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Rep:Mod:inorganicismybestfriend

2014-03-07T16:58:39Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.

{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

Due to the rule of 3N-6, where N is the number of atoms, the number of vibration modes of four isomer are all 18. However, not all the modes are IR-active. Only those vibrations with changes in overall dipole moment are active in IR spectrum. The more symmetric of the molecule structure, the easier that dipole moments could cancel out during the vibration. If the overall dipole moment is zero, the mode is then considered to be IR inactive that could not be shown on the IR spectrum. The table above has indicated that isomer 1 and isomer 3 are the molecules which owns the most number of inactive modes. Therefore, it could be deducted that isomer 1 and isomer 3 present less peaks on the IR spectra than the others due to the highly symmetric structures.

===Some comparisons between vibration frequencies of different isomers at similar mode===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Cis_mode_12.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Cis_mode_15.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

==MO analysis of the most stable Isomer==

The HPC output Log. file could be check through {{DOI|10042/27798}}

The information of calculation is summarized in the '''Table 17'''.

[[image:Trans_mo.PNG|thumb|left|350px|'''Table 17''' Calculation of MO]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.
|}

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T16:57:45Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.

{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

due to the rule of 3N-6 where N is the number of atoms, the number of vibration modes of four isomer are all 18. However, not all the modes are IR-active. Only those vibrations with changes in overall dipole moment are active in IR spectrum. The more symmetric of the molecule structure, the easier that dipole moments could cancel out during the vibration. If the overall dipole moment is zero, the mode is then considered to be IR inactive that could not be shown on the IR spectrum. The table above has indicated that isomer 1 and isomer 3 are the molecules which owns the most number of inactive modes. Therefore, it could be deducted that isomer 1 and isomer 3 present less peaks on the IR spectra than the others due to the highly symmetric structures.

===Some comparisons between vibration frequencies of different isomers at similar mode===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Cis_mode_12.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Cis_mode_15.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

==MO analysis of the most stable Isomer==

The HPC output Log. file could be check through {{DOI|10042/27798}}

The information of calculation is summarized in the '''Table 17'''.

[[image:Trans_mo.PNG|thumb|left|350px|'''Table 17''' Calculation of MO]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.
|}

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T16:55:56Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

due to the rule of 3N-6 where N is the number of atoms, the number of vibration modes of four isomer are all 18. However, not all the modes are IR-active. Only those vibrations with changes in overall dipole moment are active in IR spectrum. The more symmetric of the molecule structure, the easier that dipole moments could cancel out during the vibration. If the overall dipole moment is zero, the mode is then considered to be IR inactive that could not be shown on the IR spectrum. The table above has indicated that isomer 1 and isomer 3 are the molecules which owns the most number of inactive modes. Therefore, it could be deducted that isomer 1 and isomer 3 present less peaks on the IR spectra than the others due to the highly symmetric structures.

===Some comparisons between vibration frequencies of different isomers at similar mode===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Cis_mode_12.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Cis_mode_15.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

==MO analysis of the most stable Isomer==

The HPC output Log. file could be check through {{DOI|10042/27798}}

The information of calculation is summarized in the '''Table 17'''.

[[image:Trans_mo.PNG|thumb|left|350px|'''Table 17''' Calculation of MO]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.
|}

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T16:44:26Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Cis_mode_12.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Cis_mode_15.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

==MO analysis of the most stable Isomer==

The HPC output Log. file could be check through {{DOI|10042/27798}}

The information of calculation is summarized in the '''Table 17'''.

[[image:Trans_mo.PNG|thumb|left|350px|'''Table 17''' Calculation of MO]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.
|}

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T16:40:36Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Cis_mode_12.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Cis_mode_15.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

==MO analysis of the most stable Isomer==

[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.
|}

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T16:39:17Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Cis_mode_12.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Cis_mode_15.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

The HPC output Log. file could be check through {{DOI|10042/27796}}

==MO analysis of the most stable Isomer==

[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.
|}

=Reference=
<references/>

File:Cis mode 15.gif

2014-03-07T16:38:19Z

Tw2011:

File:Cis mode 12.gif

2014-03-07T16:38:18Z

Tw2011:

Rep:Mod:inorganicismybestfriend

2014-03-07T16:37:26Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

The HPC output Log. file could be check through {{DOI|10042/27796}}

==MO analysis of the most stable Isomer==

[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.
|}

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T16:36:56Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

The HPC output Log. file could be check through {{DOI|10042/27796}}

==MO analysis of the most stable Isomer==

[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.
|
}

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T16:36:17Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

The HPC output Log. file could be check through {{DOI|10042/27796}}

==MO analysis of the most stable Isomer==

[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T16:33:14Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>CIS_br.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

The HPC output Log. file could be check through {{DOI|10042/27796}}

==MO analysis of Isomer 3==

[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.

=Reference=
<references/>

File:CIS br.mol

2014-03-07T16:32:02Z

Tw2011: uploaded a new version of "File:CIS br.mol"

Rep:Mod:inorganicismybestfriend

2014-03-07T16:23:05Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

The HPC output Log. file could be check through {{DOI|10042/27796}}

==MO analysis of Isomer 3==

[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 3'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" |This is an '''overall strongly bonding''' orbital. There are only strong through bond bonding and through space weak bonding characters are found. The electron density of the bonding orbital is delocalized over the whole bridge. Overall, this MO interaction is a strong bonding interaction.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. The p orbitals of terminal halides overlap with p orbitals on center Al in right orientation result in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonded, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center aluminum atoms and p orbitals of the two terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This is an '''overall strongly anti-bonding''' orbital as indicated. In this MO, strong through bond antibonding and weak through space antibonding could be found without any bonding interactions. An angular node plane is in this MO . The MO is not delocalized. The aluminum has a bigger P orbital than Cl and Br due to having less electronegativity than chlorine and bromine. This MO has a very high energy, hence the less electronegativity that aluminum, contributes more to the MO. Overall, the MO has the strongest antibonding interactions in the five chose MOs.

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-07T15:26:50Z

Tw2011: /* The frequency analysis of four isomers */

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

In this set of modes, two bridging bromides stretching mode has a lower frequency than one bridging bromide and one bridging chloride mode. Because the Al-Br has a lower vibration frequency than Al-Cl, which is due to weaker bond property, therefore, the isomer with four Al-Br stretchings (two bridging bromides) should have a lower vibration frequency than two Al-Br and two Al-Cl stretchings.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

In this set of modes, the comparison is made between an isomer with two bridging chloride and one bridging chloride with one bridging bromide. The observation is that the less bridging bromide in the isomer, the larger the vibration frequency which indicates an overall stronger bond.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

In this set of modes, both isomers have the same number of bridging chlorine atoms. The difference is that two terminal bromine atoms are placed in a ''tran'' or ''cis'' manner. The two bromine sits in ''cis'' position has a slightly higher frequency than ''trans''. Frequency is directly proportional to the bond strength. It indicates that the Al-Br bond strength are very similar.

