View source for Rep:Mod:DJW300

= Compulsory Section =
== Introduction ==
Inorganic computational module David Wilson

== Structure Optimisations ==
=== Calculations performed ===

Two Calculations were performed to optimise the BH<sub>3</sub> geometry, both identical but the second was carried out using the output of the first with a finer basis set (6-31G(d,p) instead of 3-21G). This allowed a more accurate optimisation of the structure.

Two more Calculations were carried out on similar structures, one where the ligands were changed from H to Br atoms and then another where the central atom was also changed, from B to Ga. The GaBr<sub>3</sub> was carried out using pseudo potentials and the LANL2DZ basis set whereas the BBr<sub>3</sub> calculation was done using different basis sets for each atom.

All calculations carried out converged.


{| class="wikitable" border="1"
|+ Calculation Summaries
! Calculation !! BH<sub>3</sub> (1) !! BH<sub>3</sub> (2) !! GaBr<sub>3</sub> !! BBr<sub>3</sub>
|-
! File type
|.log ||.log||.log ||.log
|-
! Calculation Type
| FOPT||FOPT||FOPT||FOPT
|-
! Calculation Method
| RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
! Basis Set
| 3-21G||6-31G(d,p)||LANL2DZ||Gen
|-
! Final Energy (au)
| -26.46226429||-26.61532358||-41.70082783||-64.43645388
|-
! Gradient (au)
| 0.00008851||0.00008206||0.00000016||0.00000943
|-
! Dipole Moment (debye)
| 0.0003||0.0003||0.0000||0.0005
|-
! Point Group
| CS||CS||D3H||CS
|-
! Calculation Time
| 19.0 seconds||16.0 seconds||14.0 seconds||20.7 seconds
|-
! D-Space Link
| 1|| 2 || [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26932 GaBr3 D-Space]||[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26933 BBr3 D-Space]
|}

=== Item Tables ===

==== BH<sub>3</sub> Calculation (1) ====
<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000220     0.000450     YES
 RMS     Force            0.000106     0.000300     YES
 Maximum Displacement     0.000940     0.001800     YES
 RMS     Displacement     0.000447     0.001200     YES
 Predicted change in Energy=-1.672478D-07
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1948         -DE/DX =   -0.0002              !
 ! R2    R(1,3)                  1.1947         -DE/DX =   -0.0002              !
 ! R3    R(1,4)                  1.1944         -DE/DX =   -0.0001              !
 ! A1    A(2,1,3)              120.0157         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              119.986          -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              119.9983         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>

==== BH<sub>3</sub> Calculation (2) ====
<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000204     0.000450     YES
 RMS     Force            0.000099     0.000300     YES
 Maximum Displacement     0.000875     0.001800     YES
 RMS     Displacement     0.000418     0.001200     YES
 Predicted change in Energy=-1.452109D-07
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1928         -DE/DX =   -0.0002              !
 ! R2    R(1,3)                  1.1926         -DE/DX =   -0.0002              !
 ! R3    R(1,4)                  1.1924         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              120.0146         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              119.9866         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              119.9988         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>

==== GaBr<sub>3</sub> Calculation ====
<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000003     0.001800     YES
 RMS     Displacement     0.000002     0.001200     YES
 Predicted change in Energy=-1.282680D-12
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  2.3502         -DE/DX =    0.0                 !
 ! R2    R(1,3)                  2.3502         -DE/DX =    0.0                 !
 ! R3    R(1,4)                  2.3502         -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                 !
 --------------------------------------------------------------------------------
</pre>

==== BBr<sub>3</sub> Calculation ====
<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000016     0.000450     YES
 RMS     Force            0.000010     0.000300     YES
 Maximum Displacement     0.000067     0.001800     YES
 RMS     Displacement     0.000040     0.001200     YES
 Predicted change in Energy=-1.574159D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.934          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.934          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.9339         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              119.9971         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0011         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0018         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>

== Molecule Comparisons ==
=== Bond Distances ===

The optimised bond distances of the three molecules are shown below. With regards to the bond angles, they stayed around 120 degrees throughout. The following observations were made:

==== Changing ligands ====

Changing the ligand from H to Br in the molecule increased the length of the B - ligand bond. The average length increased from 1.19 to 1.93 Angstroms. This may be due to the Br being larger, so there is less overlap between the bonding AOs, and more electronegative, so the bond is more polar. Changing the ligands to Br makes the bond more negative on the ligand and more positive on the central atom. The bond angles were slightly closer to 120 degrees with the Br ligands. This suggests that due to the larger atoms the repulsion is larger and so the structure adapts so that there is maximal separation between ligands.

