View source for Rep:Mod:ECN0511

Name: Estella Chin Ning <br>
CID: 00697238
== Optimising a BH<sub>3</sub> Molecule ==
=== 3-21G Calculation ===
The results of the BH<sub>3</sub> 3-21G optimisation are summarised in Table 1 below.
<center>
{| class="wikitable"

|+ Table 1: BH<sub>3</sub> 3-21G Optimisation
! style="background:#cccccc; color: white;" colspan="2" " | [[Media:ECN BH3 OPT.LOG| Link to log file of 3-21G Optimised BH<sub>3</sub> Molecule]]
|-
! style="text-align: left; background: #4f4667; color: white;" | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation type
| FOPT
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;" |Basis set
|3-21G
|-
! style="text-align: left; background: #4f4667; color: white;" |Final energy
| -26.46226429 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;"  |RMS gradient norm
|0.00008851 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;"  |Dipole moment
|0.00 D
|-
! style="text-align: left; background: #4f4667; color: white;" |Point group
|C<sub>S</sub>
|-
! style="text-align: left; background: #4f4667; color: white;" |Time taken for calculation
|18.0 seconds
|}
</center>
The expected point group symmetry of D<sub>3h</sub> is not attained in the optimisation calculation above. This is because higher accuracy calculations are required to attain the correct point group symmetry of the BH<sub>3</sub> molecule. In addition, the gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.
<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=-1.672479D-07
 Optimization completed.
    -- Stationary point found.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule. 
<br> 
The total energy and RMS Gradient of each optimisation step is shown in Figure 1 and 2 respectively.

[[Image:ECN BH3 Energy0.jpg|thumb|center|400px|Figure 1: Total Energy at each Optimisation Step]]

[[Image:ECN BH3 Energy.jpg|thumb|center|400px|Figure 2: RMS Gradient at each Optimisation Step ]]

The last structure of the optimisation step has the most negative energy and the smallest gradient, suggesting that it is the energy minima structure.

=== 6-31G (d,p) Calculation ===
The results of the 6-31G (d,p) optimisation are summarised in Table 2 below.
<center>
{| class="wikitable"

|+ Table 2: BH<sub>3</sub> 6-31G (d,p) Optimisation
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN BH3 OPT 631G DP.LOG| Link to log file of 6-31G (d,p) Optimised BH<sub>3</sub> Molecule]]
|-
! style="text-align: left; background: #4f4667; color: white;" | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation type
| FOPT
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;" |Basis set
|6-31G(d,p)
|-
! style="text-align: left; background: #4f4667; color: white;" |Final energy
| -26.61532360 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |RMS gradient norm
|0.00000009 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |Dipole moment
|0.00 D
|-
! style="text-align: left; background: #4f4667; color: white;" |Point group
|C<sub>S</sub>
|-
! style="text-align: left; background: #4f4667; color: white;" |Time taken for calculation
|11.0 seconds
|}
</center>
The expected point group symmetry of D<sub>3h</sub> is not attained in the optimisation calculation above. This is because higher accuracy calculations are required to attain the correct point group symmetry of the BH<sub>3</sub> molecule. In addition, the gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.
<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     0.000001     0.000004     YES
 Predicted change in Energy=-2.827323D-13
 Optimization completed.
    -- Stationary point found.               
</pre>

The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule. 

<center>
Optimised B-H Bond Distance: 
'''1.19 Å'''<br>
Literature B-H Bond Distance<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006. 
</ref> : '''1.19 Å'''<br>
Optimised H-B-H Bond Angle: 
'''120.0 °'''<br>
There is good corroboration between the calculated B-H bond distance and that found in literature. In addition, the H-B-H bond angle is 120.0 ° as would be expected for a BH<sub>3</sub> molecule which has the D<sub>3h</sub> point group, confirming the accuracy of the optimisation calculations.
<br><br>
Total energy for the 3-21G Optimised Structure: '''-26.46226429 a.u.'''
<br>
Total energy for the 6-31G (d,p) Optimised Structure: '''-26.61532360 a.u.'''
<br>
Note that the energies of the 3-21G and 6-31G (d,p) optimised structure cannot be compared as different basis sets were used.
</center>

== Optimising a GaBr<sub>3</sub> Molecule ==
=== LanL2DZ Calculation ===
The results of the LanL2DZ optimisation are summarised in Table 3 below.
<center>
{| class="wikitable"
|+ Table 3: GaBr<sub>3</sub> LanL2DZ Optimisation
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN GABR3 OPT HPC.log| Link to log file of LanL2DZ Optimised GaBr<sub>3</sub> Molecule]]
|-
! style="background:#cccccc; color: white;" colspan="2" " |  [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26912/ Link to D-Space]
|-
! style="text-align: left; background: #4f4667; color: white;" | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation type
| FOPT
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;"  |Basis set
|LANL2DZ
|-
! style="text-align: left; background: #4f4667; color: white;"  |Final energy
| -41.70082783 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;"  |RMS gradient norm
| 0.00000016 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |Dipole moment
|0.00 D
|-
! style="text-align: left; background: #4f4667; color: white;"  |Point group
|D<sub>3h</sub>
|-
! style="text-align: left; background: #4f4667; color: white;" |Time taken for calculation
|27.6 seconds
|}
</center>
The gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.