==MO analysis of isomer 1==

[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

The HPC output Log. file could be check through {{DOI|10042/27796}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 1'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" | This MO is for the energy level 31. Here, only strong through bond bonding are showed. And there is no node in this MO. In the same time, the electron density of the bonding orbital is delocalized over the whole bridge. In conclusion, this MO has strong bonding interactions.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. And the p orbitals of terminal halides overlap with p orbitals on center Al in right orientation causing in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonding, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center Al atoms and p orbitals of terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This MO is for the energy level 60. Here, strong through bond antibonding and weak through space antibonding are showed .No bonding interaction could be discovered. An angular node plane is in this MO . As well as , this MO is not delocalized at all. Al owns bigger P orbital than Cl and Br. Due to Al is less electronegative than Cl and Br. This MO is in high energy. Finally, the less electronegative Al shows more to the MO. Eventally, this MO owns the strongest antibonding interactions than others MOs showe above.
|}

=Reference=
<references/>

File:Mo 57 a.png

2014-03-06T21:56:31Z

Tw2011: uploaded a new version of "File:Mo 57 a.png"

File:Mo 56 a.png

2014-03-06T21:56:31Z

Tw2011: uploaded a new version of "File:Mo 56 a.png"

File:Mo 40 a.png

2014-03-06T21:56:31Z

Tw2011: uploaded a new version of "File:Mo 40 a.png"

File:Mo 38 a.png

2014-03-06T21:56:30Z

Tw2011: uploaded a new version of "File:Mo 38 a.png"

Rep:Mod:inorganicismybestfriend

2014-03-06T21:26:36Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

MO
[[image:Trans_mo.PNG|left|350px| ]]

The HPC output Log. file could be check through {{DOI|10042/27798}}

The HPC output Log. file could be check through {{DOI|10042/27796}}

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 1'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" | This MO is for the energy level 31. Here, only strong through bond bonding are showed. And there is no node in this MO. In the same time, the electron density of the bonding orbital is delocalized over the whole bridge. In conclusion, this MO has strong bonding interactions.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. And the p orbitals of terminal halides overlap with p orbitals on center Al in right orientation causing in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonding, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center Al atoms and p orbitals of terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This MO is for the energy level 60. Here, strong through bond antibonding and weak through space antibonding are showed .No bonding interaction could be discovered. An angular node plane is in this MO . As well as , this MO is not delocalized at all. Al owns bigger P orbital than Cl and Br. Due to Al is less electronegative than Cl and Br. This MO is in high energy. Finally, the less electronegative Al shows more to the MO. Eventally, this MO owns the strongest antibonding interactions than others MOs showe above.
|}

=Reference=
<references/>

File:Trans mo.PNG

2014-03-06T21:24:17Z

Tw2011:

Rep:Mod:inorganicismybestfriend

2014-03-06T21:23:58Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

MO
[[image:|left|350px| ]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 1'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_38_a.png|left|300px|center]] || colspan="2" | This MO is for the energy level 31. Here, only strong through bond bonding are showed. And there is no node in this MO. In the same time, the electron density of the bonding orbital is delocalized over the whole bridge. In conclusion, this MO has strong bonding interactions.
|-
| 40 || [[image:Mo_40_a.png|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. And the p orbitals of terminal halides overlap with p orbitals on center Al in right orientation causing in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonding, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_56_a.png|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_57_a.png|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center Al atoms and p orbitals of terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60b.PNG|left|300px|]] || This MO is for the energy level 60. Here, strong through bond antibonding and weak through space antibonding are showed .No bonding interaction could be discovered. An angular node plane is in this MO . As well as , this MO is not delocalized at all. Al owns bigger P orbital than Cl and Br. Due to Al is less electronegative than Cl and Br. This MO is in high energy. Finally, the less electronegative Al shows more to the MO. Eventally, this MO owns the strongest antibonding interactions than others MOs showe above.
|}

=Reference=
<references/>

File:Mo 60 a.png

2014-03-06T21:20:50Z

Tw2011:

File:Mo 57 a.png

2014-03-06T21:20:50Z

Tw2011:

File:Mo 56 a.png

2014-03-06T21:20:49Z

Tw2011:

File:Mo 40 a.png

2014-03-06T21:20:49Z

Tw2011:

File:Mo 38 a.png

2014-03-06T21:20:48Z

Tw2011:

Rep:Mod:inorganicismybestfriend

2014-03-06T20:54:59Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

MO
[[image:|left|350px| ]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 1'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_mode31a.PNG|left|300px|center]] || colspan="2" | This MO is for the energy level 31. Here, only strong through bond bonding are showed. And there is no node in this MO. In the same time, the electron density of the bonding orbital is delocalized over the whole bridge. In conclusion, this MO has strong bonding interactions.
|-
| 40 || [[image:Mo_mode40a.PNG|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. And the p orbitals of terminal halides overlap with p orbitals on center Al in right orientation causing in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonding, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_mode56a.PNG|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_mode57a.PNG|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center Al atoms and p orbitals of terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60a.PNG|300px|]] || [[image:Mo_mode60b.PNG|left|300px|]] || This MO is for the energy level 60. Here, strong through bond antibonding and weak through space antibonding are showed .No bonding interaction could be discovered. An angular node plane is in this MO . As well as , this MO is not delocalized at all. Al owns bigger P orbital than Cl and Br. Due to Al is less electronegative than Cl and Br. This MO is in high energy. Finally, the less electronegative Al shows more to the MO. Eventally, this MO owns the strongest antibonding interactions than others MOs showe above.
|}

=Reference=
<references/>

Rep:Mod:inorganicismybestfriend

2014-03-06T20:52:53Z

Tw2011: /* The frequency analysis of four isomers */

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

MO
[[image:|left|350px| ]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 1'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_mode31a.PNG|left|300px|center]] || colspan="2" | This MO is for the energy level 31. Here, only strong through bond bonding are showed. And there is no node in this MO. In the same time, the electron density of the bonding orbital is delocalized over the whole bridge. In conclusion, this MO has strong bonding interactions.
|-
| 40 || [[image:Mo_mode40a.PNG|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. And the p orbitals of terminal halides overlap with p orbitals on center Al in right orientation causing in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonding, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_mode56a.PNG|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_mode57a.PNG|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center Al atoms and p orbitals of terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60a.PNG|300px|]] || [[image:Mo_mode60b.PNG|left|300px|]] || This MO is for the energy level 60. Here, strong through bond antibonding and weak through space antibonding are showed .No bonding interaction could be discovered. An angular node plane is in this MO . As well as , this MO is not delocalized at all. Al owns bigger P orbital than Cl and Br. Due to Al is less electronegative than Cl and Br. This MO is in high energy. Finally, the less electronegative Al shows more to the MO. Eventally, this MO owns the strongest antibonding interactions than others MOs showe above.
|}