==== Changing central atom ====

Changing the central atom from Ga to Br in the molecule increased the length of the Center - ligand bond. The average length increased from 1.93 to 2.35 Angstroms. This is because Ga is larger than B, so there is poorer bonding AO overlap, and it is less electronegative than B, making the bond more polar. The bond angles were fixed at 120 degrees for GaBr<sub>3</sub> so cannot be analysed.

{| class="wikitable" border="1"
|+ Optimised bond distances and angles
! Molecule !! BH3 !! GaBr<sub>3</sub> !! BBr<sub>3</sub>
|-
! Bond Distance 1 (Å)
|1.19243||2.35018||1.934
|-
! Bond Distance 2 (Å)
|1.19276||2.35018||1.93398
|-
! Bond Distance 3 (Å) 
|1.19264||2.35018||1.93391
|-
! Bond Angle 1 (•) 
| 119.987||120||119.997
|-
! Bond Angle 2 (•) 
|120.015||120||120.002
|-
! Bond Angle 3 (•) 
|119.999||120||120.001
|}

==== Bonding in Gaussian ====

The bonding in Gaussview is based on the internuclear distances. If the nuclear distances are too long a bond will not be drawn even though the atoms could be described as sharing a 'bonding' interaction.

The IUPAC Gold Book<ref>IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
[http://dx.doi.org/10.1351/goldbook.B00697 "IUPAC Gold Book - Bond"].</ref> definition of a bond is: <blockquote>There is a chemical bond between two atoms or groups of atoms in the case that the forces acting between them are such as to lead to the formation of an aggregate with sufficient stability to make it convenient for the chemist to consider it as an independent 'molecular species'.</blockquote>

This doesn't necessarily mean that bonding can be determined based on intermolecular distance alone. If there is significant electron density between the two atoms there may be a bond even if there is a long distance.

== Frequency Analysis ==

=== Introduction to Frequency Analysis ===

Frequency analysis is carried out to analyse the vibrational characteristics of a molecule. This can be compared with an experimental IR spectrum to see whther a synthesised compound is matches the predicted structure. It also can be used to confirm that an optimisation has achieved a minimum energy rather than a transition state (transition states will give 1 negative vibrational frequency).

The same method and basis set must be used for both the optimisation and the frequency analysis calculations because the frequency calculations rely on the energy minimum being reached. If the optimisation was carried out using a different method or basis set then the structure may no longer be a minimum and so the calculated vibrations would be wrong.

The "Low frequencies" represent the frequencies associated with the motion of the centre of mass of the molecule and are much smaller than the other vibrations.

=== Calculations performed ===

The structures obtained from the optimisations were used to find the vibrational frequencies of the atoms.

{| class="wikitable" border="1"
|+ Calculation Summaries
! Calculation !! BH<sub>3</sub> !! GaBr<sub>3</sub>
|-
! File type
|.log ||.log
|-
! Calculation Type
| FREQ||FREQ
|-
! Calculation Method
| RB3LYP||RB3LYP
|-
! Basis Set
| 6-31G(d,p)||LANL2DZ
|-
! Final Energy (au)
| -26.61532364||-41.70082783
|-
! Gradient (au)
| 0.00000001||0.00000011
|-
! Dipole Moment (debye)
| 0.0000||0.0000
|-
! Point Group
| D3H||D3H
|-
! Calculation Time
| 9.0 seconds||19.8 seconds
|-
! D-Space Link
| 1|| [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26946 GaBr3 D-Space]
|}

=== Calculation Output ===
A frequency analysis was carried out on the optimised structure of BH<sub>3</sub>. This was done at a finer level than before in order to obtain accurate frequencies. Since all the frquencies are positive an energy minimum has been reached.

