988 -DE/DX = 0.0 !
! R2 R(1,5) 1.3988 -DE/DX = 0.0 !
! R3 R(1,6) 1.0852 -DE/DX = 0.0 !
! R4 R(2,3) 1.3838 -DE/DX = 0.0 !
! R5 R(2,7) 1.0836 -DE/DX = 0.0 !
! R6 R(3,8) 1.0833 -DE/DX = 0.0 !
! R7 R(3,12) 1.3524 -DE/DX = 0.0 !
! R8 R(4,5) 1.3838 -DE/DX = 0.0 !
! R9 R(4,10) 1.0833 -DE/DX = 0.0 !
! R10 R(4,12) 1.3523 -DE/DX = 0.0001 !
! R11 R(5,11) 1.0836 -DE/DX = 0.0 !
! R12 R(9,12) 1.0168 -DE/DX = 0.0001 !
! A1 A(2,1,5) 120.0319 -DE/DX = 0.0001 !
! A2 A(2,1,6) 119.9843 -DE/DX = -0.0001 !
! A3 A(5,1,6) 119.9838 -DE/DX = -0.0001 !
! A4 A(1,2,3) 119.0948 -DE/DX = 0.0 !
! A5 A(1,2,7) 121.4866 -DE/DX = 0.0 !
! A6 A(3,2,7) 119.4186 -DE/DX = 0.0001 !
! A7 A(2,3,8) 123.9168 -DE/DX = 0.0001 !
! A8 A(2,3,12) 119.2467 -DE/DX = 0.0 !
! A9 A(8,3,12) 116.8365 -DE/DX = 0.0 !
! A10 A(5,4,10) 123.9125 -DE/DX = 0.0001 !
! A11 A(5,4,12) 119.2486 -DE/DX = 0.0 !
! A12 A(10,4,12) 116.8389 -DE/DX = 0.0 !
! A13 A(1,5,4) 119.0923 -DE/DX = 0.0 !
! A14 A(1,5,11) 121.4897 -DE/DX = 0.0 !
! A15 A(4,5,11) 119.418 -DE/DX = 0.0001 !
! A16 A(3,12,4) 123.2857 -DE/DX = 0.0 !
! A17 A(3,12,9) 118.3566 -DE/DX = 0.0 !
! A18 A(4,12,9) 118.3577 -DE/DX = 0.0 !
! D1 D(5,1,2,3) -0.0001 -DE/DX = 0.0 !
! D2 D(5,1,2,7) 180.0 -DE/DX = 0.0 !
! D3 D(6,1,2,3) -180.0001 -DE/DX = 0.0 !
! D4 D(6,1,2,7) 0.0 -DE/DX = 0.0 !
! D5 D(2,1,5,4) 0.0 -DE/DX = 0.0 !
! D6 D(2,1,5,11) -179.9999 -DE/DX = 0.0 !
! D7 D(6,1,5,4) 180.0 -DE/DX = 0.0 !
! D8 D(6,1,5,11) 0.0001 -DE/DX = 0.0 !
! D9 D(1,2,3,8) -180.0 -DE/DX = 0.0 !
! D10 D(1,2,3,12) 0.0001 -DE/DX = 0.0 !
! D11 D(7,2,3,8) 0.0 -DE/DX = 0.0 !
! D12 D(7,2,3,12) -179.9999 -DE/DX = 0.0 !
! D13 D(2,3,12,4) -0.0002 -DE/DX = 0.0 !
! D14 D(2,3,12,9) -179.9999 -DE/DX = 0.0 !
! D15 D(8,3,12,4) 179.9999 -DE/DX = 0.0 !
! D16 D(8,3,12,9) 0.0002 -DE/DX = 0.0 !
! D17 D(10,4,5,1) 179.9998 -DE/DX = 0.0 !
! D18 D(10,4,5,11) -0.0002 -DE/DX = 0.0 !
! D19 D(12,4,5,1) 0.0 -DE/DX = 0.0 !
! D20 D(12,4,5,11) 179.9999 -DE/DX = 0.0 !
! D21 D(5,4,12,3) 0.0001 -DE/DX = 0.0 !
! D22 D(5,4,12,9) 179.9999 -DE/DX = 0.0 !
! D23 D(10,4,12,3) -179.9997 -DE/DX = 0.0 !
! D24 D(10,4,12,9) 0.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Frequency analysis ====
[[File:NC5H6 FREQ AVC.png|thumb|left|Figure 46: Gaussview image of optimised pyridinium molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:NC5H6 FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23249. A Gaussview image of the molecule is shown in Figure 46. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 19 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>NC5H6 FREQ AVC.mol</uploadedFileContents>
<text>Molecule 19</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Pyridinium Frequency
|-
! colspan="3" style="text-align: center;"|NC5H6_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 1
|-
| Spin || Singlet
|-
| Total energy || -248.66806594 a.u.
|-
| RMS Gradient Norm || 0.00004948 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 9.6404 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 4 minutes 37.1 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000973 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-1.515341D-07
Optimization completed.
-- Stationary point found.
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -6.3814 -0.0003 0.0003 0.0005 11.1870 13.9458
Low frequencies --- 391.5402 404.4359 620.4576
</pre>