Rep:Mod:inorganicismybestfriend

2014-03-06T20:52:06Z

Tw2011: /* The frequency analysis of four isomers */

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
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|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
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<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
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The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

MO
[[image:|left|350px| ]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 1'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_mode31a.PNG|left|300px|center]] || colspan="2" | This MO is for the energy level 31. Here, only strong through bond bonding are showed. And there is no node in this MO. In the same time, the electron density of the bonding orbital is delocalized over the whole bridge. In conclusion, this MO has strong bonding interactions.
|-
| 40 || [[image:Mo_mode40a.PNG|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. And the p orbitals of terminal halides overlap with p orbitals on center Al in right orientation causing in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonding, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_mode56a.PNG|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_mode57a.PNG|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center Al atoms and p orbitals of terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60a.PNG|300px|]] || [[image:Mo_mode60b.PNG|left|300px|]] || This MO is for the energy level 60. Here, strong through bond antibonding and weak through space antibonding are showed .No bonding interaction could be discovered. An angular node plane is in this MO . As well as , this MO is not delocalized at all. Al owns bigger P orbital than Cl and Br. Due to Al is less electronegative than Cl and Br. This MO is in high energy. Finally, the less electronegative Al shows more to the MO. Eventally, this MO owns the strongest antibonding interactions than others MOs showe above.
|}

Rep:Mod:inorganicismybestfriend

2014-03-06T20:50:43Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A
The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

MO
[[image:|left|350px| ]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 1'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_mode31a.PNG|left|300px|center]] || colspan="2" | This MO is for the energy level 31. Here, only strong through bond bonding are showed. And there is no node in this MO. In the same time, the electron density of the bonding orbital is delocalized over the whole bridge. In conclusion, this MO has strong bonding interactions.
|-
| 40 || [[image:Mo_mode40a.PNG|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. And the p orbitals of terminal halides overlap with p orbitals on center Al in right orientation causing in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonding, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_mode56a.PNG|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_mode57a.PNG|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center Al atoms and p orbitals of terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60a.PNG|300px|]] || [[image:Mo_mode60b.PNG|left|300px|]] || This MO is for the energy level 60. Here, strong through bond antibonding and weak through space antibonding are showed .No bonding interaction could be discovered. An angular node plane is in this MO . As well as , this MO is not delocalized at all. Al owns bigger P orbital than Cl and Br. Due to Al is less electronegative than Cl and Br. This MO is in high energy. Finally, the less electronegative Al shows more to the MO. Eventally, this MO owns the strongest antibonding interactions than others MOs showe above.
|}

Rep:Mod:inorganicismybestfriend

2014-03-06T20:33:14Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A
The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

MO
[[image:|left|350px| ]]

{| class="wikitable" border="1"
|+ '''Molecular Orbital Analysis of isomer 1'''
! MO number || Structure ||colspan="2" | Analysis
|-
| 38 ) || [[Image:Mo_mode31a.PNG|left|300px|center]] || colspan="2" | This MO is for the energy level 31. Here, only strong through bond bonding are showed. And there is no node in this MO. In the same time, the electron density of the bonding orbital is delocalized over the whole bridge. In conclusion, this MO has strong bonding interactions.
|-
| 40 || [[image:Mo_mode40a.PNG|left|300px|center]] || colspan="2" | This is an '''overall strongly bonding''' orbital. Orthogonal p orbitals on both bridging chlorides and center Al align and overlap together to turn out a strongly bonding region in the middle of the molecule. And the p orbitals of terminal halides overlap with p orbitals on center Al in right orientation causing in strong bonding interaction. Only weak through-space antibonding interactions present between adjacent terminal halides. Overall, it is highly bonding, with a nodal plane in the bridging region.
|-
| 56 || [[image:Mo_mode56a.PNG|left|300px|center]] ||colspan="2" | This is an '''Overall slightly anti-bonding''' orbital. As showed, there are four anti-bonding interactions through the overlap of terminal halide p orbital and s orbital of center Al. And a nodal plane is discovered between the anti-bonding region. There exists weak anti-bonding interaction between bridging halide and center Al, however due to orientation mis-match, the overlap is not pretty strong. Also Weak through-space anti-bonding interaction between two Al and weak through-space bonding interaction between adjacent terminal halides present .
|-
| 57 || [[image:Mo_mode57a.PNG|left|300px|center]] ||colspan="2" | This is an '''overall anti-bonding''' orbital. Bonding region only exist between two center Al atoms and p orbitals of terminal halides. All these interactions are through-space. Anti-bonding overlaps exist between terminal halides and center Al (through bond), and between bridging chloride and center Al (through space). Considering the relatively high energy of this unoccupied MO, the anti-bonding interaction outweighs the bonding interaction, and the MO is anti-bonding overall. Besides, two angular nodes exist in the bridging chloride, which indicates zero electron density around the center bromide.
|-
| 60 || [[image:Mo_mode60a.PNG|300px|]] || [[image:Mo_mode60b.PNG|left|300px|]] || This MO is for the energy level 60. Here, strong through bond antibonding and weak through space antibonding are showed .No bonding interaction could be discovered. An angular node plane is in this MO . As well as , this MO is not delocalized at all. Al owns bigger P orbital than Cl and Br. Due to Al is less electronegative than Cl and Br. This MO is in high energy. Finally, the less electronegative Al shows more to the MO. Eventally, this MO owns the strongest antibonding interactions than others MOs showe above.
|}

Rep:Mod:inorganicismybestfriend

2014-03-06T20:27:21Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
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<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A
The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:Mode_11_isomer_a.gif|400px]]||[[Image:Mode_11_isomer_b.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:Mode_13_isomer_b.gif|400px]]||[[Image:Mode_12_isomer_d.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:Mode_15_isomer_c.gif|400px]]||[[Image:Mode_15_isomer_d.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

File:Mode 15 isomer d.gif

2014-03-06T20:19:38Z

Tw2011:

File:Mode 15 isomer c.gif

2014-03-06T20:19:38Z

Tw2011:

File:Mode 12 isomer d.gif

2014-03-06T20:19:37Z

Tw2011:

File:Mode 13 isomer b.gif

2014-03-06T20:19:37Z

Tw2011:

File:Mode 11 isomer b.gif

2014-03-06T20:19:36Z

Tw2011:

File:Mode 11 isomer a.gif

2014-03-06T20:19:36Z

Tw2011:

Rep:Mod:inorganicismybestfriend

2014-03-06T20:11:15Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A
The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:.gif|400px]]||[[Image:.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 13,12||[[Image:.gif|400px]]||[[Image:.gif|400px]]
|-
| Frequency||257||309
|-
| Intensity||10||2
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:.gif|400px]]||[[Image:.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