==== BH<sub>3</sub> ====
<pre>Low frequencies ---   -9.3741   -9.3588   -0.0753    0.0007    0.5350    2.4499
Low frequencies --- 1162.9902 1213.1495 1213.1497</pre>

==== GaBr<sub>3</sub> ====
<pre>Low frequencies ---   -0.5252   -0.5247   -0.0024   -0.0010    0.0235    1.2010
Low frequencies ---   76.3744   76.3753   99.6982</pre>

=== Vibrational Modes ===

{| class="wikitable" border="1"
|+ BH<sub>3</sub> Vibrational Modes Summary
! No. !! Form of the vibration !! Frequency (cm<sup>-1</sup>) !! Intensity !! Symmetry D<sub>3h</sub>
point group
|-
! 1
|[[File:DW BH3 Mode 1.PNG|thumb|Bending of all three B-H bonds perpendicular to the plane of the molecule, all in phase]]||1163||92.5666||A<sub>2</sub>"  
|-
! 2
|[[File:DW BH3 Mode 2.PNG|thumb|A combined scissoring and wagging in the plane of the molecule]]||1213||14.0557||E' 
|-
! 3
|[[File:DW BH3 Mode 3.PNG|thumb|Scissoring of two B-H bonds in the plane of the molecule]]||1213||14.0552||E' 
|-
! 4
|[[File:DW BH3 Mode 4.PNG|thumb|Bond stretching of all three B-H bonds, all in phase with each other]]||2583||0.0000||A<sub>1</sub>' 
|-
! 5
|[[File:DW BH3 Mode 5.PNG|thumb|Bond Stretching of two B-H bonds in opposite phases]]||2716||126.3339||E' 
|-
! 6
|[[File:DW BH3 Mode 6.PNG|thumb|Bond stretching of all three B-H bonds with two of the bond stretches in phase and one in opposite phase]]||2716||126.3279||E' 

|}

{| class="wikitable" border="1"
|+ GaBr<sub>3</sub> Vibrational Modes Summary
! No. !! Form of the vibration !! Frequency (cm<sup>-1</sup>) !! Intensity !! Symmetry D<sub>3h</sub>
point group
|-
! 1
|[[File:DW GaBr3 Mode 1.PNG|thumb|A combined scissoring and wagging in the plane of the molecule]]||76||3.3447||E' 
|-
! 2
|[[File:DW GaBr3 Mode 2.PNG|thumb|Scissoring of two Ga-Br bonds in the plane of the molecule]]||76||3.3447||E' 
|-
! 3
|[[File:DW GaBr3 Mode 3.PNG|thumb|Bending of all three Ga-Br bonds perpendicular to the plane of the molecule, all in phase]]||100||9.2161||A<sub>2</sub>" 
|-
! 4
|[[File:DW GaBr3 Mode 4.PNG|thumb|Bond stretching of all three Ga-Br bonds, all in phase with each other]]||197||0.0000||A<sub>1</sub>' 
|-
! 5
|[[File:DW GaBr3 Mode 5.PNG|thumb|Bond Stretching of two Ga-Br bonds in opposite phases]]||316||57.0704||E' 
|-
! 6
|[[File:DW GaBr3 Mode 6.PNG|thumb|Bond stretching of all three Ga-Br bonds with two of the bond stretches in phase and one in opposite phase]]||316||57.0746||E' 

|}

==== Vibrational Spectrum ====

[[File:DW BH3 IR Spectrum.PNG|thumb|Calculated IR spectrum of BH<sub>3</sub>]]
[[File:DW GaBr3 IR Spectrum.PNG|thumb|Calculated IR spectrum of GaBr<sub>3</sub>]]

The vibrational spectrum of BH<sub>3</sub> only shows 3  peaks rather than the 6 expected from 3N-6 because there are two pairs of vibrational modes with overlapping energies (at 121.cm<sup>-1</sup> and 258.cm<sup>-1</sup>), which appear as a single peak, and also the vibration at 2583cm<sup>-1</sup> has 0 intensity and so doesn't show on the spectrum. the reason that this frequency has zero intensity is that the vibration mode is completely symmetrical and so there is no associated change in dipole. Absorptions only occur when there is a change in the dipole moment associated with them.