==== Population analysis ====

MO analysis was carried out on the fully optimised pyridinium molecule. The output log file is linked [[Media:NC5H6 POP AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23266.

==== NBO analysis ====
[[File:NC5H6 NBO colour AVC.png‎‎‎|thumb|left|Figure 20: Gaussview image of charged pyridinium molecule.]]
[[File:NC5H6 NBO number AVC.png|thumb|right|Figure 21: Gaussview image of charged pyridinium molecule.]]

Natural Bond Orbital Analysis was carried out on a molecule of pyridinium. Figure 20 shows a Gaussview image of the charged molecule. Bright red represents a highly negative charge and bright green indicates a highly positive charge. The charge range for the NBO of pyridinium is -0.483 to +0.483.

 
 
 
 

 

 
=== Borazine ===

==== Optimisation - low level basis set ====
[[File:BORAZINE 321G AVC.png|thumb|left|Figure 47: Gaussview image of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G totalenergy AVC.png|thumb|left|Figure 48: Total energy of optimised borazine molecule (3-21G).]]
[[File:BORAZINE 321G rmsgradient AVC.png|thumb|left|Figure 49: Gradient of optimised borazine molecule (3-21G).]]

A molecule of borazine was created and optimised in Gaussview. Since it is a fairly large molecule, a low level basis set (3-21G) was initially used to ensure the structure was roughly correct. The output log file of this optimisation is linked to [[Media:BORAZINE 321G AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23242. A Gaussview image of the optimised molecule is shown in Figure 47. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 20 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 321G AVC.mol</uploadedFileContents>
<text>Molecule 20</text>
</jmolAppletButton>
</jmol>

The summary table below shows the important information about the calculation:

{|<table align="center">align=”center” class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_321G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 3-21G
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -241.35696458 a.u.
|-
| RMS Gradient Norm || 0.00005974 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0001 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 1 minutes 32.2 seconds</table>
|}
The total energy curve (Figure 48) shows the program moving along the potential energy surface (PES) of the borazine molecule and finding the minimum energy structure.

The RMS (root mean square) gradient curve (Figure 49) shows that the gradient goes to zero as the minimum is approached.