Rep:Mod:inorganicismybestfriend

2014-03-06T20:06:21Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A
The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:.gif|400px]]||[[Image:.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer c'''
| align="center" style="background:#f0f0f0;"|'''Isomer d'''
|-
| 15||[[Image:.gif|400px]]||[[Image:.gif|400px]]
|-
| Frequency||421||438
|-
| Intensity||420||411
|-
|
|}

Rep:Mod:inorganicismybestfriend

2014-03-06T20:02:43Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A
The result of frequency is shown in the below table.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''1(D2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''2(C1)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''3(C2h)'''
| align="center" style="background:#f0f0f0;"|''' '''
| align="center" style="background:#f0f0f0;"|'''4(C2v)'''
| align="center" style="background:#f0f0f0;"|''' '''
|-
| Mode||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared||Frequency(cm-1)||Infrared
|-
| 1||15||0||17||0||18||0||17||0
|-
| 2||63||0||56||0||49||0||51||0
|-
| 3||86||0||80||0||73||0||79||0
|-
| 4||87||0||92||1||105||0||99||0
|-
| 5||108||5||107||0||110||0||103||3
|-
| 6||111||0||110||5||117||9||121||13
|-
| 7||126||8||121||8||120||13||123||6
|-
| 8||135||0||149||5||157||0||157||0
|-
| 9||138||7||154||6||160||6||158||5
|-
| 10||163||0||186||1||192||0||194||2
|-
| 11||197||0||211||21||263||0||264||0
|-
| 12||241||100||257||10||280||29||279||25
|-
| 13||247||0||289||48||308||0||309||2
|-
| 14||341||161||384||154||413||149||413||149
|-
| 15||467||347||424||274||421||438||420||411
|-
| 16||494||0||493||107||459||0||461||35
|-
| 17||608||0||574||122||574||0||570||32
|-
| 18||616||332||614||197||579||316||582||278
|-
| Total Number of Inactive Mode:||||11||||4||||11||||6
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Mode'''
| align="center" style="background:#f0f0f0;"|'''Isomer a'''
| align="center" style="background:#f0f0f0;"|'''Isomer b'''
|-
|11 ||[[Image:.gif|400px]]||[[Image:.gif|400px]]
|-
| Frequency||197||263
|-
| Intensity||0||0
|-
|
|}

Rep:Mod:inorganicismybestfriend

2014-03-06T16:28:44Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

For Frequency analysis

The HPC output Log. file could be check through {{DOI|10042/27858}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

Low frequencies --- -0.0057 -0.0054 -0.0044 1.3568 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

Therefore, the minimal structure was found.

The association energy of the most stable isomer is calculated by :

ΔEassociation=E(Isomer 3)-2*E(monomer)= -2352.41631610-2*(-1176.19013679)= -0.03604252 a.u.

The corresponding association energy is -0.03604252 a.u. which is -95 kJ/mol. A negative association energy indicates that the dissociation process is endothermic, so that the dimer is more stable than the monomer. The aluminum has 6 valence electrons which is electron-deficient, however, by accepting an lone pair of electrons from bromine of another monomer that forms a dative bond, the electron deficiency could then be relieved. Therefore, dimer form of the AlBrCl2 is more stable.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|left|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|left|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|left|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A

Rep:Mod:inorganicismybestfriend

2014-03-06T15:04:25Z

Tw2011: /* The frequency analysis of four isomers */

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

<pre> Low frequencies --- -2.4283 -0.0011 0.0014 0.0024 2.8330 2.9094

Low frequencies --- 120.5195 133.8367 185.7804</pre>

It can be observed that we have find the minimal structure.

 

The association energy of the most stable isomer is calculated by:

ΔEassociation=E(Isomer 1)-2*E(monomer)= -2352.41631610-2*(-1176.19013697)= -0.03604216 a.u.

This corresponds to an energy of -95 kJ/mol. Thus, the corresponding dissociation energy is 95 kJ/mol. A positive dissociation energy indicates that the dissociation process is endothermic, and our dimer is more stable than the two isolated monomers. We can explain this as in monomer, the valence electrons of Al is 6, and this is unfavoured as Al is electron deficient. This electron deficiency can be relieved by accepting one lone pair of another bromide, forming dative covalent bond. Therefore, dimerisation is favored, and the dimer is more stable than the isolated monomers.

==The frequency analysis of four isomers==

'''Isomer 1'''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|right|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|right|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|right|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A

Rep:Mod:inorganicismybestfriend

2014-03-06T15:02:26Z

Tw2011: /* Mini project (Week 2) */

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The HPC output Log. file could be check through {{DOI|10042/27793}}

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies information:

<pre> Low frequencies --- -2.4283 -0.0011 0.0014 0.0024 2.8330 2.9094

Low frequencies --- 120.5195 133.8367 185.7804</pre>

It can be observed that we have find the minimal structure.

 

The association energy of the most stable isomer is calculated by:

ΔEassociation=E(Isomer 1)-2*E(monomer)= -2352.41631610-2*(-1176.19013697)= -0.03604216 a.u.

This corresponds to an energy of -95 kJ/mol. Thus, the corresponding dissociation energy is 95 kJ/mol. A positive dissociation energy indicates that the dissociation process is endothermic, and our dimer is more stable than the two isolated monomers. We can explain this as in monomer, the valence electrons of Al is 6, and this is unfavoured as Al is electron deficient. This electron deficiency can be relieved by accepting one lone pair of another bromide, forming dative covalent bond. Therefore, dimerisation is favored, and the dimer is more stable than the isolated monomers.

==The frequency analysis of four isomers==

''Isomer 1''

The HPC output Log. file could be check through {{DOI|10042/27794}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|left|600px|'''Figure 4''' The IR spectrum of Isomer 1]]

'''Isomer 2'''

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|right|600px|'''Figure 5''' The IR spectrum of Isomer 2]]

'''Isomer 3'''

The HPC output Log. file could be check through {{DOI|10042/27797}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|right|600px|'''Figure 6''' The IR spectrum of Isomer 3]]

'''Isomer 4'''

The HPC output Log. file could be check through {{DOI|10042/27796}}

The Log. file was checked if the calculations have been completed.

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculations has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|right|600px|'''Figure 7''' The IR spectrum of Isomer 4]]

A

Rep:Mod:inorganicismybestfriend

2014-03-06T14:16:29Z

Tw2011: /* Mini project (Week 2) */

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

The corresponding monomer AlBrCl2 has also been optimised in order to find the dissociation energy of the most stable dimer. The basis set 6-31G(d,p) was applied on Al and Cl, pseudo potential LANL2DZdp was used to optimised Br.

