View source for Rep:Mod:Td81121

==BH<sub>3</sub> molecule Optimisation==

The molecule BH<sub>3</sub> was optimised using two different basis: 3-21G and 6-31G(d,p). Thereafter, the energy values obtained from both methods were compared.

===3-21G Basis Set===

[[https://wiki.ch.ic.ac.uk/wiki/images/3/38/TC_bh3_opt.log BH<sub>3</sub> 3-21G optimisation log file]]
{| class="wikitable"
|-
|+ Summary Table
|-
! Property !! Value 
|-
| File Name || TC_bh3_opt 
|-
| File Type || .log 
|-
| Calculation Type || FOPT 
|-
| Calculation Method || RB3LYP 
|-
| Basis Set || 3-21G 
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Energy || -26.46226429 a.u.
|-
| RMS Gradient Norm || 0.00008851 a.u. 
|-
| Dipole Moment || 0.00 D 
|-
| Point Group || CS
|-
| Computational Time || 32.5 sec
|}

<pre>
Item               Value     Threshold  Converged?
 Maximum Force            0.000220     0.000450     YES
 RMS     Force            0.000106     0.000300     YES
 Maximum Displacement     0.000709     0.001800     YES
 RMS     Displacement     0.000447     0.001200     YES
 Predicted change in Energy=-1.672479D-07
 Optimization completed. 
</pre>

===6-31G Basis Set===

[[https://wiki.ch.ic.ac.uk/wiki/images/b/b8/TC_bh3_opt_631g_dp.log BH3 - 6-31G(d,p) optimisation log file]]

{| class="wikitable"
|-
! Property !! Value 
|-
| File Name || TC_bh3_opt_631g_dp 
|-
| File Type || .log 
|-
| Calculation Type || FOPT 
|-
| Calculation Method || RB3LYP 
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Energy ||  -26.61532358 a.u.
|-
| RMS Gradient Norm || 0.00008207 a.u. 
|-
| Dipole Moment || 0.00 D 
|-
| Point Group || CS
|-
| Computational Time || 4sec
|}

<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=-1.452205D-07
 Optimization completed.
</pre>

{| class="wikitable"
|-
! Property !! Value 
|-
| BH<sub>3</sub> optimised bond length || 1.19 Å
|-
| BH<sub>3</sub> optimised H-B-H bond angle || 120.0<sup>o</sup>
|}

The literature value for the BH bond length is quoted to be 1.190 Å. <ref>K. Kawaguchi, ''J Chem Phys'' , 1992, '''96''', 3411-3415 [http://scitation.aip.org/content/aip/journal/jcp/96/5/10.1063/1.461942 DOI: 10.1063/1.461942] </ref>  The computed bond length is in good agreement with the literature value.

===Total Energies===
{| class="wikitable"
|-
! Method !! Energy 
|-
| 3-21G || -26.46226429 a.u.
|-
| 6-31G(d,p) || -26.61532358 a.u.
|}

The calculated energies are different as different methods have been for the optimisation process. The 6-31G(d,p) incorporates more functions and so would give a better measure of the real energy value.

==GaBr<sub>3</sub> Optimisation==

The optimisation of GaBr<sub>3</sub> was carried out using a different basis set as the molecule has far larger electron density then the previous boron molecules. The chosen basis set was LanL2DZ, which sets the core electrons to an accurate constant (therefore modelled by a function called pseudo-potential) and performs optimisation on the valence electrons using the 6-31G basis set.

[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26885 GaBr<sub>3</sub> LanL2DZ optimisation D-space Link]]
[[https://wiki.ch.ic.ac.uk/wiki/images/5/54/TC_GaBr3_opt_LanL2DZ.log GaBr<sub>3</sub> LanL2DZ optimisation .Log file]]

{| class="wikitable"
|-
! Property !! Value 
|-
| File Name || TC_gabr3_opt_LanL2Dz 
|-
| File Type || .log 
|-
| Calculation Type || FOPT 
|-
| Calculation Method || RB3LYP 
|-
| Basis Set || LANL2DZ
|-
| Energy || -41.70082783.u.
|-
| RMS Gradient Norm || 0.00000016 a.u. 
|-
| Dipole Moment || 0.00 D 
|-
| Point Group || D3H
|}

<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.
</pre>

{| class="wikitable"
|-
! Property !! Value 
|-
| GaBr<sub>3</sub> optimised bond length || 2.35 Å
|-
| GaBr<sub>3</sub> optimised Br-Ga-Br bond angle || 120.0<sup>o</sup>
|}

Literature value - GaBr<sub>3</sub> bond length: 2.239A <ref>B. Reffy, M. Hargittai, M. Kolonits and B. Reffy, ''J. Mol. Struct.'', 1998 , '''445''', 139 - 148 [http://www.sciencedirect.com/science/article/pii/S0022286097004201 DOI: 10.1016/S0022-2860(97)00420-1]</ref>. This is slightly different could perhaps be imporved by using a larger basis set.