<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=-1.282690D-12
 Optimization completed.
    -- Stationary point found.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule. 
<center>
Optimised Ga-Br Bond Distance: 
'''2.35 Å'''<br>
Literature Ga-Br Bond Distance<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006. 
</ref> : 
'''2.3525 Å'''<br>
Optimised Br-Ga-Br Bond Angle: '''120.0 °'''
</center>
There is good corroboration between the calculated Ga-Br bond distance and that found in literature. In addition, the Br-Ga-Br bond angle is 120.0 ° as would be expected for a GaBr<sub>3</sub> molecule which has the D<sub>3h</sub> point group, confirming the accuracy of the optimisation calculations.

== Optimising a BBr<sub>3</sub> Molecule ==
=== 6-31G (d,p) and LanL2DZ Calculation ===
The results of the 6-31G (d,p) and LanL2DZ optimisation are summarised in Table 4 below.
<center>
{| class="wikitable"

|+ Table 4: BBr<sub>3</sub> 6-31G (d,p) and LanL2DZ Optimisation
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN GABR3 OPT HPC.log| Link to log file of Optimised BBr<sub>3</sub> Molecule]]
|-
! style="background:#cccccc; color: white;" colspan="2" " |  [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26913/ Link to D-Space]
|-
! style="text-align: left; background: #4f4667; color: white;" | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation type
| FOPT
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;"  |Basis set
|GEN (6-31G (d,p) and LanL2DZ)
|-
! style="text-align: left; background: #4f4667; color: white;"  |Final energy
| -64.43645388 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;"  |RMS gradient norm
| 0.00000943 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |Dipole moment
|0.00 D
|-
! style="text-align: left; background: #4f4667; color: white;" |Point group
|C<sub>S</sub>
|-
! style="text-align: left; background: #4f4667; color: white;" |Time taken for calculation
|39.3 seconds
|}

</center>
The expected point group symmetry of D<sub>3h</sub> is not attained in the optimisation calculation above. This is because higher accuracy calculations are required to attain the correct point group symmetry of the BBr<sub>3</sub> molecule. In addition, the gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.

<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.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule. 
<center>
Optimised B-Br Bond Distance: '''1.93 Å'''<br>
Literature B-Br Bond Distance <ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006. 
</ref>: '''1.893 Å'''<br>
Optimised Br-B-Br Bond Angle: '''120.0 °'''</center>
There is good corroboration between the calculated B-Br bond distance and that found in literature. In addition, the Br-B-Br bond angle is 120.0 ° as would be expected for a BBr<sub>3</sub> molecule which has the D<sub>3h</sub> point group, confirming the accuracy of the optimisation calculations.

== Comparing the Bond Distances of BH<sub>3</sub>, BBr<sub>3</sub> & GaBr<sub>3</sub>  ==
The summary of the different bond distances between BH<sub>3</sub>, BBr<sub>3</sub> & GaBr<sub>3</sub> is shown in Table 5 below.
<center>
{| class="wikitable"

|+ Table 5: Comparison of Bond Distances
! style="background: #4f4667; color: white;" | Molecule
! style="background: #4f4667; color: white;" | Bond Distance (Å)
|-
! style="text-align: left;" | BH<sub>3</sub>
! style="text-align: left;"| 1.19
|-
! style="text-align: left;"|BBr<sub>3</sub>
! style="text-align: left;"| 1.93
|-
! style="text-align: left;"| GaBr<sub>3</sub>
! style="text-align: left;"| 2.35
|}


</center> 

The bond distances increase in the order: B – H (1.19 Å) > B – Br (1.93 Å) > Ga – Br (2.35 Å).

Comparing the bond distances of B – H and B – Br where the central atom (B) is kept constant, when the ligand is changed from H to Br, the bond distance increases. Both H and Br have 1 unpaired electron; the electronic configuration of H is 1s<sup>1</sup>, while that of Br is [Ar] 4s<sup>2</sup>3d<sup>10</sup>4p<sup>5</sup>, which allows the formation of a covalent bond with B. However, this causes the B – H bond to have a larger s-character than the B – Br bond, where the unpaired electron from the Br is from the 4p orbital. In simpler terms, since the atomic size of the H ligand is smaller than that of the Br ligand, the Br atomic orbitals are more diffused, hence there is better orbital overlap between B and H as compared to B and Br, leading to the formation of stronger and shorter B – H bonds than B – Br bonds.