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

The information of the calculation is shown in '''Table 16'''
[[Image:Albrcl2_optim.PNG|thumb|left|600px|'''Table 16''' Optimisation for monomer]]

The HPC output Log. file could be check through the link {{DOI|10042/27793}}

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Frequency
isomer a

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27794}}

isomer b
Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

isomer c

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27797}}

isomer d

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27796}}

Rep:Mod:inorganicismybestfriend

2014-03-06T14:08:47Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer '''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine atom rather than bridging chlorine atom, which significantly raise the energy.The aluminum and chlorine atoms are in the same period that their orbital overlap is 3p-3p which is better than that of aluminum and bromine atom (3p-4p). Therefore the bridging bromide is unfavourable than bridging chloride, which forms a weaker bond ,in return, raising the energy of the structure. The isomer 1 has two bridging bromides, which is expected to have a higher energy than isomer 2 that has one.

Monomer

<jmol><jmolApplet><title>File:Moner_optim.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Moner_optim.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:Albrcl2_optim.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27793}}

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Frequency
isomer a

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27794}}

isomer b
Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

isomer c

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27797}}

isomer d

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27796}}

Rep:Mod:inorganicismybestfriend

2014-03-05T18:10:27Z

Tw2011:

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy====
To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=Mini project (Week 2)=

==Geometry optimisation==

The optimisation information has been shown in '''Table 14'''.

{| class="wikitable" border="1"
|+ '''Table 14''' Summary of energies of isomers
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || Cs || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

The Log. files were checked if the calculations have been completed.

isomer 1

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.
-- Stationary point found.

isomer 2

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

isomer 3

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer 4

Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Referring to the Log. files, the calculations have all been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

A summary of four isomers and their energies have been reported in '''Table 15''' in a increasing order.

{| class="wikitable" border="1"

|+ '''Table 15''' Summary of energies of isomers

! Isomer No. !! Energy i(a.u.) !! Energy (kJ/mol) !! Relative energy to the most stable isomer (kJ/mol)

|-

| Isomer 3 || -2352.41631610 || -6176268.14 || 0

|-

| Isomer 4 || -2352.41626680 || -6176268.01 || 0.13

|-

| Isomer 2 || -2352.41109945 || -6176254.45 || 13.70

|-

| Isomer 1 || -2352.40630792 || -6176241.87 || 26.28

|}

The Isomer 3 is the most stable isomer which has two terminal bromine atom aligning ''trans'' to each other. The isomer 4, is the second most stable isomer due to two large terminal bromine atoms aligning ''cis'' to each other considered to be having unfavourable ''flagpole'' interaction in between. There is a relatively larger rise in energy for Isomer 2 as well as for the least stable isomer 1. These two isomers have bridging bromine rather than chlorine, which

The structure indicates that with bridging bromide instead of chloride, energy of the molecule raises significantly. Thus, we observe isomer 3 with 2 bridging bromides, to be the most unstable isomer. The main reason behind this is that Al and Cl atom are in the same period, and their orbitals overlap (3p-3p) is better than the overlaps between Al and Br atom, where bromine 4p orbital has poorer overlap with 3p orbital of Cl. Thus, bridging bromide structure is less favored than the bridging chloride structure, resulting in a more unstable structure and weaker covalent bonding.

Monomer

<uploadedFileContents>Moner_optim.mol</uploadedFileContents> [[Image:Albrcl2_optim.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27793}}

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Frequency
isomer a

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27794}}

isomer b
Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

isomer c

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27797}}

isomer d

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27796}}

Rep:Mod:inorganicismybestfriend

2014-03-04T22:24:52Z

Tw2011: /* NBO Analysis of NH3 */

=Inorganic computational lab (week 1)=
==Day 1==
===Optimization of BH3 molecule===

A BH3 molecule has been drawn with three B-H bond distances set to 1.53 Å, 1.54 Å and 1.55 Å respectively. The geometry optimization was carried out by Gaussian using B3LYP method and 3-21G as basis sets.

===Analysing the optimised BH3 molecule using two basis sets===

The original output Log. file could be check through [[Media:BH3_OPTIM2.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 1'''.

[[Image:Bh3_optim_2.PNG|thumb|left|450px|'''Table 1''' Calculation of BH3 molecule via 3-21G basis set ]]

The log file was then checked to figure out whether the calculation has been to completion.

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.
----------------------------
! 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 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, all four values for force and displacement listed were converged to their minimum which were all smaller than the threshold value given. Therefore, it could be confirmed that the calculation has completed.

It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о.

===The better basis set for BH3 optimisation===

A more accurate basis set, 6-31G(d,p), was used to optimise BH3 molecule

The original output Log. file could be check through [[Media:BH3_BETTER_SET.LOG|BH3-321-OPT]]

A table of the information of calculation is summarized in '''Table 2'''.

[[Image:Bh3_better.PNG|thumb|left|450px|'''Table 2''' Calculation of BH3 molecule via 6-31G(d,p) basis set ]]

Again, the Log. file was checked if the calculation has been to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000030 0.001200 YES
Predicted change in Energy=-7.533272D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1924 -DE/DX = 0.0 !
! R2 R(1,3) 1.1924 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9991 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0031 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed.
It could be found in the Log. file that the optimised B-H bond distance is 1.19 Å, and the optimised bond angle of H-B-H is 120.0о. The value calculated perfectly agrees to the literature value given for the B-H bond distance of a BH3 molecule which is 1.19Å.<ref name="BHbondlength">"Physical Constants of Organic Compounds", in ''CRC Handbook of Chemistry and Physics, Internet Version 2005'', David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.</ref>

==Day 2==
===Use of psuedo-potentials and large basis sets for GaBr3===

Pseudo-potentials could be used to easily model the core electrons of an atom from period 3 or higher. In order to investigate a 136-electron system of GaBr3, the pseudo-potential was used with the basic set adjusted to a medium level. The limitation needs mentioning that the symmetry of GaBr3 molecule should always be D3h.

The output Log. file could be check through {{DOI|10042/}}

A table of the information of calculation is summarized in '''Table 3'''.

[[Image:Gabr3.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule via LANL2DZ basis set]]

The Log. file was checked if the calculation has gone to completion.

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=-6.895727D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3581 -DE/DX = 0.0 !
! R2 R(1,3) 2.3581 -DE/DX = 0.0 !
! R3 R(1,4) 2.3581 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised Ga-Br bond distance is 2.36 Å, which shows a slight deviation to the literature value 2.249 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-Ga-Br bond angle is 120.0о.

The calculated value of Ga-Br bond distance is longer than that of literature reported, which indicates the need of a better basis set for the calculation. On the other hand, crystal packing of the molecule was not considered in the calculation; also, the calculation was carried out assuming the molecule is in its gas phase whereas the experimental value was determined using the closely-packed crystalline solid. Hence, the experimental value is supposed to be less than the value predicted. It could be certain that, the result predicted above is reasonable.