==BBr<sub>3</sub> Optimisation ==

In optimising the BBr<sub>3</sub> molecule, the basis set "GEN" with the keyword "pseudo=read gfinput" was utilised which allows the ability to specify pseudo potentials for individual atoms. The 6-31G(d,p) basis set was used for boron and LanL2DZ was used for the bromine atoms.

[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26891 BBr<sub>3</sub> GEN optimisation D-Space Link]]
[[https://wiki.ch.ic.ac.uk/wiki/images/1/17/TC_bbr3_opt_GEN.log BBr<sub>3</sub> GEN optimisation .log file]]

{| class="wikitable"
|-
|+ Summary Table
|-
! Property !! Value 
|-
| File Name || TC_bbr3_opt_GEN
|-
| File Type || .log 
|-
| Calculation Type || FOPT 
|-
| Calculation Method || RB3LYP 
|-
| Basis Set || GEN
|-
| Energy || -64.43645355 a.u.
|-
| RMS Gradient Norm || 0.00001020 a.u. 
|-
| Dipole Moment || 0.00 D 
|-
| Point Group || CS
|}

===Item Table===
<pre>
 Item               Value     Threshold  Converged?
 Maximum Force            0.000017     0.000450     YES
 RMS     Force            0.000010     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000043     0.001200     YES
 Predicted change in Energy=-1.759239D-09
 Optimization completed.
</pre>

{| class="wikitable"
|-
! Property !! Value 
|-
| BBr<sub>3</sub> optimised bond length || 1.93 Å
|-
| BBr<sub>3</sub> optimised Br-B-Br bond angle || 120.0<sup>o</sup>
|}

Literature value: 1.903 Å<ref> I. Krossing and G. Santiso-Quinones, ''Z. Anorg. Allg. Chem.'', 2008, '''634''', 4, 704 - 707  [http://onlinelibrary.wiley.com/doi/10.1002/zaac.200700510/abstract DOI: 10.1002/zaac.200700510] </ref>. This reference value is in good agreement with the computed value and further enhances the reliability of the calculations.

==Bond comparison of BH<sub>3</sub> BBr<sub>3</sub> and GaBr<sub>3</sub>==

{| class="wikitable"
|-
! Molecule || Bond Distance (Å)
|-
| BH<sub>3</sub>|| 1.19  
|-
| BBr<sub>3</sub> || 1.93  

|-
| GaBr<sub>3</sub> || 2.35 
|-
|}

The bond distances of these compounds are compared and a discussion is outlined below.

===Bond Distance Comparison===
====Changing The Ligand==== 
Changing the ligand to a heavier ligand causes the bond length to increase and thus forming a weaker bond. Both hydrogen and bromine are X-type donors and donates 1 electron to the central atom in forming a bond.  However, bromine has more electrons and thus larger orbitals and so forms longer and weaker bonds.

====Changing The Central Atom====
Changing the central atom to a heavier atom also causes the bond length to increase. Both boron and gallium are in group 13 and therefore forms 3 single bonds with 3 bromine atoms. However, as gallium is a bigger atom and therefore has a larger and more diffused orbitals compared to boron. This causes a weaker overlap between the central atom and ligand, resulting in weaker and longer bonds compared to the B-Br single bonds.

===Bond Discission===
====Gaussview does not draw in bonds, where bonds might be expected==== 
In some cases, gaussview does not draw in the bonds when they may be expected, this does not necessarily mean there is no bond. Gaussview draws bonds based on distance criteria and in some cases, the distances between atoms exceeds the pre-defined parameters, thus resulting in gaussview no drawing in bonds. 

====Definition of a Bond====
A bond is a directional attraction between two atoms, normally an electrostatic attraction, that has a stabilising effect. In the case of covalent bonds, the valence electrons from both atoms are attracted to both nuclei and thus shared between the two nuclei and forming a covalent bond. In the case of ionic bonds, electron is transferred from an electropositive atom (normally a metal)to an electronegative atom, in doing so, the former forms a positive ion and the latter forms a negative ion. An ionic bond is therefore the electrostatic attraction between the two ions. A metallic bond is one where the metal atoms in the metal lattice donates electrons to the commonly shared 'sea of electrons', resulting in the attraction between the positive metal ion and the surrounding electrons. Weaker intermolecular bonding interactions also exists and these are due to dipole-dipole interactions. For example, differences in electronegativity between different atoms often causes the formation of dipoles, these difference in dipoles leads to dipole interactions between different molecules and can result in permanent dipoles such as hydrogen bonding (in the case of nitrogen, oxygen and fluorine) or temporary dipoles such as dispersion forces. Because of the type of interactions involved and the degree of attraction between atoms is also different. The relative strengths of the bonds, in decreasing order is covalent, ionic, metallic, hydrogen bonding, dipole-dipole interactions and london dispersion forces.