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 
 

 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-7.625951D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.019 -DE/DX = 0.0 !
! R2 R(2,8) 1.1943 -DE/DX = 0.0001 !
! R3 R(3,11) 1.019 -DE/DX = 0.0 !
! R4 R(4,7) 1.1943 -DE/DX = 0.0001 !
! R5 R(5,12) 1.019 -DE/DX = 0.0 !
! R6 R(6,9) 1.1943 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4456 -DE/DX = -0.0001 !
! R8 R(7,12) 1.4456 -DE/DX = 0.0 !
! R9 R(8,10) 1.4456 -DE/DX = -0.0001 !
! R10 R(8,11) 1.4455 -DE/DX = 0.0 !
! R11 R(9,10) 1.4455 -DE/DX = 0.0 !
! R12 R(9,12) 1.4456 -DE/DX = -0.0001 !
! A1 A(4,7,11) 121.5043 -DE/DX = 0.0 !
! A2 A(4,7,12) 121.5069 -DE/DX = 0.0 !
! A3 A(11,7,12) 116.9888 -DE/DX = 0.0 !
! A4 A(2,8,10) 121.5015 -DE/DX = 0.0 !
! A5 A(2,8,11) 121.5095 -DE/DX = 0.0 !
! A6 A(10,8,11) 116.989 -DE/DX = 0.0 !
! A7 A(6,9,10) 121.5094 -DE/DX = 0.0 !
! A8 A(6,9,12) 121.5046 -DE/DX = 0.0 !
! A9 A(10,9,12) 116.986 -DE/DX = 0.0 !
! A10 A(1,10,8) 118.4985 -DE/DX = 0.0 !
! A11 A(1,10,9) 118.4888 -DE/DX = 0.0 !
! A12 A(8,10,9) 123.0127 -DE/DX = 0.0 !
! A13 A(3,11,7) 118.493 -DE/DX = 0.0 !
! A14 A(3,11,8) 118.4965 -DE/DX = 0.0 !
! A15 A(7,11,8) 123.0106 -DE/DX = 0.0 !
! A16 A(5,12,7) 118.5014 -DE/DX = 0.0 !
! A17 A(5,12,9) 118.4857 -DE/DX = 0.0 !
! A18 A(7,12,9) 123.0129 -DE/DX = 0.0 !
! D1 D(4,7,11,3) 0.0001 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0003 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0004 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0003 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -179.9994 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0009 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0011 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0003 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) -0.0002 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0004 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0002 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0 -DE/DX = 0.0 !
! D17 D(6,9,10,1) 0.0004 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9992 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0009 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0014 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0009 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 179.9989 -DE/DX = 0.0 !
! D23 D(10,9,12,5) 179.9986 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0017 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

==== Optimisation - high level basis set ====
[[File:BORAZINE 631G AVC.png|thumb|left|Figure 50: Gaussview image of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G totalenergy AVC.png|thumb|left|Figure 51: Total energy of optimised borazine molecule (6-31G(d,p)).]]
[[File:BORAZINE 631G rmsgradient AVC.png|thumb|left|Figure 52: Gradient of optimised borazine molecule (6-31G(d,p)).]]

Following the successful optimisation of the borazine molecule with a low level basis set, a new optimisation was carried out on the HPC using a higher level basis set. The output log file is linked to [[Media:BORAZINE 631G AVC.log| here]] and the link to the D-space is http://dx.doi.org/10042/23243. A Gaussview image of the optimised molecule is shown in Figure 50. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 21 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE 631G AVC.mol</uploadedFileContents>
<text>Molecule 21</text>
</jmolAppletButton>
</jmol>

The total energy and gradient curves for the optimised borazine molecule are shown in Figures 51 and 52, respectively.

The summary table below shows all the important information about the calculation.

{| class="wikitable" border="1"
|+ Borazine Optimisation
|-
! colspan="3" style="text-align: center;"|BORAZINE_631G_AVC
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011477 a.u.
|-
| Imaginary Freq ||
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 2 minutes 52.1 seconds
|} 

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

 
 
 
 
 
 