===Combining basis-sets and psuedo-potentials===

If a molecule under analysis contains heavy atoms and light atoms, it should be analyzed by combining psuedo-potentials and basis-set rather than applying them individually. For BBr3, Br atoms were calculated using LANL2DZ whereas B atom was calculated via 6-31G(d,p) basis set.

The HPC output Log. file could be check through {{DOI|10042/27680}}

A table of the information of calculation is summarized in '''Table 4'''.

[[Image:BBR3GEN.PNG|thumb|left|450px|'''Table 3''' Calculation of GaBr3 molecule using combination of basis-sets and psuedo-potentials]]

The output Log. file was checked whether the calculation has completed

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000069 0.001800 YES
RMS Displacement 0.000041 0.001200 YES
Predicted change in Energy=-1.505648D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,4) 1.9339 -DE/DX = 0.0 !
! R2 R(2,4) 1.934 -DE/DX = 0.0 !
! R3 R(3,4) 1.9339 -DE/DX = 0.0 !
! A1 A(1,4,2) 120.0018 -DE/DX = 0.0 !
! A2 A(1,4,3) 120.0008 -DE/DX = 0.0 !
! A3 A(2,4,3) 119.9974 -DE/DX = 0.0 !
! D1 D(1,4,3,2) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised B-Br bond distances is 1.93 Å, which shows a slight deviation to the literature value 1.893 Å<ref name=GaBrbondlength>W. M. Haynes, D. R. Lide and T. J. Bruno, ''CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data'', '''2012''', ''93'', 9–23. </ref> measured by Gas phase electron diffraction. The optimised Br-B-Br bond angle is 120.0о.

The calculated value of B-Br bond distance is longer than that of literature reported. This is again attributed to the difference in state of the molecule, and also without consideration of crystal packing of the molecule. Overall, the result is reasonable.

===Structure comparison===

The bond length of B-H, Ga-Br and B-Br bonds have been summarized in '''Table 5'''.

{| class="wikitable" border="1"
|+ '''Table 5''' The predicted bond lengths of B-H, Ga-Br, B-Br
! Bond type !! Optimised bond length !! Literature bond length<ref name=GaBrbondlength></ref>
|-
| B-H || 1.1946 Å || 1.19 Å
|-
| Ga-Br || 2.3581 Å || 2.249 Å
|-
| B-Br || 1.924 Å || 1.893 Å
|}

Comparing BH3 and BBr3, the optimised bond lengths agree to the literature values which are experimentally determined. The B-H bond length is shorter than that of B-Br, which shows that replacing the H atoms as ligands by Br atoms elongates the bond. Both hydrogen and bromine form standard 2c-2e bonds with boron, and both of the have higher electronegativity than boron. The electronegativity difference between boron and bromine is larger than that of hydrogen and boron, therefore, the B-Br bond has a higher polarity and hence it has a longer bond length. On the other hand, the bromine has a more diffuse valence orbitals than hydrogen. In B-Br bond, boron and bromine has a poor overlap between 4p orbital of bromine and sp2 hybridized orbital of boron due to size mismatch. However, the B-H bond has a better orbital overlap between 1s orbital of hydrogen and sp2 hybridized orbital of boron. The better overlap between two atoms, the stronger bond they form, and shorter bond length the bond would be. Therefore, the B-Br bond is expected to be longer.

Comparing BBr3 and GaBr3, it could be seen that Ga-Br is a longer bond than B-Br, which shows that by replacing the central atom with a heavier atom would also elongate the bond. both gallium and boron form standard 2c-2e bonds with bromine as well. However, due to the difference in ground state electronic configuration, gallium has a poorer orbital overlap with bromine, which is 4p-4p overlap, comparing to 2p-4p overlap between boron and bromine. Therefore, the Ga-Br has a longer bond. It could also be explained by the larger atomic radius of gallium comparing to that of boron. Additionally, the electronegativity difference between gallium and bromine is larger than that of boron and bromine, so that the Ga-Br bond is more polar than B-Br bond contributing to a longer bond formed between gallium and bromine.

It could be seen that sometimes the Gaussview does not present a bond between bonding atoms as expected. It does not indicates that no bond is formed, however, it means that the bond length is not in the pre-defined range.

"Bond" is defined as the electronic attraction between atoms with opposite charge, which forms a new substance . Generally, The bonds are characterized into four types which are ionic, covalent, van der vaals' force and hydrogen bonding<ref>Carl R. Nave (2005). HyperPhysics http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Retrieved May 18, 2005.</ref>.

==Day 3==
===Frequency analysis of BH3===

The frequency analysis was carried out for the optimized BH3 molecule to analysis its structure. The symmetry of the BH3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27681}}

A table of the information of calculation is summarized in '''Table 6''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Bh3_frequency.PNG|thumb|left|800px|'''Table 6''' Frequency calculation of BH3]]

The Log. file was checked if the calculation has gone to completion.

Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000059 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
Predicted change in Energy=-8.300040D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -22.2540 -0.0009 -0.0006 -0.0002 14.2099 16.5951
Low frequencies --- 1163.0042 1213.2113 1213.2913

The low frequencies lines are displayed above. the range of the low frequencies are within a range of 15cm-1.

===Vibrational modes===

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''NO.'''
| align="center" style="background:#f0f0f0;"|'''Form of Vibration'''
| align="center" style="background:#f0f0f0;"|'''Frequency(cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Internsity'''
| align="center" style="background:#f0f0f0;"|'''Infrared( D3h)'''
|-
| 1||[[Image:Bh31.gif|thumb|left]]All hydrogen atoms move in the same direction whereas the boron moves towards the opposite direction||1163||93||A2"
|-
| 2||[[Image:Bh33.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. In the plane of molecule, the other two hydrogen atoms move towards each other symmetrically||1213||14||E' (degenerate)
|-
| 3||[[Image:Bh32.gif|thumb|left]]The boron atom is stationary. In the plane of molecule, three hydrogen atoms bend asymmetrically. Two of the hydrogen atoms are moving in the same phase leaving the other hydrogen atom moving in the opposite direction.||1213||14||E' (degenerate)
|-
| 4||[[Image:Bh34.gif|thumb|left]]The boron atom is stationary. The three hydrogen atoms stretch along the bond symmetrically.||2582||0||A1' totally symmetric
|-
| 5||[[Image:Bh36.gif|thumb|left]]The boron atom and one of the hydrogen atoms are stationary. The other two hydrogen atoms are stretching along the bond asymmetrically. ||2715||126||E' (degenerate)
|-
| 6||[[Image:Bh35.gif|thumb|left]]The boron atom is stationary. All three hydrogen atoms are stretching asymmetrically. Two of the H atoms are moving in the same direction while the other moving in the opposite phase.||2715||126||E' (degenerate)
|-
|
|}

The predicted IR spectrum is shown in '''Figure 1'''

[[Image:Bh3_ir.PNG|thumb|left|600px|'''Figure 1''' The predicted IR spectrum of BH3]]

Referring to the IR spectrum, three peaks have been detected, which are 1163 cm-1, 1213 cm-1, 2715 cm-1 respectively. Although there are six different modes calculated, three peaks were found on the spectrum because Mode 2 and 3 are degenerate, also the Mode 5 and 6 are degenerate. Additionally, the Mode 4 is a symmetrical stretching which does not show any peak on IR due to no change in dipole moment. Therefore the three peaks indicates the Mode 1, Mode 2 and 3 as well as Mode 4 and 5.