==Frequency analysis for BH<sub>3</sub> and BBr<sub>3</sub>==
A couple of attempts to compute the frequency of BH<sub>3</sub> were firstly carried out in order to obtain the appropriate low frequency required. Thereafter, the frequency analysis was performed for GaBr<sub>3</sub> in order to compare the two different molecules.

===Frequency Analysis for BH<sub>3</sub>===

[[https://wiki.ch.ic.ac.uk/wiki/images/d/d0/TC_bh3_freq.log BH<sub>3</sub> initial frequency analysis log file]]

{| class="wikitable"
|-
|+Summary Table
! Property !! Value 
|-
| File Name || TC_bh3_freq
|-
| File Type || .log 
|-
| Calculation Type || FREQ 
|-
| Calculation Method || RB3LYP 
|-
| Basis Set || 6-31G(d,p)
|-
| Energy || -26.61532358 a.u.
|-
| RMS Gradient Norm || 0.00008198 a.u. 
|-
| Dipole Moment || 0.00 D 
|-
| Point Group || CS
|}

<pre>
Low frequencies ---    0.0005    0.0005    0.0011   33.8055   41.5584   43.6982
Low frequencies --- 1163.5017 1213.4677 1213.5865
</pre>

The first line of the frequencies are far higher than the required low frequency values. Therefore, the optimisation calculations were performed again by constraining the BH<sub>3</sub> geometry to D<sub>3H</sub>.

====Optimisation using D<sub>3H</sub> point group====
 
[[https://wiki.ch.ic.ac.uk/wiki/images/b/b5/TC_bh3_freq3.log BH<sub>3</sub> (constrained geometry) frequency analysis log file ]]

{| class="wikitable"
|-
|+ Summary Table
! Property !! Value 
|-
| File Name || TC_bh3_freq3
|-
| File Type || .log 
|-
| Calculation Type || FREQ 
|-
| Calculation Method || RB3LYP 
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Energy ||  -26.61532363 a.u.
|-
| RMS Gradient Norm || 0.00000291 a.u. 
|-
| Dipole Moment || 0.00 D 
|-
| Point Group || D3H
|}

<pre>
Item               Value     Threshold  Converged?
 Maximum Force            0.000006     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000023     0.001800     YES
 RMS     Displacement     0.000015     0.001200     YES
 Predicted change in Energy=-2.012165D-10
 Optimization completed.
</pre>

<pre>
 Low frequencies ---   -0.9432   -0.8611   -0.0054    5.7455   11.7246   11.7625
 Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>

{| class="wikitable"
|-
! No. !! Form of vibration || Frequency || Intensity || Symmetry D<sub>3H</sub> point group 
|-
| 1 || [[File: TC BH3 Freq 1.gif|thumb|center|all the hydrogens move forward and back together in a concerted motion and the boron atom move backwards and forwards in the opposite direction to the hydrogen atoms]] || 1163 || 93 || A<sub>2</sub>''
|-
| 2 || [[File:TC BH3 Freq 2.gif|thumb|center|two of the hydrogens move in a scissoring fashion, the last hydrogen moves slightly up and down together with the boron atom ]] || 1213 || 14 || E'  
|-
| 3 || [[File:TC BH3 Freq 3.gif|thumb|center|the three hydrogens all move left and right, resulting in two sets of scissoring motions]] || 1213 || 14|| E'
|-
| 4|| [[File:TC BH3 Freq 4.gif|thumb|center|the hydrogen atoms all move in and out together in a concerted motion and the boron atom is stationary]] || 2582 || 0 || A<sub>1</sub>'
|-
| 5|| [[File:TC BH3 Freq 5.gif|thumb|center|two of the hydrogens moves in a asymmetric stretching fashion. The remaining hydrogen is relatively stationary with the boron atom moving slightly to the sides]] || 2715|| 126 || E'
|-
| 6 || [[File:TC BH3 Freq 6.gif|thumb|center|two of the hydrogens move in a symmetrical stretching fashion with the last hydrogen moving in a asymmetrical stretching manner relative to the other two hydrogens. The boron moves slightly to the sides.]] || 2715||126 || E'
|}

===IR spectrum===

[[File:BH3 IR spectrum.jpeg]]

There are two sets of two vibrations with the same frequencies and therefore, they would overlap and only appear as a single peak. In addition, the vibration which is totally symmetrical does not have a dipole and hence does not show up in the IR spectrum. These factors result in the IR spectrum only showing 3 peaks where there are actually six vibrations.