The large difference in the value of the frequencies for BH<sub>3</sub> and GaBr<sub>3</sub> indicates that the B-H bonds and the GaBr bonds differ in strength and that the atoms themselves have different masses.

The modes are in a different order in the two spectra, with A<sub>2</sub>" higher energy than E' in the GaBr<sub>3</sub> spectrum and lower in energy than the E' in the BH<sub>3</sub> spectrum.

The spectra both show 3 peaks and the energies are of the three peaks are similarly distributed with two low energy peaks closer together and one higher energy peak. The GaBr3 peaks are lower in energy and more closely spaced.

In both spectra the A<sub>2</sub>" and the E' and the A<sub>1</sub> and the E' have quite similar energies. This is because the vibrational modes within both pairs are quite similar. In the lower energy pair (A<sub>2</sub>" and the E') the bonds don't change in length very much during the vibrations. For the other pair, the bonds vary dramatically in length throughout the vibration.

== MOs Analysis ==

The LCAOs match the real orbitals for BH<sub>3</sub> very closely. This suggests that MO theory could be quite useful to analyse the bonding in simple molecules. For larger molecules the bonding is more complex and so might not match the LCAO orbitals as closely.

[[File:DW BH3 MO Diagram.png|thumb|MO diagram derived from LCAOs for BH<sub>3</sub>, showing the corresponding calculated MOs]]

{| class="wikitable" border="1"
|+ BH<sub>3</sub> Molecular Orbitals
! MO !! Image !! Symmetry group
|-
! A
|[[File:DW BH3 MO1.PNG|thumb|Caption]]||A<sub>2</sub>"  
|-
! B
|[[File:DW BH3 MO2.PNG|thumb|Caption]]||E' 
|-
! C
|[[File:DW BH3 MO3.PNG|thumb|Caption]]||E' 
|-
! D
|[[File:DW BH3 MO4.PNG|thumb|Caption]]||A<sub>1</sub>' 
|}

=== NBOs Analysis ===

==== Calculation Summaries ====

{| class="wikitable" border="1"
|+ NH<sub>3</sub> Calculation Summaries
! Calculation !! NH<sub>3</sub> (Opt) !! NH<sub>3</sub> (Freq) !! NH<sub>3</sub> (Pop)
|-
! File type
|.log ||.log||.log
|-
! Calculation Type
| FOPT||FREQ||SP
|-
! Calculation Method
| RB3LYP||RB3LYP||RB3LYP
|-
! Basis Set
| 6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
! Final Energy (au)
| -56.55776872||-56.55776872||-56.55776856
|-
! Gradient (au)
| 0.00000010||0.00000035||0.00000016
|-
! Dipole Moment (debye)
| 1.8465||1.8465||1.8465
|-
! Point Group
| C1||C1||C1
|-
! Calculation Time
| 1 minute 10.1 seconds||34.0 seconds||32.1 seconds
|-
! D-Space Link
| [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26967 NH<sub>3</sub> (opt) D-Space]||[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26969 NH<sub>3</sub> (freq) D-Space] || [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26972 NH<sub>3</sub> (pop) D-Space]
|}

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000001     0.000006     YES
 RMS     Displacement     0.000000     0.000004     YES
 Predicted change in Energy=-1.239174D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.018          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.018          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.018          -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              105.7444         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7444         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7444         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8634         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------</pre>

<pre> Low frequencies ---   -7.6513   -5.9823   -3.2701    0.0012    0.0022    0.0022
 Low frequencies --- 1089.3490 1693.9240 1693.9288</pre>

==== Charge Distributions ====

For NH<sub>3</sub>, the charges were -1.125 on the N and +0.375 on each H atom.