Similarly, by comparing the bond distances of B – Br and Ga – Br where the ligand (Br) is kept constant, when the central atom is changed from B to Ga, the bond distance increases. Both B and Ga belong to Group 13 of the periodic table and hence they have similar chemical bonding properties.  However, B and Ga are found in Period 2 and 4 of the periodic table respectively, hence, B has a smaller atomic size and fewer atomic orbitals than Ga. This causes the B – Br bond to be shorter and stronger than the Ga – Br bond, as the Ga atomic orbitals are more diffused and hence the B – Br bond is formed closer to the central atom atomic nucleus than that of the Ga – Br bond.

A chemical bond can be defined as the attractive interactions between two atoms, which are normally attributed to electrostatic forces of attraction between the oppositely-charged induced dipoles of 2 atoms, or between 2 ions.  In the optimisation process of the molecule, bonds are not observed between the central and ligand atoms in Gaussview. This does not indicate the absence of bonds between the atoms; it just shows that according to calculations, the atoms are too far apart as compared to a normal covalent bond length. In fact, since the atoms do not have the same electronegativities, one is bound to induce a dipole in the other, causing some form of interaction.  The absence of the indicated bonds may just suggest that the atoms are too weakly bonded to be considered as sharing a covalent bond.

== BH<sub>3</sub> Frequency Analysis ==
=== Frequency Calculation ===
The results of the 6-31G (d,p) frequency calculations are summarised in Table 6 below.
<center>
{| class="wikitable"
|+ Table 6: BH<sub>3</sub> 6-31G (d,p) Frequency Calculations
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN BH3 OPT 631G DP FREQ.LOG|Link to log file of Frequency analysis of BH<sub>3</sub>]]
|-
! style="background:#cccccc; color: white;" colspan="2" " | [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26926/ Link to D-Space]
|-
! style="text-align: left; background: #4f4667; color: white;"  | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation type
| FOPT
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;"  |Basis set
|6-31G(d,p)
|-
! style="text-align: left; background: #4f4667; color: white;"  |Final energy
| -26.61532364 a.u. (Same (up to last 2 d.p.) as that recorded in optimisation step)
|-
! style="text-align: left; background: #4f4667; color: white;" |RMS gradient norm
| 0.00000001 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;"  |Dipole moment
|0.00 D
|-
! style="text-align: left; background: #4f4667; color: white;" |Point group
|D<sub>3h</sub>
|-
! style="text-align: left; background: #4f4667; color: white;" |Time taken for calculation
|5.0 seconds
|}
</center>
The gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.
<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=-1.040964D-15
 Optimization completed.
    -- Stationary point found.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule.
<pre>
Low frequencies ---   -9.3484   -9.3330   -0.0724    0.0010    0.5365    2.5464
Low frequencies --- 1162.9903 1213.1496 1213.1498
</pre>
The low frequencies are within the range of ± 15 cm<sup>-1</sup> and close to 0, indicating that the method employed in the frequency calculations was sufficiently accurate.

=== Summary of BH<sub>3</sub> Vibrations ===
The summary of BH<sub>3</sub> vibrational modes can be found in Table 7 below.
{| class="wikitable"
|+ Table 7: Vibrational modes of BH<sub>3</sub> 
! style="background: #4f4667; color: white;" | <center>No.</center>
! style="background: #4f4667; color: white;" | <center>Vibration</center>
! style="background: #4f4667; color: white;" | <center>Description </center>
! style="background: #4f4667; color: white;" | <center>Frequency (cm<sup>-1</sup>)</center>
! style="background: #4f4667; color: white;" | <center>Intensity</center>
! style="background: #4f4667; color: white;" | <center>Symmetry D<sub>3h</sub> Point Group</center> 
|-
| <center>1.</center>
| <center>[[Image:ECN BH3 Vib1.gif|150px| ]] </center>
| <center>All the H atoms move up and down together in a concerted motion </center>
| <center>1163</center>
| <center>93</center>
| <center>A<sub>2</sub>"</center>
|-
| <center>2.</center>
| <center>[[Image:ECN BH3 Vib2.gif|150px| ]]</center>
| <center> All the H atoms move towards and away from each other in a concerted motion, from left to right </center>
| <center>1213</center>
| <center>14</center>
| <center>E'</center>
|-
| <center>3.</center>
| <center>[[Image:ECN BH3 Vib3.gif|150px| ]]</center>
| <center>2 H atoms move towards and away from each other in a concerted motion, from left to right </center>
| <center> 1213 </center>
| <center> 14 </center>
| <center> E' </center>
|-
| <center> 4. </center>
| <center> [[Image:ECN BH3 Vib4.gif|150px| ]] </center>
| <center> All the H atoms move in and out together in a concerted motion, the B atom is stationary </center>
| <center> 2583 </center>
| <center> 0 </center>
| <center> Totally symmetric A<sub>1</sub>'</center>
|-
| <center> 5. </center>
| <center> [[Image:ECN BH3 Vib5.gif|150px| ]] </center>
| <center> 2 H atoms move in and out in an alternating motion</center>
| <center> 2716 </center>
| <center> 156</center>
| <center> E'</center>
|-
| <center> 6.</center>
| <center>[[Image:ECN BH3 Vib6.gif|150px| ]]</center>
| <center> 2 H atoms move in and out in a concerted motion, alternating with the in and out motion of the last H atom</center>
| <center> 2716</center>
| <center> 126 </center>
| <center> E'</center>
|}