===Frequency analysis for GaBr<sub>3</sub>===

[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26941 GaBr<sub>3</sub> frequency analysis D-space link]]
[[https://wiki.ch.ic.ac.uk/wiki/images/2/2c/TC_bbr3_freq.log GaBr<sub>3</sub> frequency analysis log file]] 

{| class="wikitable"
|-
! No. !! Form of vibration || Frequency (cm<sup>-1</sup>) || Intensity || Symmetry D<sub>3H</sub> point group 
|-
| 1 || [[File:TC GaBr3 1.gif|thumb|center|two of the bromines moves in a asymmetric stretching fashion. The remaining hydrogen is relatively stationary with the gallium atom moving slightly to the sides]] || 76 || 3|| E'
|-
| 2 || [[File:TC GaBr3 2.gif|thumb|center|two of the bromines move in a scissoring fashion, the last bromine moves slightly up and down together with the gallium atom ]] || 76 || 3 || E'  
|-
| 3 || [[File:TC GaBr3 3.gif|thumb|center|all the bromines move forward and back together in a concerted motion and the gallium atom move backwards and forwards in the opposite direction to the hydrogen atoms]]|| 100 || 10|| A<sub>2</sub>''
|-
| 4|| [[File:TC GaBr3 4.gif|thumb|center|the bromine atoms all move in and out together in a concerted motion and the gallium atom is stationary]] || 197  || 0|| A<sub>1</sub>'
|-
| 5|| [[File:TC GaBr3 5.gif|thumb|center|two of the bromines moves in a asymmetric stretching fashion. The remaining bromine is relatively stationary with the gallium atom moving slightly to the sides]] || 316 || 57 || E'
|-
| 6 || [[File:TC GaBr3 6.gif|thumb|center|two of the bromines move in a symmetrical stretching fashion with the last bromine moving in a asymmetrical stretching manner relative to the other two bromines. The gallium moves slightly to the sides.]] || 316 ||57 || E'
|}

<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 lowest "real" normal mode of vibrations are the 76 cm<sup>-1</sup> frequency vibrations, corresponding to the first two degenerate E' modes of vibration.

====IR spectrum====

[[File:GaBr3 IR spectrum.jpeg]]

There are six vibrational modes but only three peaks visible on the IR spectrum. This is because some of the vibrations are degenerate in energy (vibration 1 & 2 and vibrations 5 & 6) and so show up as a single peak. The forth vibration has no particular dipole moment, as such does not have a signal in the IR spectrum.

===Vibration comparisons===

{| class="wikitable"
|-
! No. !! BH<sub>3</sub> vibrational frequencies (cm<sup>-1</sup>)|| GaBr<sub>3</sub> vibrational frequencies (cm<sup>-1</sup>) 
|-
| 1 || 1164 || 76
|-
| 2 || 1213 || 76
|-
| 3 || 1213 || 100
|-
| 4 || 2582|| 197
|-
| 5 || 2715|| 316
|-
| 6 || 2715 || 316
|}

The large differences in frequency values of BH<sub>3</sub> compared to GaBr<sub>3</sub> indicate that the GaBr<sub>3</sub> bonds are much weaker. As suggested before the large difference between electronegativities contribute to enhanced electrostatic attraction between B and H and hence affording stronger bonds.

Although the two spectra are similar in that they both have three peaks, an reordering of modes can also be observed, in particular, the A<sub>2</sub> level for GaBr<sub>3</sub> higher in energy then its E' energy level, whereas the opposite can be seen for the BH<sub>3</sub> molecule. This is likely to be due to differences in the size of the atoms. For example, in the BH<sub>3</sub> molecule, the central atom boron is heavier than hydrogens and therefore, the substituent atoms, i.e. hydrogens, move with the central atom staying relatively stationary for the A<sub>2</sub> level. The case is reversed for the GaBr<sub>3</sub> molecule, in that the central atom is lighter than its substituent atoms and thus, the central atom vibrate more with the heavier bromine substituents relatively more stationary in the A<sub>2</sub> level. This difference lead to the shift in relative energies compared to their relative E' levels and hence a reordering can be seen. The vibrational frequency can be calculated using the equation:

<math>
v= 2 \pi{\sqrt{\frac{k}{m}}}</math>

where k is the force constant for the restoring force: <math> \mathbf{F}=-k\mathbf{x} </math>

Therefore, when comparing a molecule's vibrational frequency, because a particular vibrational motion would need less force to restore, the force constant would be lower and hence the vibrational frequency would be less.

In addition, it can be seen that for both the spectra, two modes lie fairly close together, the A<sub>2</sub> and E', and another two modes, the A<sub>1</sub>' and E' lie fairly close together but higher in energy. This is because for the first set of vibrations the type of vibration are all bending of the bonds, whereas, in the higher energy set of frequencies the type of vibration are all stretching vibrations. Similar type of vibration leads to similar vibrational frequencies, therefore, two sets of two modes of vibration can be seen, where one set of vibrations is close to each other and another is close to each other but higher in energy. 