[[File:DW NH3 Charge Distribution.PNG|thumb|Charge distribution on NH<sub>3</sub>]]

=== Association Energy ===

==== Calulation Summaries ====


{| class="wikitable" border="1"
|+ NH<sub>3</sub>BH<sub>3</sub> Calculation Summaries
! Calculation !! NH<sub>3</sub>BH<sub>3</sub> (Opt) !! NH<sub>3</sub>BH<sub>3</sub> (Freq) !! NH<sub>3</sub>BH<sub>3</sub> (Pop)
|-
! File type
|.log ||.log||.log
|-
! Calculation Type
| FOPT||FREQ||SP
|-
! Calculation Method
| RB3LYP||RB3LYP||RB3LYP
|-
! Basis Set
| 6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
! Final Energy (au)
| -83.22468909||-83.22468909||-83.22468949
|-
! Gradient (au)
| 0.00000001||0.00000009||0.00000000
|-
! Dipole Moment (debye)
| 5.5646||5.5646||5.5646
|-
! Point Group
| C3||C3||C3
|-
! Calculation Time
| 3 minutes 22.5 seconds||1 minute 24.4 seconds||35.9 seconds
|-
! D-Space Link
| [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26968 NH<sub>3</sub>BH<sub>3</sub> (opt) D-Space]||[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26970 NH<sub>3</sub>BH<sub>3</sub> (freq) D-Space] || [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26971 NH<sub>3</sub>BH<sub>3</sub> (pop) D-Space]
|}

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000000     0.000006     YES
 RMS     Displacement     0.000000     0.000004     YES
 Predicted change in Energy=-1.879536D-15
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,8)                  1.2098         -DE/DX =    0.0                 !
 ! R2    R(2,8)                  1.2098         -DE/DX =    0.0                 !
 ! R3    R(3,8)                  1.2098         -DE/DX =    0.0                 !
 ! R4    R(4,7)                  1.0185         -DE/DX =    0.0                 !
 ! R5    R(5,7)                  1.0185         -DE/DX =    0.0                 !
 ! R6    R(6,7)                  1.0185         -DE/DX =    0.0                 !
 ! R7    R(7,8)                  1.6677         -DE/DX =    0.0                 !
 ! A1    A(4,7,5)              107.8758         -DE/DX =    0.0                 !
 ! A2    A(4,7,6)              107.8758         -DE/DX =    0.0                 !
 ! A3    A(4,7,8)              111.0231         -DE/DX =    0.0                 !
 ! A4    A(5,7,6)              107.8758         -DE/DX =    0.0                 !
 ! A5    A(5,7,8)              111.0231         -DE/DX =    0.0                 !
 ! A6    A(6,7,8)              111.0231         -DE/DX =    0.0                 !
 ! A7    A(1,8,2)              113.8739         -DE/DX =    0.0                 !
 ! A8    A(1,8,3)              113.8739         -DE/DX =    0.0                 !
 ! A9    A(1,8,7)              104.5974         -DE/DX =    0.0                 !
 ! A10   A(2,8,3)              113.8739         -DE/DX =    0.0                 !
 ! A11   A(2,8,7)              104.5974         -DE/DX =    0.0                 !
 ! A12   A(3,8,7)              104.5974         -DE/DX =    0.0                 !
 ! D1    D(4,7,8,1)             60.0011         -DE/DX =    0.0                 !
 ! D2    D(4,7,8,2)           -179.9989         -DE/DX =    0.0                 !
 ! D3    D(4,7,8,3)            -59.9989         -DE/DX =    0.0                 !
 ! D4    D(5,7,8,1)           -179.9989         -DE/DX =    0.0                 !
 ! D5    D(5,7,8,2)            -59.9989         -DE/DX =    0.0                 !
 ! D6    D(5,7,8,3)             60.0011         -DE/DX =    0.0                 !
 ! D7    D(6,7,8,1)            -59.9989         -DE/DX =    0.0                 !
 ! D8    D(6,7,8,2)             60.0011         -DE/DX =    0.0                 !
 ! D9    D(6,7,8,3)           -179.9989         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------</pre>

<pre> Low frequencies ---   -0.1419   -0.0600   -0.0212    2.3587    2.3918    7.4922
 Low frequencies ---  263.6238  632.9757  638.5004</pre>

==== Calculation ====

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (AU)
|-
! NH<sub>3</sub>
| -56.55776872
|-
! BH<sub>3</sub>
| -26.61532364
|-
! NH<sub>3</sub>BH<sub>3</sub>
| -83.22468909
|}