===Frequency Analysis of GaBr3===

The frequency analysis was carried out for the optimized GaBr3 to investigate the structure of GaBr3 molecule. The symmetry of the GaBr3 molecule was restricted to D3h.

The HPC output Log. file could be check through {{DOI|10042/27683}}

A table of the information of calculation is summarized in '''Table 7''', noted that the term "Imaginary frequency" has a value of 0, which means that the molecule is in its stable form.

[[Image:Gabr3FRE.PNG|thumb|left|450px|'''Table 7''' Frequency Calculation of GaBr3]]

The Log. file was checked if the calculation has been completed.

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=-6.142863D-13
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

The lowest "real" normal mode is 76 cm-1.

The IR spectrum of the GaBr3 is shown in '''Figure 2'''.

[[Image:Gabr3ir.PNG|thumb|left|600px|'''Figure 2''' The IR spectrum of GaBr3]]

===Comparison between vibrational frequencies===

A comparison between vibrational frequencies of GaBr3 and BH3 has been summarized in '''Table 8'''

{| class="wikitable" border="1"

|+ '''Table 8''' Vibration comparison between BH3 and GaBr3

! No. !! BH3 Frequency (cm-1) !! BH3 Intensity !! BH3 Symmetry D3h point group !! No. !! GaBr3 Frequency (cm-1) !! GaBr3 Intensity !! GaBr3 Symmetry D3h point group

|-

| 1 || 1163 || 93 || A2" || 1 || 76 || 3 || E' (degenerate)

|-

| 2 || 1213 || 14 || E' (degenerate) || 2 || 76 || 3 || E' (degenerate)

|-

| 3 || 1213 || 14 || E' (degenerate) || 3 || 100 || 9 || A2"

|-

| 4 || 2582 || 0 || totally symmetric A1' || 4 || 197 || 0 || totally symmetric A1'

|-

| 5 || 2715 || 126 || E' (degenerate) || 5 || 316 || 57 || E' (degenerate)

|-

| 6 || 2715 || 126 || E' (degenerate) || 6 || 316 || 57 || E' (degenerate)

|}

From the table shown, it could be seen that there is a large difference between each frequency of vibrational mode of GaBr3 and BH3. Due to having a higher vibrational frequencies,B-H is a stronger bond comparing to Ga-Br. It is also found that the peak intensities of GaBr3 is lower than that of BH3. This is attributed to lower change in the dipole moment of GaBr3 molecule during vibration. For a non-linear molecule containing four atoms, there are supposed to be six different vibrational modes, but each IR spectrum gives only three peaks. This is because that there are two sets of degenerate modes, and also a totally symmetric vibrational mode which is IR inactive.

By comparing to the vibrational frequencies of A2" vibration mode and E' vibration modes for two different molecules. It could be seen that the A2" has a lower vibrational frequency than E' in BH3, whereas for Ga-Br, the vibrational frequency of A2" is higher than that of E'. This trend is due to long Ga-Br bond length.

Each molecule has an IR spectrum of three peaks which attribute to two degenerate modes and one individual mode. There is a slight difference in peak intensities. The results in shifting of degenerate mode into lower frequencies. It could also be seen that for each spectrum, the mode A2" has a similar energy to the mode E', whereas the mode A1' has a higher energy and it has a similar energy to another mode E'. This is related to different vibration motions. The mode A2" and the first degenerate mode E' are related to the bending motion, while the mode A1' and the second degenerate mode E' are related to stretching motions. The stretching motions are considered to have a relatively larger force constant than bending motions that results in higher energies required for stretching the bonds.

The reason why we have to use the same method and basis set for both the optimisation and frequency analysis calculation is that if two different method and basis set are used in optimisation, there would be two different optimised structures generated having two different total energies. The frequency analysis is used to examine whether the structure is fully optimised. Therefore, same method and basis set should be applied to optimisation and frequency analysis or otherwise the frequency analysis would be inaccurate for the structure.

The purpose of carrying out a frequency analysis is to minimize the structure. On the other hand, the vibrational modes of the structure as well as the IR spectrum could be predicted.

The term "Low frequencies" represent the motions on a molecule's mass centre. The number of the modes could be calculated following 3N-6 (for non-linear molecule) or 3N-5 (for linear molecule) where N is the number of atoms in the molecule.

===Molecular Orbitals of BH3===

The HPC output could be check through {{DOI|10042/27684}}

The information is summarized in '''Table 8'''

[[Image:BH3_MO.PNG|thumb|left|600px|'''Table 8''' Molecular Orbital Calculation of BH3]]

The molecular diagram has been shown in '''Figure 3'''

[[Image:BH3MO diagram.PNG|thumb|left|700px|'''Figure 3''' Molecular Orbital diagram of BH3]]

As it can be seen that there is a significant difference between the real MOs and LCAO MOs, as LCAO MOs only show the orbitals on each individual atom of a molecule, however, the real MOs delocolized on the whole, which indicates the electronic distributions. Therefore, real MOs could predict the electron density and distribution of a molecule but LCAO MOs cannot.

The qualitative MO theory could be use to predict the position of orbitals and the their combination. And the nodal planes of the combined orbitals could be predicted. However, the delocalized electron distribution and the shape of electron density could not be predicted by qualitative MO theory.

===NBO Analysis of NH3===

A NH3 was drawn. The molecule was optimizatized and frequency, MO analysis was carried out.

====Geometry optimisation====

The HPC output Log. file could be check through {{DOI|10042/27688}}

The information is summarized in '''Table 9'''

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 9''' The NH3 optimisation]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844270D-11
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

It could be found that the optimised bond length is 1.01 Å, and the optimised H-N-H bond angle is 105.7o.

====Frequency analysis====

The information of calculation is summarized in the '''Table 10'''.

The HPC output Log. file could be check through {{DOI|10042/27685}}

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 10''' Frequency analysis of NH3]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131315D-10
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0130 -0.0028 -0.0019 7.0747 8.1044 8.1047
Low frequencies --- 1089.3849 1693.9369 1693.9369

The low frequencies have been shown above and they are in the range of ±15cm-1.

====Population (MO) analysis====

The information of calculation is summarized in the '''Table 11'''.

The HPC output Log. file could be check through {{DOI|10042/27786}}

[[Image:Nh3_mo.PNG|thumb|left|450px|'''Table 11''' MO calculation of NH3]]

====NBO Analysis====

The diagram of charge distribution is shown on '''Figure 3'''.