Nevertheless, both IR spectra exhibit the same number of modes, this is due to both molecules having the same symmetry and same number of atoms (where vibrational modes is governed by 3N-6, N=4).

The same method and basis for both the optimisation and frequency analysis much be used as the assumptions used by the one may not be compatible with the other and for both to afford correctly calculated values, the same inputs needs to be used.

The purpose of carrying out an frequency analysis is that, by investigating the frequency using computational methods, the result can be used to compare with experimental results and thus offering a higher reliability of the overall result. Also, it may be in some cases that, experimental means are not easily accessible and so computational calculations can be seen as a possible alternative method of investigation.

The top line of the low frequencies represent the translational and rotational degrees of freedom, corresponding to motion in the x, y and z axes. The bottom line of low frequencies represent the vibrational frequencies.

==Molecular Orbitals of BH<sub>3</sub>==

A population analysis was carried out using the previously optimised BH<sub>3</sub> molecule with 631G(d,p) with keywords "pop=full, opt=tight, int=ultrafine, scf=conver=9"

[[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27319 BH<sub>3</sub> population analysis D-space link]]
[[https://wiki.ch.ic.ac.uk/wiki/images/5/52/TC_BH3_MO_2.log BH<sub>3</sub> population analysis log file]]

[[File:BH3 MO diagram (JPEG).jpg]]

The LCAO MOs as predicted by the MO theory are similar to the real MO as computed by gaussian. This indicates that, while MO theory may be limited in cases where the molecule is relatively complicated, for the case of simple molecules such as BH<sub>3</sub>, MO theory is generally accurate.

==NH<sub>3</sub> Computational Analysis==

Computational study of the NH<sub>3</sub> molecule was carried out in order to perform an NBO analysis. 

===Optimisation===

The optimisation of the NH<sub>3</sub> molecule was performed using the 6-31G(d,p) basis set with the keywords "opt=tight, int=ultrafine, scf=conver=9"

[[https://wiki.ch.ic.ac.uk/wiki/images/3/37/TC_NH3_631g_d_p_int_scf.log NH<sub>3</sub> optimisation log file]]

{| class="wikitable"
|-
|+ Summary Table
! Property !! Value 
|-
| File Name || NH3_opt_631G_d_p
|-
| File Type || .log 
|-
| Calculation Type || FOPT 
|-
| Calculation Method || RB3LYP 
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Energy ||  -56.55776873 a.u.
|-
| RMS Gradient Norm || 0.00000323 a.u. 
|-
| Dipole Moment || 1.85 D 
|-
| Point Group || C3V
|-
|Computational Time || 29.8 Sec
|}

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000006     0.000015     YES
 RMS     Force            0.000004     0.000010     YES
 Maximum Displacement     0.000012     0.000060     YES
 RMS     Displacement     0.000008     0.000040     YES
 Predicted change in Energy=-9.846059D-11
 Optimization completed.
    -- Stationary point found.
</pre>

===Frequency Analysis===

The frequency analysis of the NH<sub>3</sub> molecule was carried out using the above optimised molecule with the keywords "opt=tight, int=ultrafine, scf=conver=9".

[[https://wiki.ch.ic.ac.uk/wiki/images/2/24/TC_NH3_freq_int_scf.log NH<sub>3</sub>Frequency Analysis log file]]

<pre>
 Low frequencies ---   -0.0129   -0.0016   -0.0012    7.0768    8.0933    8.0936
 Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

{| class="wikitable"
|-
|+Table of NH<sub>3</sub> Vibrational Frequencies
! No. !! Form of vibration !! Frequency (cm<sup>-1</sup>)|| Intensity || Symmetry of C<sub>1</sub> point group 
|-
| 1 || [[File:TC NH3 freq 1.gif|thumb|center|all the hydrogen atoms move downwards in a concerted motion]] || 1089 || 145 || A1
|-
| 2 || [[File:TC NH3 freq 2.gif|thumb|center|the hydrogens move in a scissoring motions with the nitrogen relatively stationary]] || 1694 || 14 || E
|-
| 3|| [[File:TC NH3 freq 3.gif|thumb|center|two of the hydrogens move in a scissoring fashion with the last hydrogen moving up and down]] || 1694 || 14 || E
|-
| 4 || [[File:TC NH3 freq 4.gif|thumb|center|all the hydrogens exhibit symmetrical stretching with the nitrogen atom relatively stationary]] || 3461 || 1 || A1
|-
| 5|| [[File:TC NH3 freq 5.gif|thumb|center|two of the hydrogens exhibit asymmetrical stretching and the remaining hydrogen relatively stationary]] || 3590||0|| E   
|-
| 6|| [[File:TC NH3 freq 6.gif|thumb|center|two of the hydrogens vibrate in a symmetrical manner with the remaining hydrogen vibrating in an asymmetrical manner relative to the other two]] || 3590|| 0 || E
|}

====IR Spectrum====

[[File:TC NH3 IR.jpeg|450px]]

NH<sub>3</sub> IR spectrum shows two peaks only, whereas there are 6 modes of vibration. This is due to two of the modes of vibration having similar vibrations and the fact that 3 of the modes have no dipole moment and hence does not give a signal in the IR spectra.