ΔE = E(NH<sub>3</sub>BH<sub>3</sub>) - [E(NH<sub>3</sub>) + E(BH<sub>3</sub>)]

ΔE = -0.05159673AU = -135.5kJ/mol

Bond dissociation energy is therefore 135.5kJ/mol

This is significantly weaker than a methane C-H bond which is 439.3kJ/mol<ref>S. J. Blanksby and G. B. Ellison, Acc. Chem. Res., 2003, 36, 255–263.[http://dx.doi.org/10.1021/ar020230d "10.1021/ar020230d"]</ref> but similar in magnitude to a I-I bond at 151.0kJ/mol<ref>M. Stans, NIST, 1972 [http://www.nist.gov/data/nsrds/NSRDS-NBS31.pdf "NSRDS-NBS31"]</ref>. This might be expected due to the dative nature of the bond where the highly electronegative N atom is donating an electron pair to the lewis acid BH<sub>3</sub>.

= Investigation of Aromaticity Project =

== Introduction ==

Aromaticity is a concept that is familiar to every chemistry student to some degree but not really explained beyond 'delocalised pi electrons'. This project aims to investigate the aromatic character of four molecules and compare the computational results with common ideas about aromaticity.

The four moleclues investigated were; benzene, used as a reference for the other molecules, boratabenzene<sup>-</sup>, pyridinium<sup>+</sup> and borazine. This allowed the elucidation of the effects of changing carbon atoms in benzene to other elements.

== Calculations performed ==

For the aromaticity investigation the calculations were all done in one go on the molecules using exactly the same calulation method and basis set. The calulation carried out an optimisation of the geometry, followed by NBO analysis and frequency analysis. All the optimisation calculations successfully converged to a stationary point and not a transition state, as confirmed by the frequency analysis.

The optimised benzene geometry showed bond lengths of 1.40Å. This is very similar value to experiment at 1.39Å<ref>R. C. Bingham and M. J. S. Dewar, 1972, 859, 9107–9112.[http://dx.doi.org/10.1021/ja00781a020 "10.1021/ja00781a020"]</ref>.

{| class="wikitable" border="1"
|+ Calculation Summaries
! Calculation !! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
! File type
|.log ||.log||.log ||.log
|-
! Calculation Type
| FREQ||FREQ||FREQ||FREQ
|-
! Calculation Method
| RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
! Basis Set
| 6-31G(d,p)||6-31G(d,p)||6-31G(d,p)||6-31G(d,p)
|-
! Charge
| 0||-1||+1||0
|-
! Final Energy (au)
| -232.25820551||-219.02052985||-248.66807380||-242.68458739
|-
! Gradient (au)
| 0.00009549||0.00015728||0.00008342||0.00006610
|-
! Dipole Moment (debye)
| 0.0001||2.8465||1.8732||0.0002
|-
! Point Group
| C1||C1||C1||C1
|-
! Calculation Time
| 5 minutes 8.4 seconds||5 minutes 8.6 seconds||4 minutes 27.1 seconds||4 minutes 9.7 seconds
|-
! D-Space Link
| [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27164 Benzene D-Space]|| [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27165 Boratabenzene D-Space] || [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27167 Pyridinium D-Space]||[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27166 Borazine D-Space]
|}

=== Benzene ===

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.000212     0.000450     YES
 RMS     Force            0.000085     0.000300     YES
 Maximum Displacement     0.000991     0.001800     YES
 RMS     Displacement     0.000315     0.001200     YES
 Predicted change in Energy=-5.157444D-07
 Optimization completed.
    -- Stationary point found.
</pre>

<pre> Low frequencies ---  -17.2814  -14.5862   -9.6619    0.0004    0.0005    0.0006
 Low frequencies ---  413.7969  414.4697  620.8546
</pre>

=== Boratabenzene ===

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000159     0.000450     YES
 RMS     Force            0.000068     0.000300     YES
 Maximum Displacement     0.000803     0.001800     YES
 RMS     Displacement     0.000321     0.001200     YES
 Predicted change in Energy=-7.121479D-07
 Optimization completed.
    -- Stationary point found.
</pre>