=== Infrared (IR) Spectrum ===
The infrared spectrum of GaBr3 is illustrated in Figure 3 below.
[[Image:ECN BH3 IR.jpg|550px|thumb|center|Figure 3: Infrared Spectrum of BH<sub>3</sub>  ]]


Although there are a total of 6 vibrational modes, only 3 corresponding peaks are present in the IR spectrum. This can be attributed to the fact that vibrational modes 2 and 3 vibrate at the same frequency (1213.15 cm<sup>-1</sup>) and vibrational modes 5 and 6 vibrate at the same frequency (2715.66 cm<sup>-1</sup>), giving rise to overlapping peaks in the infrared spectrum. Vibrational modes with the same frequency are called degenerate modes, as the vibrations are associated with the same energy. In addition, only vibrations that cause a change in the overall dipole moment of the molecule will give rise to peaks in the infrared spectrum. For the A<sub>1</sub>' totally symmetric mode, there is no change in overall dipole moment associated with the vibration and hence the intensity of the peak in the infrared spectrum is '0'. Thus, there are 3 infrared peaks in total.

== GaBr<sub>3</sub> Frequency Analysis  ==
=== Frequency Calculation ===
The results of the GaBr<sub>3</sub> LANL2DZ frequency analysis are summarised in Table 8 below.
<center>
{| class="wikitable"

|+ Table 8: GaBr<sub>3</sub> LANL2DZ frequency analysis
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN GABR3 OPT HPC1 Freq.log| Link to log file of Frequency analysis of GaBr<sub>3</sub>]]
|-
! style="background:#cccccc; color: white;" colspan="2" " | [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26915/ Link to D-space]
|-
! style="text-align: left; background: #4f4667; color: white;"  | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation type
| FOPT
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;" |Basis set
|LANL2DZ
|-
! style="text-align: left; background: #4f4667; color: white;"  |Final energy
| -41.70082783 a.u. (Same (up to last 2 d.p.) as that recorded in optimisation step)
|-
! style="text-align: left; background: #4f4667; color: white;" |RMS gradient norm
| 0.00000011 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |Dipole moment
|0.00 D
|-
! style="text-align: left; background: #4f4667; color: white;" |Point group
|D<sub>3h</sub>
|-
! style="text-align: left; background: #4f4667; color: white;" |Time taken for calculation
|21.9 seconds
|}
</center>
The gradient is less than 0.0001 (expected gradient = 0 for a stationary point) and close to 0, indicating that the molecule has indeed been optimised.
<pre>
Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000002     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
 Predicted change in Energy=-6.142862D-13
 Optimization completed.
    -- Stationary point found.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule.
<pre>
 Low frequencies ---   -0.5252   -0.5247   -0.0024   -0.0010    0.0235    1.2010
 Low frequencies ---   76.3744   76.3753   99.6982
</pre>
The low frequencies are within the range of ± 15 cm-1, indicating that the method employed in the frequency calculations was sufficiently accurate.
<br>
The lowest "real" normal mode of GaBr<sub>3</sub> is the '''E'''' mode at '''76 cm<sup>-1</sup>'''.