[[File:NBO-pz.png|400px|thumb|left|'''Figure 3''' NH3 charge distribution (charge range:-1.0 to +1.0)]]

The diagram of specific NBO charges for each atom is shown on '''Figure 4'''.

[[File:Specific NBO.png|400px|thumb|left|'''Figure 4''' NH3 NBO charges]]

The nitrogen has a charge of -1.125 while hydrogen has a charge of 0.375.
===Association energies: Ammonia-Borane===
====Optimisation of ammonia-borane (NH3BH3)====

The HPC output Log. file could be check through {{DOI|10042/27687}}

The information of the optimisation is summarized in the '''Table 12'''.

[[Image:NH3OPTIM.PNG|thumb|left|600px|'''Table 12''' Optimisation of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

====Frequency Analysis====
The HPC output Log. file could be check through {{DOI|10042/27686}}

The information of calculation is summarized in the '''Table 13'''.

[[Image:NH3FRE.PNG|thumb|left|600px|'''Table 13''' Frequency analysis of ammonia-borane]]

The Log. file was checked if the calculation has been completed.

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000732 0.001800 YES
RMS Displacement 0.000412 0.001200 YES
Predicted change in Energy=-2.067408D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Referring to the Log. file, the calculation has been completed as the force and displacement values have converged to their minimum values that are smaller than threshold values.

Low frequencies --- -0.0245 -0.0029 0.0011 17.6808 17.6833 37.1786
Low frequencies --- 265.6718 632.2168 639.3347

The low frequencies are close to zero and within the range of ±15 cm-1 .

====Association Energy==== Normal 0 false false false EN-GB X-NONE X-NONE

To find the association energy of H3NBH3, the following table was constructed.
{| class="wikitable"
|+ Table 14: Results for Energy Calculation of H3NBH3
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Energy'''
|-
| BH3 (a.u.)||-26.61532363
|-
| NH3 (a.u.)||-56.55776872
|-
| H3NBH3 (a.u.)||-83.22468907
|-
| Dissociation Energy (a.u.)||-0.05159672
|-
| Dissociation Energy (kJ/mol)||-135.47
|-
|}

According to Table '''17''', NH3BH3 is more stable than the individual NH3 and BH3, because of a new dative bond formed from the donation of lone pair electrons from the sp3 orbital of nitrogen atom to the vacant p orbital of boron atom, lowering the total energy of the whole system. Therefore, the process is spontaneous.

=mini project=
{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Table. 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Sturucture||<jmol><jmolApplet><title>File:2br in the middle3</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_a_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:1_br_in_the_middle.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_b_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Trans_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_c_optim.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>File:CIS_br.mol</title><color>white</color>
<size>200</size><script>measure 1 3 22;zoom 150; cpk -20;</script>
<uploadedFileContents>Isomer_d_optim.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| File Name
| js-isomer a-clean-opt||js-isomer b-clean-opt ||js-isomer c-clean-opt ||js-isomer d-clean-opt
|-
| File Type
| .log||.log ||.log ||.log
|-
| Calculation Type
| FOPT||FOPT ||FOPT ||FOPT
|-
| Calculation Method
| RB3LYP|| RB3LYP|| RB3LYP || RB3LYP
|-
| Basis Set
| Gen|| Gen || Gen || Gen
|-
| Charge
| 0|| 0 || 0 ||0
|-
| Spin
| Singlet|| Singlet || Singlet || Singlet
|-
| E(RB3LYP)
| -2352.40630798 a.u || -2352.41109946 a.u || -2352.41631610 a.u || -2352.41626680 a.u
|-
| RMS Gradient Norm
| 0.00000182 a.u || 0.00000701 a.u || 0.00001373 a.u || 0.00001283 a.u
|-
| Imaginary Frequency
| || || ||
|-
| Dipole Moment
| 0.0002 Debye || 0.1393 Debye || 0.0013 Debye ||0.1661 Debye
|-
| Point Group
| C1|| C1 || CS || C2v
|-

|Link to D-Space
|{{DOI|10042/27791}}|| {{DOI|10042/27789}}|| {{DOI|10042/27788}}||{{DOI|10042/27792}}
|-
| Real point Group
| D2h|| C1 || C2h || C2v
|}

isomer a optim

Item Value Threshold Converged?
Maximum Force 0.000142 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000881 0.001800 YES
RMS Displacement 0.000486 0.001200 YES
Predicted change in Energy=-2.549175D-07
Optimization completed.

isomer b optim

Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.001790 0.001800 YES
RMS Displacement 0.000815 0.001200 YES
Predicted change in Energy=-5.669497D-07
Optimization completed.
-- Stationary point found.

-- Stationary point found.

isomer c optim

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-8.697724D-10
Optimization completed.
-- Stationary point found.

isomer d optim
Item Value Threshold Converged?
Maximum Force 0.000133 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.000130 0.001800 YES
RMS Displacement 0.000060 0.001200 YES
Predicted change in Energy=-1.697961D-08
Optimization completed.
-- Stationary point found.

Monomer
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

<uploadedFileContents>Moner_optim.mol</uploadedFileContents> [[Image:Albrcl2_optim.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27793}}

Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.

Frequency
isomer a

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000293 0.001800 YES
RMS Displacement 0.000143 0.001200 YES
Predicted change in Energy=-4.006395D-09
Optimization completed.
-- Stationary point found.

Low frequencies --- -5.1277 -4.9552 -3.1726 -0.0055 -0.0055 -0.0053
Low frequencies --- 14.8534 63.2885 86.0886

[[Image:Isomer_a_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27794}}

isomer b
Item Value Threshold Converged?
Maximum Force 0.000034 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000897 0.001800 YES
RMS Displacement 0.000373 0.001200 YES
Predicted change in Energy=-2.934869D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -2.2705 -0.0013 -0.0008 0.0009 1.2791 3.3179
Low frequencies --- 17.1478 55.9562 80.0556

[[Image:Isomer_b_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27795}}

isomer c

Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.001443 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
Predicted change in Energy=-2.272991D-07
Optimization completed.
-- Stationary point found.

Low frequencies --- -3.7454 -1.6438 -0.1927 0.0029 0.0032 0.0036
Low frequencies --- 17.6893 48.9677 72.9414

[[Image:Isomer_c_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27797}}

isomer d

Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000153 0.001200 YES
Predicted change in Energy=-1.221637D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -3.8138 -1.7954 -1.7806 0.0032 0.0033 0.0036
Low frequencies --- 17.7004 50.8811 72.1676

[[Image:Isomer_d_ir.PNG|thumb|right|600px|Picture. 13]]

The HPC output Log. file could be check through the link {{DOI|10042/27796}}

Rep:Mod:inorganicismybestfriend

2014-03-04T20:46:03Z

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