<pre>
 Low frequencies ---  -13.1258   -0.0009   -0.0007   -0.0004   15.0651   18.1748
 Low frequencies ---  371.3454  404.2332  565.2512
</pre>

=== Pyridinium ===

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000129     0.000450     YES
 RMS     Force            0.000045     0.000300     YES
 Maximum Displacement     0.000964     0.001800     YES
 RMS     Displacement     0.000278     0.001200     YES
 Predicted change in Energy=-2.284852D-07
 Optimization completed.
    -- Stationary point found.
</pre>

<pre>
 Low frequencies ---   -1.3593   -0.0006   -0.0005    0.0003   16.6022   17.1077
 Low frequencies ---  392.3631  404.1329  620.4711
</pre>

=== Borazine ===

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000093     0.000450     YES
 RMS     Force            0.000033     0.000300     YES
 Maximum Displacement     0.000338     0.001800     YES
 RMS     Displacement     0.000096     0.001200     YES
 Predicted change in Energy=-1.027048D-07
 Optimization completed.
    -- Stationary point found.
</pre>

<pre>
 Low frequencies ---  -17.1539  -10.8007   -6.2385    0.0009    0.0010    0.0011
 Low frequencies ---  288.8470  289.6791  404.1666
</pre>

== Electronic Analysis ==

=== Charge Distributions ===

{| class="wikitable floatright" border="1"
|+ Charge Distributions
! Molecule !! Image
|-
! Benzene
|[[File:DW Benzene Charge Distribution.PNG|thumb]]
|-
! Boratabenzene
|[[File:DW Boratabenzene Charge Distribution.PNG|thumb]]
|-
! Pyridinium
|[[File:DW Pyridinium Charge Distribution.PNG|thumb]]
|-
! Borazine
|[[File:DW Borazine Charge Distribution.PNG|thumb]]
|}

In benzene the charge density is evenly spread throughout the ring with all carbons having -0.239 and the hydrogens all having +0.239. This would be expected given the symmetry of the ring.

In boratabenzene one carbon has been replaced by a more electropositive Boron atom and the total charge is -1 rather than 0. As a result there is more electron density on the hydrogen attached to the boron and less on the boron (which is actually +0.202). The other carbon atoms in the ring have more electron density than in benzene, especially the carbons α (-0.588) and γ (-0.340). The β carbons only have slightly more electron density than in benzene (-0.250)

In pyridinium one carbon has been replaced by a nitrogen atom and the total charge is +1. Since N is highly electronegative there is significant electron density on the N and less on the carbon atoms in the ring. The magnitude of the change of electron density follows the same pattern as in boratabenzene with the carbons being, in order of magnitude of change from benzene, α (0.071) > γ (-0.122) > β (-0.241). Perhaps most suprising is that the β carbon has more electron density than in benzene, even though the molecule is positively charged <i>and</i> an electronegative atom has been added into the ring.

Borazine shows a charge distribution that might be expected after analysing the three previous molecules, with the electronegative nitrogen atoms carrying the most electron density and the electropositive boron atoms carrying the least. For the hydrogen atoms the more electropositive the atom to which they were bound, the more electron density they have.

=== MOs Analysis ===

[[File:DW Benzene MO Diagram.png|thumb|left|MO diagram derived from LCAOs for Benzene, showing the corresponding calculated MOs]]

{| class="wikitable floatleft" border="1"
|+ BH<sub>3</sub> Vibrational Modes Summary Captions show energy in Hartrees and degeneracy
! Molecule !! MO 1 !! MO 2 !! MO 3
|-
! Benzene
|[[File:DW Benzene MO 1.PNG|thumb|(-0.24691, 2)]]||[[File:DW Benzene MO 2.PNG|thumb|(-0.33960, 2)]]||[[File:DW Benzene MO 3.PNG|thumb|(-0.84677, 1)]]
|-
! Boratabenzene
|[[File:DW Boratabenzene MO 1.PNG|thumb|(-0.01094, 1)]]||[[File:DW Boratabenzene MO 2.PNG|thumb|(-0.09172, 1)]]||[[File:DW Boratabenzene MO 3.PNG|thumb|(-0.60434, 1)]]
|-
! Pyridinium
|[[File:DW Pyridinium MO 1.PNG|thumb|(-0.50850, 1)]]||[[File:DW Pyridinium MO 2.PNG|thumb|(-0.57434, 1)]]||[[File:DW Pyridinium MO 3.PNG|thumb|(-1.21406, 1)]]
|-
! Borazine
|[[File:DW Borazine MO 1.PNG|thumb|(-0.27591, 2)]]||[[File:DW Borazine MO 2.PNG|thumb|(-0.31993, 2)]]||[[File:DW Borazine MO 3.PNG|thumb|(-0.88852, 1)]]
|}