=== Summary of Vibrations ===
The summary of GaBr<sub>3</sub> vibrational modes can be found in Table 9 below.
{| class="wikitable"
|+ Table 9: Vibrational modes of GaBr<sub>3</sub>
! style="background: #4f4667; color: white;" | <center>No.</center>
! style="background: #4f4667; color: white;" | <center>Vibration</center>
! style="background: #4f4667; color: white;" | <center>Description </center>
! style="background: #4f4667; color: white;" | <center>Frequency (cm<sup>-1</sup>)</center>
! style="background: #4f4667; color: white;" | <center>Intensity</center>
! style="background: #4f4667; color: white;" | <center>Symmetry D<sub>3h</sub> Point Group</center> 
|-
| <center>1.</center>
| <center>[[Image:ECN GaBr3 Vib2.gif|150px| ]] </center>
| <center>All the Br atoms move towards and away from each other in a concerted motion, from left to right </center>
| <center>76</center>
| <center>3</center>
| <center>E'</center>
|-
| <center>2.</center>
| <center>[[Image:ECN GaBr3 Vib3.gif|150px| ]]</center>
| <center> 2 Br atoms move towards and away from each other in a concerted motion, from left to right </center>
| <center>76</center>
| <center>3</center>
| <center>E'</center>
|-
| <center>3.</center>
| <center>[[Image:ECN GaBr3 Vib1.gif|150px| ]]</center>
| <center>All the Br atoms move up and down together in a concerted motion </center>
| <center> 100</center>
| <center> 9 </center>
| <center> A<sub>2</sub>"</center>
|-
| <center> 4. </center>
| <center> [[Image:ECN GaBr3 Vib4.gif|150px| ]] </center>
| <center> All the Br atoms move in and out together in a concerted motion, the Ga atom is stationary </center>
| <center> 197 </center>
| <center> 0 </center>
| <center> Totally symmetric A<sub>1</sub>'</center>
|-
| <center> 5. </center>
| <center> [[Image:ECN GaBr3 Vib5.gif|150px| ]] </center>
| <center> 2 Br atoms move in and out in an alternating motion, while the Ga atom moves up and down</center>
| <center> 316 </center>
| <center> 57 </center>
| <center> E'</center>
|-
| <center> 6.</center>
| <center>[[Image:ECN GaBr3 Vib6.gif|150px| ]]</center>
| <center> 2 Br atoms move towards and away from the central Ga atom in a concerted motion, alternating with the in and out motion of the last Br atom</center>
| <center> 316 </center>
| <center> 57 </center>
| <center> E'</center>
|}

=== Infrared (IR) Spectrum ===
The infrared spectrum of GaBr<sub>3</sub> is illustrated in Figure 4 below.
[[Image:ECN GaBr3 IR.jpg|450px|thumb|center|Figure 4: Infrared Spectrum of GaBr<sub>3</sub> ]]

== Comparing Vibrational Frequencies ==
The comparison table between the vibrational frequencies of BH<sub>3</sub> and GaBr<sub>3</sub> is shown in Table 10 below.
{| class="wikitable"

|+ Table 10: Comparison between the vibrational frequencies of BH<sub>3</sub> and GaBr<sub>3</sub>
! style="background: #4f4667; color: white; text-align: center;" rowspan="2"  | 
No.
! style="background: #4f4667; color: white; text-align: center;" rowspan="2" | Symmetry D<sub>3h</sub> Point Group
! style="background:#4f4667; color: white; text-align: center;" rowspan="2" | 
Description
! style="background:#4f4667; color: white; text-align: center;" colspan="2" | BH<sub>3</sub>
! style="background: #4f4667; color: white; text-align: center;" colspan="2" | GaBr<sub>3</sub>
|-
! style="background:#4f4667; color: white;text-align: center;" | Vibration
! style="background: #4f4667; color: white;text-align: center;" | Frequency (cm<sup>-1</sup>)
! style="background: #4f4667; color: white;text-align: center;" | Vibration
! style="background: #4f4667; color: white;text-align: center;" | Frequency (cm<sup>-1</sup>)
|-
! style="text-align: center;"| 1.
! style="text-align: center;"|A<sub>2</sub>"
! style="text-align: center;"| 
All the 3 substituent atoms move up and down together in a concerted motion
! style="text-align: center;"| <center>[[Image:ECN BH3 Vib1.gif|100px| ]] </center>
! style="text-align: center;"|1163
! style="text-align: center;"| <center>[[Image:ECN GaBr3 Vib1.gif|100px| ]] </center>
! style="text-align: center;"|100
|-
! style="text-align: center;"|2.
! style="text-align: center;"|E'
! style="text-align: center;"|All the substituent atoms move towards and away from each other in a concerted motion, from left to right

! style="text-align: center;"|  <center>[[Image:ECN BH3 Vib2.gif|100px| ]] </center>
! style="text-align: center;"|1213

! style="text-align: center;"|<center>[[Image:ECN GaBr3 Vib2.gif|100px| ]] </center>
! style="text-align: center;"|76
|-
! style="text-align: center;"|3.
! style="text-align: center;"|E'
! style="text-align: center;"|2 substituent atoms move towards and away from each other in a concerted motion, from left to right
! style="text-align: center;"| <center>[[Image:ECN BH3 Vib3.gif|100px| ]] </center>
! style="text-align: center;"|1213

! style="text-align: center;"|<center>[[Image:ECN GaBr3 Vib3.gif|100px| ]] </center>
! style="text-align: center;"|76
|-
! style="text-align: center;"|4.
! style="text-align: center;"|A<sub>1</sub>'
! style="text-align: center;"|All the substituent atoms move in and out together in a concerted motion

! style="text-align: center;"| <center>[[Image:ECN BH3 Vib4.gif|100px| ]] </center>
! style="text-align: center;"|2583

! style="text-align: center;"|<center>[[Image:ECN GaBr3 Vib4.gif|100px| ]] </center>
! style="text-align: center;"|197             
|-
! style="text-align: center;"|5.
! style="text-align: center;"|E'
! style="text-align: center;"|2 substituent atoms move in and out in an alternating motion