 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000052 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-4.245908D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,10) 1.0098 -DE/DX = 0.0 !
! R2 R(2,8) 1.195 -DE/DX = 0.0001 !
! R3 R(3,11) 1.0098 -DE/DX = 0.0 !
! R4 R(4,7) 1.195 -DE/DX = 0.0001 !
! R5 R(5,12) 1.0098 -DE/DX = 0.0 !
! R6 R(6,9) 1.195 -DE/DX = 0.0001 !
! R7 R(7,11) 1.4306 -DE/DX = 0.0 !
! R8 R(7,12) 1.4306 -DE/DX = 0.0 !
! R9 R(8,10) 1.4306 -DE/DX = 0.0 !
! R10 R(8,11) 1.4306 -DE/DX = 0.0 !
! R11 R(9,10) 1.4306 -DE/DX = 0.0 !
! R12 R(9,12) 1.4306 -DE/DX = 0.0 !
! A1 A(4,7,11) 121.4542 -DE/DX = -0.0001 !
! A2 A(4,7,12) 121.4549 -DE/DX = -0.0001 !
! A3 A(11,7,12) 117.0909 -DE/DX = 0.0001 !
! A4 A(2,8,10) 121.4534 -DE/DX = -0.0001 !
! A5 A(2,8,11) 121.4557 -DE/DX = -0.0001 !
! A6 A(10,8,11) 117.0909 -DE/DX = 0.0001 !
! A7 A(6,9,10) 121.456 -DE/DX = -0.0001 !
! A8 A(6,9,12) 121.4546 -DE/DX = -0.0001 !
! A9 A(10,9,12) 117.0895 -DE/DX = 0.0001 !
! A10 A(1,10,8) 118.5469 -DE/DX = 0.0001 !
! A11 A(1,10,9) 118.5434 -DE/DX = 0.0001 !
! A12 A(8,10,9) 122.9097 -DE/DX = -0.0001 !
! A13 A(3,11,7) 118.5448 -DE/DX = 0.0001 !
! A14 A(3,11,8) 118.5459 -DE/DX = 0.0001 !
! A15 A(7,11,8) 122.9092 -DE/DX = -0.0001 !
! A16 A(5,12,7) 118.5479 -DE/DX = 0.0001 !
! A17 A(5,12,9) 118.5423 -DE/DX = 0.0001 !
! A18 A(7,12,9) 122.9098 -DE/DX = -0.0001 !
! D1 D(4,7,11,3) 0.0003 -DE/DX = 0.0 !
! D2 D(4,7,11,8) 180.0002 -DE/DX = 0.0 !
! D3 D(12,7,11,3) -180.0003 -DE/DX = 0.0 !
! D4 D(12,7,11,8) -0.0003 -DE/DX = 0.0 !
! D5 D(4,7,12,5) 0.0001 -DE/DX = 0.0 !
! D6 D(4,7,12,9) -180.0002 -DE/DX = 0.0 !
! D7 D(11,7,12,5) 180.0006 -DE/DX = 0.0 !
! D8 D(11,7,12,9) 0.0004 -DE/DX = 0.0 !
! D9 D(2,8,10,1) 0.0004 -DE/DX = 0.0 !
! D10 D(2,8,10,9) 179.9998 -DE/DX = 0.0 !
! D11 D(11,8,10,1) -180.0001 -DE/DX = 0.0 !
! D12 D(11,8,10,9) -0.0006 -DE/DX = 0.0 !
! D13 D(2,8,11,3) 0.0 -DE/DX = 0.0 !
! D14 D(2,8,11,7) -180.0 -DE/DX = 0.0 !
! D15 D(10,8,11,3) 180.0004 -DE/DX = 0.0 !
! D16 D(10,8,11,7) 0.0005 -DE/DX = 0.0 !
! D17 D(6,9,10,1) -0.0005 -DE/DX = 0.0 !
! D18 D(6,9,10,8) -179.9999 -DE/DX = 0.0 !
! D19 D(12,9,10,1) 180.0001 -DE/DX = 0.0 !
! D20 D(12,9,10,8) 0.0007 -DE/DX = 0.0 !
! D21 D(6,9,12,5) -0.0002 -DE/DX = 0.0 !
! D22 D(6,9,12,7) 180.0 -DE/DX = 0.0 !
! D23 D(10,9,12,5) -180.0008 -DE/DX = 0.0 !
! D24 D(10,9,12,7) -0.0005 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

==== Frequency analysis ====
[[File:BORAZINE FREQ AVC.png|thumb|left|Figure 53: Gaussview image of optimised borazine molecule.]]