===NH3 NBO===
The NBO analysis was carried out using the above optimised molecule with the keywords "pop=full, opt=tight, int=ultrafine, scf=conver=9"

[[https://wiki.ch.ic.ac.uk/wiki/images/e/e8/TC_NH3_MO_int_scf.log NH<sub>3</sub> MO analysis]]

====Colour Atom by Charge====

[[File:TC NH3 NBO.tiff|300px]]

It can be seen that the majority of the negative charge is resident on the nitrogen atom. This is expected as nitrogen is the atom with the relatively higher electronegativity value. 

'''Charge range: -1.125 to 1.125'''

====Charge Number Shown====

[[File:TC NH3 NBO charges.jpg|300px]]

The charge number for the various atoms are shown above (N: -1.125; H: 0.375 each). It can also be seen that the sum of all the charges adds up to zero, in accordance with NH<sub>3</sub> being a neutral molecule.

====Information from the .log file====

Additional information from the NBO analysis .log file were also investigated.

=====Summary of natural population analysis=====

<pre>
    Natural Population 
                Natural  -----------------------------------------------
    Atom  No    Charge         Core      Valence    Rydberg      Total
 -----------------------------------------------------------------------
      N    1   -1.12514      1.99982     6.11104    0.01429     8.12514
      H    2    0.37505      0.00000     0.62250    0.00246     0.62495
      H    3    0.37505      0.00000     0.62250    0.00246     0.62495
      H    4    0.37505      0.00000     0.62250    0.00246     0.62495
 =======================================================================
   * Total *    0.00000      1.99982     7.97852    0.02166    10.00000
</pre>

The electron density is outlined above and the majority of electrons are seen to be from nitrogen, as the nitrogen donates electron density and act of a Lewis base whereas hydrogen accepts electrons and act as a Lewis acid.

=====Bond orbital/Coefficient/Hydride=====

<pre>
       (Occupancy)   Bond orbital/ Coefficients/ Hybrids
 ---------------------------------------------------------------------------------
     1. (1.99909) BD ( 1) N   1 - H   2  
                ( 68.83%)   0.8297* N   1 s( 24.86%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000  0.0000
                                            0.0000  0.8155  0.0277 -0.2910  0.0052
                                            0.0000  0.0000 -0.0281 -0.0087  0.0014
                ( 31.17%)   0.5583* H   2 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000  0.0000 -0.0289  0.0072
     2. (1.99909) BD ( 1) N   1 - H   3  
                ( 68.83%)   0.8297* N   1 s( 24.86%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000 -0.7062
                                           -0.0239 -0.4077 -0.0138 -0.2910  0.0052
                                            0.0076  0.0243  0.0140  0.0044  0.0014
                ( 31.17%)   0.5583* H   3 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000  0.0250  0.0145  0.0072
     3. (1.99909) BD ( 1) N   1 - H   4  
                ( 68.83%)   0.8297* N   1 s( 24.86%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000  0.7062
                                            0.0239 -0.4077 -0.0138 -0.2910  0.0052
                                           -0.0076 -0.0243  0.0140  0.0044  0.0014
                ( 31.17%)   0.5583* H   4 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000 -0.0250  0.0145  0.0072
     4. (1.99982) CR ( 1) N   1           s(100.00%)
                                            1.0000 -0.0002  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
     5. (1.99721) LP ( 1) N   1           s( 25.38%)p 2.94( 74.52%)d 0.00(  0.10%)
                                            0.0001  0.5036 -0.0120  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.8618 -0.0505
                                            0.0000  0.0000  0.0000  0.0000 -0.0310
</pre>

The information highlights that the electrodensity in the bond are mostly from the nitrogen (~70% from nitrogen, ~30 from H)

=====Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis=====

<pre>
 Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis

     Threshold for printing:   0.50 kcal/mol
</pre>

As the threshold for printing is below 20 kcal/mol, the information about interaction from bonding NBOs into non-bonding or antibonding orbitals is not of interest.