! style="text-align: center;"| <center>[[Image:ECN BH3 Vib5.gif|100px| ]] </center>
! style="text-align: center;"|2716

! style="text-align: center;"|<center>[[Image:ECN GaBr3 Vib5.gif|100px| ]] </center>
! style="text-align: center;"|316
|-
! style="text-align: center;"|6.
! style="text-align: center;"|E'
! style="text-align: center;"|2 substituent atoms move in and out in a concerted motion, alternating with the in and out motion of the last substituent atom

! style="text-align: center;"| <center>[[Image:ECN BH3 Vib6.gif|100px| ]] </center>
! style="text-align: center;"|2716

! style="text-align: center;"|<center>[[Image:ECN GaBr3 Vib6.gif|100px| ]] </center>
! style="text-align: center;"|316
|}

As evident from the summary table, the frequency values for BH<sub>3</sub> are much larger than that of GaBr<sub>3</sub>. As frequencies are directly proportional to the bond strength of the molecule, higher frequencies of BH<sub>3</sub> suggests that the B – H bond is much stronger than the Ga – Br bond. This corresponds to the difference in the optimised calculated bond strength between B – Br and Ga –Br, as shown in Table 5 above.
<br><br>
There has been a reordering of modes between the A<sub>2</sub>” and 2 degenerate E’ modes. For BH<sub>3</sub>, the doubly degenerate E’ modes vibrate at higher frequency, while for GaBr<sub>3</sub>, the A<sub>2</sub>" mode vibrates at higher frequency.
<br><br>
Both the BH<sub>3</sub> and GaBr<sub>3</sub> infrared spectra have 3 peaks, despite having 6 vibrational modes. This is due to the presence of 2 degenerate (E’) vibrational modes and a totally symmetric A<sub>1</sub>’ vibrational mode which has an infrared peak at 0 intensity, reasons of which have been explained before.
<br><br>
For both spectra, the A<sub>2</sub>” and 2 degenerate E’ modes vibrate at similar lower frequencies, while the A1’ and the other 2 degenerate E’ modes vibrate at similar higher frequencies. This is because the A<sub>2</sub>” and the 2 degenerate E’ modes (No. 2 and 3 in the table above) are bending vibrational modes (wagging and scissoring respectively), which are relatively low energy vibrations and hence produce low frequencies. In contrast, the A<sub>1</sub>’ mode and the other 2 degenerate E’ modes (No. 5 and 6 in the table above) are high energy stretching modes, the former being a symmetrical stretching vibrational mode, while the latter 2 are asymmetrical stretching modes. Stretching vibrational modes are relatively higher in energy than the bending modes. Hence, the A<sub>1</sub>’ and E’ modes have higher energy frequencies as compared to the A<sub>2</sub>” and E’ modes.
<br><br>
The chosen method determines the type of approximations that are made in solving the Schrodinger equation, while the basis set determines the accuracy of the optimisation process. These provide the potential energy surface on which optimisation and frequency calculations are made on. Optimisation analysis calculations provide the stationary points of a potential energy surface of a particular molecule, that is, the Schrodinger equation is solved for the nuclear and electronic positions at different molecular coordinates to find the lowest energy configuration. Frequency analysis calculations provide the second derivative of that stationary point derived from the optimisation in the same potential energy surface. Hence, it is vital to use the same method and basis set since both the optimisation and frequency calculations are based on the same optimised potential energy surface; using a different set of method and basis sets will cause the frequency calculations to be inaccurate as it will now be based on a different potential energy surface. 

<br><br>
A frequency analysis provides information whether the optimised stationary point is a minimum point, maximum point, or a point of inflection. Frequencies are the second derivatives of a stationary point; positive frequencies indicate a minimum stationary point, while negative frequencies indicate a maximum stationary point. Since we are looking for the lowest energy configuration, i.e. a minimum point, the frequencies should be positive.                                                                                                                                                            
<br><br>
The "Low frequencies" represent the translational and rotational degrees of freedom of a given molecule; they are the "-6" component in the "3n-6" calculations of vibrational degrees of freedom for a non-linear molecule, or the "-5" component in the "3n-5" calculations of vibrational degrees of freedom for a linear molecule, where "n" represents the number of atoms in the molecule.

== Molecular Orbitals of BH<sub>3</sub> ==
The Molecular Orbital diagram of BH<sub>3</sub> is shown in Figure 5 below, which shows the similarities between the real and expected LCAO MOs.

[[File:MO Diagram Pic.jpg|thumb|center|600px|Figure 5: MO Diagram of BH<sub>3</sub>]]

There are no significant differences between the real and expected LCAO MOs. As such, it can be inferred that qualitative MO theory is accurate in predicting the shapes, orientations and phases of actual molecular orbitals. This is especially useful as we now have a better picture of the electron density present in a given molecule.
<br>
N.B. The totally symmetric 1A<sub>1</sub>' molecular orbital was generated, although this is not seen in the MO diagram drawn which only depicts valence electrons.