The common conception of aromaticity is that it is just the pi electrons that are delocalised around the ring and the 3 highest occupied orbitals and 3 lowest unoccupied orbitals are all just made up of pi orbitals. As these calculations show, there are two occupied orbitals of higher energy than the lowest energy purely pi orbital that is made up of sigma bonding orbitals.

Huckel's rule states that a system is aromatic if it contains 4n+2 pi electrons.

The MOs tend to show more diffuse orbitals around the boron atoms than the nitrogen atoms. This correlates with finding of lower electron density on the boron atoms than on the nitrogen atoms.

Comparing MO 1 across the four molecules, the orbitals are more diffuse around the boron atoms than around the nitrogen atoms. The orbital was lower in energy for the pyridinium than the boratabenzene. The borazine and benzene energies were similar. It was the HOMO for all of the molecules except for boratabenzene.

For MO 2, again the orbitals are more tightly bound to the nitrogen atoms and more diffuse around the boron atoms. 

For MO 3, The MO is totally bonding and in all four molecules it was the first orbital above the core orbitals. The orbital shape follows the electron density with the cloud centered more on the electronegative atom. This means that in the pyridinium the electron cloud is shifted towards the nitrogen and in boratabenzene it is centered more away from the boron. In borazine the cloud is centered more on each of the nitrogen atoms.

Changing the atoms from benzene to boratabenzene and pyridinium broke the symmetry of the molecule (point group went from D<sub>6h</sub> to C<sub>2v</sub>) and so the degeneracy of the MOs was reduced. Going from benzene to borazine (point group went from D<sub>6h</sub> to D<sub>3h</sub>), the symmetry was not reduced as much and so the degeneracy of the MOs did not change.

=== NBO Bonding Analysis ===

The NBO bonding analysis shows the bonding in benzene as sp<sup>2</sup> bonds between each adjacent pair of carbon atoms and between each carbon and hydrogen pair. There are then 3 C-C bonds composed exclusively of p orbitals.

This analysis doesn't give any indication of the aromaticity of the molecule because it tries to put the electrons into 2c-2e bonds. Aromaticity is due to delocalised electrons and so doesn't lend itself to a description using discrete 2c-2e bonds. This inevitably leads to a poor description of the bonding situation and is misleading in how localised it suggests the electrons are.

== Vibrational Analysis ==

[[File:DW Benzene Vibrational Spectrum.GIF|thumb|Benzene Vibrational Spectrum]]
[[File:DW Boratabenzene Vibrational Spectrum.GIF|thumb|Boratabenzene Vibrational Spectrum]]
[[File:DW Pyridinium Vibrational Spectrum.GIF|thumb|Pyridinium Vibrational Spectrum]]
[[File:DW Borazine Vibrational Spectrum.GIF|thumb|Borazine Vibrational Spectrum]]

The vibrational spectra of the four molecules show different patterns. There are many more vibrational modes with non-zero intensity in the spectra of the polar pyridinium and boratabenzene molecules.

The benzene only shows four absorptions at 693,1066, 1525 and 3200cm<sup>-1</sup> and they are very weak in intensity due to the low polarity of the bonds in the molecule.

The pyridinium only shows some low energy vibrations whereas the most significant absorptions in the boratabenzene spectrum are much higher in energy and stronger intensity.

Since Borazine is more symmetrical, fewer vibrational modes are expected, and fewer are observed. Due to the high polarity of the atoms in the molecule the intensity of the vibrations that are present is very high.

= References =
<references/>