=====Natural Bond Orbital Summary=====

<pre>
 Natural Bond Orbitals (Summary):

                                                            Principal Delocalizations
           NBO                        Occupancy    Energy   (geminal,vicinal,remote)
 ====================================================================================
 Molecular unit  1  (H3N)
     1. BD (   1) N   1 - H   2          1.99909    -0.60417   
     2. BD (   1) N   1 - H   3          1.99909    -0.60417   
     3. BD (   1) N   1 - H   4          1.99909    -0.60417   
     4. CR (   1) N   1                  1.99982   -14.16768   
     5. LP (   1) N   1                  1.99721    -0.31757  16(v),20(v),24(v),17(v)
                                                    21(v),25(v)
</pre>

The relative energies of the N-H bonds, the lone pair and core orbitals can be seen. The core orbital is very higher in energy and as such are often left off the MO diagram.

==NH<sub>3</sub>BH<sub>3</sub> Computational Anlysis==
The optimisation, frequency analysis were completed in order to calculated the association energy for combining a molecule of NH<sub>3</sub> with one of BH<sub>3</sub>.
 
===Optimisation===
The optimisation of NH<sub>3</sub>BH<sub>3</sub> was completed using the basis set 6-31G(d,p) with the keywords "opt=tight, int=ultrafine, scf=conver=9".

[[https://wiki.ch.ic.ac.uk/wiki/images/a/a4/TC_NH3BH3_opt_631g_d_p_opt_int_scf.log NH<sub>3</sub>BH<sub>3</sub> optimisation analysis file]]

{| class="wikitable"
|+Summary Table
|-
! Property !! Value 
|-
| File Name || TC_NH3BH3_opt_631g_d_p_opt_int_scf
|-
| File Type || .log 
|-
| Calculation Type || FOPT 
|-
| Calculation Method || RB3LYP 
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Spin || Singlet
|-
| Energy ||  -83.22468906 a.u.
|-
| RMS Gradient Norm || 0.00000124 a.u. 
|-
| Dipole Moment || 5.56 D 
|-
| Point Group || C1
|-
| Calculation time || 3 min 53.3 sec
|}

<pre>
  Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000015     YES
 RMS     Force            0.000001     0.000010     YES
 Maximum Displacement     0.000026     0.000060     YES
 RMS     Displacement     0.000009     0.000040     YES
 Predicted change in Energy=-8.958388D-11
 Optimization completed.
    -- Stationary point found.
</pre>

===Frequency Analysis===
The frequency analysis of NH<sub>3</sub>BH<sub>3</sub> was carried out using the above optimised molecule with the keywords "opt=tight, int=ultrafine, scf=conver=9".

[[https://wiki.ch.ic.ac.uk/wiki/images/d/d9/TC_NH3BH3_freq_opt_int_scf.log NH<sub>3</sub>BH<sub>3</sub> Frequency Analysis file]]

<pre>
 Low frequencies ---   -6.5596   -2.8712   -0.0003    0.0008    0.0009    5.6712
 Low frequencies ---  263.5388  632.9505  638.4074
</pre>