== NH<sub>3</sub> ==
=== Optimisation: 6-31G (d,p) Calculation ===
The results of the NH<sub>3</sub> 6-31G (d,p) Optimisation can be found in Table 11 below.
<center>
{| class="wikitable"

|+ Table 11: NH<sub>3</sub> 6-31G (d,p) Optimisation
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN GABR3 OPT HPC.log| Link to the log file of 6-31G(d,p) Optimised NH<sub>3</sub> Molecule]]
|-
! style="text-align: left; background: #4f4667; color: white;" | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation type
| FOPT
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;"  |Basis set
|6-31G(d,p)
|-
! style="text-align: left; background: #4f4667; color: white;" |Final energy
| -56.55776872 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |RMS gradient norm
| 0.00000013 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;"  |Dipole moment
|1.85 D
|-
! style="text-align: left; background: #4f4667; color: white;" |Point group
|C<sub>1</sub>
|-
! style="text-align: left; background: #4f4667; color: white;" |Time taken for calculation
|9.0 seconds
|}
</center>
The expected point group symmetry of C<sub>3v</sub> is not attained in the optimisation calculation above. This is because higher accuracy calculations are required to attain the correct point group symmetry of the NH<sub>3</sub> molecule. In addition, the gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.
<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     0.000001     0.000004     YES
 Predicted change in Energy=-2.600465D-13
 Optimization completed.
    -- Stationary point found.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule.

=== Frequency Analysis ===
The results of the NH<sub>3</sub> 6-31G (d,p) frequency analysis can be found in Table 12 below.
<center>
{| class="wikitable"

|+ Table 12: NH<sub>3</sub> 6-31G (d,p) Frequency analysis
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN NH3 OPT 631G DP Freq log.log|Link to log file of Frequency Analysis of NH<sub>3</sub>]]
|-
! style="background:#cccccc; color: white;" colspan="2" " |  [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26950/ Link to D-Space]
|-
! style="text-align: left; background: #4f4667; color: white;" | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation type
| FREQ
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;" |Basis set
|6-31G(d,p)
|-
! style="text-align: left; background: #4f4667; color: white;" |Final energy
| -56.55776872 a.u. (Same (up to last 2 d.p.) as that recorded in optimisation step)
|-
! style="text-align: left; background: #4f4667; color: white;"  |RMS gradient norm
| 0.00000020 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |Dipole moment
|1.85 D
|-
!! style="text-align: left; background: #4f4667; color: white;" |Point group
|C<sub>1</sub>
|-
! style="text-align: left; background: #4f4667; color: white;"  |Time taken for calculation
|33.9 seconds
|}
</center>
The expected point group symmetry of C<sub>3v</sub> is not attained in the optimisation calculation above. This is because higher accuracy calculations are required to attain the correct point group symmetry of the NH<sub>3</sub> molecule. In addition, the gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.
<pre>
       Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000002     0.000006     YES
 RMS     Displacement     0.000001     0.000004     YES
 Predicted change in Energy=-8.193705D-13
 Optimization completed.
    -- Stationary point found.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule.
<pre>
Low frequencies ---   -8.2887   -6.5533   -4.4302    0.0005    0.0008    0.0014
Low frequencies --- 1089.3394 1693.9228 1693.9270
</pre>
The low frequencies are within the range of ± 15 cm-1 and close to 0, indicating that the method employed in the frequency calculations was sufficiently accurate.

=== MO Analysis ===
[[Media:ECN NH3 MO.txt| Link to the log file]]
<br>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26955/ Link to D-Space]

=== NBO Analysis ===
The NH<sub>3</sub> NBO charge distribution is illustrated in Figure 6 below.
<center>
[[Image:ECN NH3 OPT 631G DP NBO1.jpg|250px|thumb|center|Figure 6: NH<sub>3</sub> NBO charge distribution ]]

</center>

<center>
Charge Distribution: '''-1.125 - 1.125'''
<br>
Specific NBO charge for Nitrogen: '''-1.125'''
<br>
Specific NBO charge for Hydrogen: '''0.375'''

</center>

== NH<sub>3</sub>BH<sub>3</sub> ==
=== Optimisation: 6-31G (d,p) Calculation ===
The results of the NH<sub>3</sub>BH<sub>3</sub> 6-31G (d,p) Optimisation can be found in Table 13 below.
<center>


{| class="wikitable"

|+ Table 13: NH<sub>3</sub>BH<sub>3</sub>6-31G (d,p)Optimisation
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN NH3BH3 OPT 631G DP 1.LOG| Link to log file of 6-31G(d,p) Optimised NH<sub>3</sub>BH<sub>3</sub> Molecule]]
|-
! style="text-align: left; background: #4f4667; color: white;" | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation type
| FOPT
|-
! style="text-align: left; background: #4f4667; color: white;"  |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;" |Basis set
|6-31G(d,p)
|-
! style="text-align: left; background: #4f4667; color: white;" |Final energy
| -83.22468911 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;"  |RMS gradient norm
| 0.00000009 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |Dipole moment
|5.56 D
|-
! style="text-align: left; background: #4f4667; color: white;" |Point group
|C<sub>1</sub>
|-
! style="text-align: left; background: #4f4667; color: white;" |Time taken for calculation
|44.0 seconds
|}
</center>
The gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.
<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=-1.593712D-14
 Optimization completed.
    -- Stationary point found.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule.