Frequency analysis was carried out on the fully optimised (6-31G(d,p)) structure to confirm the minimum energy structures. The output log file is linked to [[Media:BORAZINE FREQ AVC.log| here]] and the link to the D-space file is http://dx.doi.org/10042/23244. A Gaussview image of the molecule is shown in Figure 53. 

The optimised molecule was reproduced as a Java file and can be opened by clicking on the Molecule 22 button: <jmol>
<jmolAppletButton>
<uploadedFileContents>BORAZINE FREQ AVC.mol</uploadedFileContents>
<text>Molecule 22</text>
</jmolAppletButton>
</jmol>

The summary table below shows all the important information about the calculation. As you can see, the total energy is the same as that recorded for the optimisation.

{| class="wikitable" border="1"
|+ Borazine Frequency
|-
! colspan="3" style="text-align: center;"|BORAZINE_FREQ_AVC
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Total energy || -242.68459787 a.u.
|-
| RMS Gradient Norm || 0.00011475 a.u.
|-
| Imaginary Freq || 0
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group|| C1
|-
| Calculation Time|| 5 minutes 31.5 seconds
|}

The information below, extracted from the output log file, shows that the job has converged and the optimisation was successful. 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000282 0.000450 YES
RMS Force 0.000115 0.000300 YES
Maximum Displacement 0.000590 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
Predicted change in Energy=-4.266156D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

The output log file also shows the important frequencies of the calculation (see below).

<pre>
Low frequencies --- -9.5775 -0.0008 -0.0005 0.0002 3.6840 11.3544
Low frequencies --- 288.6082 290.5790 404.6112
</pre>

==== Population analysis ====

==== NBO analysis ====

=== Analysis of charge distribution ===

The table below summarises the charge distributions of benzene, boratabenzene and pyridinium.

{| class="wikitable" border="1"
|+ Charge distributions
! Benzene !! Boratazene !! Pyridinium
|-
| [[File:BENZENE NBO colour AVC.png‎‎‎|200px|]] || [[File:BC5H6 NBO colour AVC.png‎‎‎|200px|]] || [[File:NC5H6 NBO colour AVC.png|200px|]]
|-
| [[File:BENZENE NBO number AVC.png|200px|]] || [[File:BC5H6 NBO number AVC.png|200px|]] || [[File:NC5H6 NBO number AVC.png|200px|]]
|}

In the benzene molecule, the delocalised electrons are evenly spread around the six carbon atoms. The distribution of negative charge around the ring results in all six carbon atoms being equally electronegative, with a charge value of -0.239. The six electropositive hydrogen atoms donate electron density into the carbon ring, with an equal charge distribution of opposite charge (+0.239).

In the boratabenzene molecule, the boron atom is electropositive with a charge of +0.202. In order to counteract this positive charge, the five carbon atoms in the ring all vary in their degree of electronegativity. The two neighbouring carbon atoms have a large negative charge of -0.588 and appear bright red in the Gaussview image, whereas the remaining three carbon atoms are less electronegative. Furthermore, the hydrogen atom bonded to the boron appears to have a very small negative charge, which is influenced by the electropositivity of the boron as well as the -1 charge of the system. The other five hydrogen atoms are all positively charged, with various values depending on the carbon ring to which they are attached.

The pyridinium molecule is, in some ways, opposite to the boratabenzene molecule. The nitrogen atom is electronegative as expected, with a charge of -0.476. In order to compensate for this highly negative charge, the five carbon atoms in the ring vary greatly in their charge. The two neighbouring carbon atoms are slightly electropositive with a value of +0.071, whereas the other three carbons are electronegative due to delocalisation of charge around the system. Unlike the boratabenzene molecule, all six hydrogen atoms in pyridinium are positively charged. The hydrogen attached to the nitrogen atom is most electropositive, with a charge equal and opposite to the nitrogen, as denoted by the bright green colour. The other five hydrogen atoms are less electropositive with values between +0.285 and +0.297, and they all appear to be the same shade of green.