{| class="wikitable"
|-
! No. !! Form of the vibration || Frequency (cm<sup>-1</sup>) || Intensity
|-
| 1 || [[File:TC NH3BH3 freq 1.gif|thumb|center| The boron and nitrogen hydrogens all rotate forwards and backwards around the central boron-hydrogen bond in opposite directions to one another. The central atoms remain stationary]] || 264 || 0   
|-
| 2 || [[File:TC NH3BH3 freq 2.gif|thumb|center| The central boron and nitrogen bond stretches with the hydrogen following suit, but nevertheless, stationary relative to their central atoms]] || 633 || 14   
|-
| 3 || [[File:TC NH3BH3 freq 3.gif|thumb|center| The hydrogen atoms perform scissoring action with hydrogen from the other central atom in a symmetrical manner]] || 638 || 4 
|-
| 4 ||[[File:TC NH3BH3 freq 4.gif|thumb|center|The hydrogen atoms perform scissoring action with hydrogen from the other central atom in an asymmetrical manner]] || 638 || 4
|-
| 5 ||[[File:TC NH3BH3 freq 5.gif|thumb|center| Two of the hydrogen atoms from the boron and nitrogen atom perform symmetrical scissoring and the remaining hydrogen perform symmetrical scissoring but in an asymmetrical manner to the other 4]] || 1069 || 41
|-
| 6 ||[[File:TC NH3BH3 freq 6.gif|thumb|center| The hydrogen atoms all vibrate to the left and right in a concerted manner]] || 1069|| 41
|-
| 7 ||[[File:TC NH3BH3 freq 7.gif|thumb|center| The boron hydrogens move in and out together in a concerted fashion whereas the nitrogen and its hydrogens remain stationary]] || 1196 || 109
|-
| 8 ||[[File:TC NH3BH3 freq 8.gif|thumb|center| Two of the boron hydrogens move in a scissoring motion with the remaining hydrogen moving perpendicular to the other two, whereas the nitrogen and its hydrogens remain stationary]] || 1204 || 3
|-
| 9 ||[[File:TC NH3BH3 freq 9.gif|thumb|center| Scissoring motion was performed by two of the boron hydrogens with the remaining hydrogen moving in a different axis to the other two, whereas the nitrogen and its hydrogens remain stationary]] || 1204 || 3
|-
| 10 ||[[File:TC NH3BH3 freq 10.gif|thumb|center| The nitrogen hydrogens move in and out together in a concerted fashion whereas the boron and its hydrogens remain stationary]] || 1329 || 114
|-
| 11 ||[[File:TC NH3BH3 freq 11.gif|thumb|center| Two of the boron hydrogens move in a scissoring motion with the remaining hydrogen moving perpendicular to the other two, whereas the nitrogen and its hydrogens remain stationary]] || 1676 || 28
|-
| 12 ||[[File:TC NH3BH3 freq 12.gif|thumb|center| Scissoring motion was performed by two of the nitrogen hydrogens with the remaining hydrogen moving in a different axis to the other two, whereas the boron and its hydrogens remain stationary]] || 1676 || 28
|-
| 13 ||[[File:TC NH3BH3 freq 13.gif|thumb|center| The boron hydrogen atoms all undergo concerted symmetrical stretching. The boron atom as well as the nitrogen and its hydrogens remain stationary]] || 2472 || 67
|-
| 14 ||[[File:TC NH3BH3 freq 14.gif|thumb|center| Two of the boron hydrogens exhibit asymmetric stretching with the remaining hydrogen and the boron atom moving slightly to compensate for the stretching. The nitrogen atom and its hydrogens are relatively stationary]] || 2532 || 231
|-
| 15 ||[[File:TC NH3BH3 freq 15.gif|thumb|center| Two of the boron hydrogens perform symmetrical stretching with the remaining hydrogen exhibiting an asymmetric stretching pattern compared to the other two boron hydrogens. The nitrogen atom and its hydrogens remain stationary ]] || 2532 || 231
|-
| 16 ||[[File:TC NH3BH3 freq 16.gif|thumb|center| The nitrogen hydrogen atoms all undergo concerted symmetrical stretching. The nitrogen atom as well as the boron and its hydrogens remain stationary]] || 3464 || 3
|-
| 17 ||[[File:TC NH3BH3 freq 17.gif|thumb|center| Two of the nitrogen hydrogens exhibit asymmetric stretching with the remaining hydrogen and the nitrogen atom moving slightly to compensate for the stretching. The boron atom and its hydrogens are relatively stationary]] || 3581 || 28
|-
| 18 ||[[File:TC NH3BH3 freq 18.gif|thumb|center| Two of the nitrogen hydrogens perform symmetrical stretching with the remaining hydrogen exhibiting an asymmetric stretching pattern compared to the other two nitrogen hydrogens. The boron atom and its hydrogens remain stationary ]] || 3581 || 28
|}

====NH<sub>3</sub>BH<sub>3</sub> IR Spectrum====

Below is the IR spectrum from the frequency analysis calculations.

[[File:TC NH3BH3 IR spectrum.jpeg|450px]]

===Association Energy===

An analysis of the association energy for combining a molecule of NH<sub>3</sub> with one of BH<sub>3</sub> is outlined below:

{| class="wikitable"
|+ Table of Reactant and Product Energies
|-
!Molecule !! Energy (a.u.)
|-
|BH<sub>3</sub> || -26.61532358 
|-
|NH<sub>3</sub> || -56.55776873
|-
|NH<sub>3</sub>BH<sub>3</sub> || -83.22468906
|}

The bond energy is the energy difference between the reactants and products. This can be calculated according to the equation:

<math>
\Delta E = E(NH_3BH_3) - (E(BH_3) + E(NH_3))
</math>

<math>
\Delta E = -83.22468906 (a.u.) - ((-26.61532358  (a.u.)) + (-56.55776873 (a.u.)))
</math>

<math>
\Delta E = -0.05159675 (a.u.)
</math>

The energy value can be converted from AU to kJ/mol by multiplying the AU energy value by N<sub>a</sub> and a factor of 4.359810x10<sup>-18</sup> and dividing by 1000:

<math>
\Delta E = -135.49 kJ/mol
</math>

The calculated bond energy is reasonable as it is within the range of normal bond energies, i.e. within the range of ~100 kJ/mol - ~500kJ/mol. In addition, the calculated value is negative, which indicate that the process of forming NH<sub>3</sub> is favourable and therefore spontaneous process. The bond energy is +135.49 kJ/mol.

==References==
<references />