=== Frequency Analysis ===
The results of the NH<sub>3</sub>BH<sub>3</sub> 6-31G (d,p) frequency analysis can be found in Table 14 below.
<center>
{| class="wikitable"

|+ Table 14: NH<sub>3</sub>BH<sub>3</sub>6-31G (d,p) frequency analysis
! style="background:#cccccc; color: white;" colspan="2" " |  [[Media:ECN NH3BH3 OPT 631G DP Freq.log| Link to log file of Frequency Analysis of NH<sub>3</sub>BH<sub>3</sub>]]
|-
! style="background:#cccccc; color: white;" colspan="2" " |  [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26962/ Link to D-Space]
|-
! style="text-align: left; background: #4f4667; color: white;" | File Type
| .log
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation type
| FREQ
|-
! style="text-align: left; background: #4f4667; color: white;" |Calculation method
|RB3LYP
|-
! style="text-align: left; background: #4f4667; color: white;" |Basis set
|6-31G(d,p)
|-
! style="text-align: left; background: #4f4667; color: white;" |Final energy
| -83.22468911 a.u. (Same (up to last 2 d.p.) as that recorded in optimisation step)
|-
! style="text-align: left; background: #4f4667; color: white;"  |RMS gradient norm
| 0.00000009 a.u.
|-
! style="text-align: left; background: #4f4667; color: white;" |Dipole moment
|5.56 D
|-
! style="text-align: left; background: #4f4667; color: white;"  |Point group
|C<sub>1</sub>
|-
! style="text-align: left; background: #4f4667; color: white;"  |Time taken for calculation
| 153.9 seconds
|}
</center>
The gradient is less than 0.0001 (expected gradient = 0 for a stationary point), indicating that the molecule has indeed been optimised.
<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=-6.087130D-13
 Optimization completed.
    -- Stationary point found.
</pre>
The table above shows that the forces have converged, meaning that for a small displacement, the energy does not change. This further confirms the successful optimisation of the molecule.                           
<pre>
  Low frequencies ---   -2.8702   -1.3787   -0.0007    0.0008    0.0009    3.5768
 Low frequencies ---  263.3606  632.9766  638.4460
</pre>
The low frequencies are within the range of ± 15 cm-1 and close to 0, indicating that the method employed in the frequency calculations was sufficiently accurate.

=== Comparison of Reaction Energies ===
The comparison table of reaction energies between NH<sub>3</sub>, BH<sub>3</sub>, and NH<sub>3</sub>BH<sub>3</sub> can be found in Table 15 below.
<center>
{| class="wikitable"


|+ Table 15: Comparison of NH<sub>3</sub>, BH<sub>3</sub>, and NH<sub>3</sub>BH<sub>3</sub> reaction energies
! style="text-align: left; background: #4f4667; color: white;" | E (NH<sub>3</sub>) / a.u.
| - 56.55776872 
|-
! style="text-align: left; background: #4f4667; color: white;"  |E (BH<sub>3</sub>) / a.u.
| - 26.61532360 
|-
! style="text-align: left; background: #4f4667; color: white;"  |E (NH<sub>3</sub>BH<sub>3</sub>) / a.u.
| - 83.22468911 
|-
! style="text-align: left; background: #4f4667; color: white;"  |Energy Difference/ a.u.
| - 83.22468911 - ( - 26.61532360 - 56.55776872) <br> = - 0.05159679
|-
! style="text-align: left; background: #4f4667; color: white;" |Energy Difference = Association Energy / kJmol<sup>-1</sup>
| - 0.05159679 x 2625.50 <br> = - 140 (Accuracy to 10 kJ/mol)
|-
! style="text-align: left; background: #4f4667; color: white;" |Dissociation Energy / kJmol<sup>-1</sup>
| 140 (Accuracy to 10 kJ/mol)
|}

</center>
As typical bond dissociation energies range from 100 kJmol<sup>-1</sup> to 500 kJmol<sup>-1</sup>, the N - B bond dissociation energy in NH<sub>3</sub>BH<sub>3</sub> of 140 kJmol<sup>-1</sup>  is a sensible value. In addition, since the bond present between NH<sub>3</sub> and BH<sub>3</sub> can be considered as a weak, dative interaction, the relatively low bond dissociation energy calculated seems reasonable.

== References ==
<References/>