Rep:Mod:NBC1234

Week One

Day One

3-21G

The BH₃ optimisation file is linked to here

BH₃ info.
Q	A
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	3-21G
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-26.46226338 ±0.003808780 a.u.
Gradient	0.00020672 a.u.
Dipole Moment	0.00 ±0.01 Debye
Point Group	D_3h
Job Time	0 days 0 hours 0 minutes 14.0 seconds

The corresponding log book:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000413     0.000450     YES
 RMS     Force            0.000271     0.000300     YES
 Maximum Displacement     0.001610     0.001800     YES
 RMS     Displacement     0.001054     0.001200     YES
 Predicted change in Energy=-1.071764D-06
 Optimization completed.

6-31G(d,p)

The BH₃ optimisation (6-31G(d,p)) file is linked to here

BH₃ info.
Q	A
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-26.61532363 ±0.003808780 a.u.
Gradient	0.00000235 a.u.
Dipole Moment	0.00 ±0.01 Debye
Point Group	D_3h
Job Time	0 days 0 hours 0 minutes 47.0 seconds

The corresponding log book:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000019     0.001800     YES
 RMS     Displacement     0.000012     0.001200     YES
 Predicted change in Energy=-1.305135D-10
 Optimization completed.

The optimised B-H bond distance: 1.19 ±0.01 Å

the optimised H-B-H bond angle: 30.0^ο ±0.01^ο

The total energy for 3-21G optimised structure: -26.46226338 ±0.003808780 a.u.

The total energy for 6-31G(d,p) optimised structure: -26.61532363 ±0.003808780 a.u.

Day Two

GaBr₃

Link to "D-space": DOI:10042/25222

GaBr₃ info.
Q	A
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	6-31G(d)
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-9638.24603597 ±0.003808780 a.u.
Gradient	0.00006765 a.u.
Dipole Moment	0.00 ±0.01 Debye
Point Group	D_3h
Job Time	0 days 0 hours 0 minutes 52.5 seconds

The corresponding log book:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000135     0.000450     YES
 RMS     Force            0.000089     0.000300     YES
 Maximum Displacement     0.000814     0.001800     YES
 RMS     Displacement     0.000533     0.001200     YES
 Predicted change in Energy=-1.781658D-07
 Optimization completed.

The optimised Ga-Br bond distance: 2.26 ±0.01 Å

The optimised Br-Ga-Br bond angle: 120.0^ο ±0.1^ο

The literature value of Ga-Br bond distance is found to be 2.249 Å (method ED) ^[1]

The difference between experimental value of Ga-Br bond distance and literature value of Ga-Br bond distance is 0.01 Å which is quite small. One of the reasons accounting for the difference is that two different calculation methods are used. Also, the chosen basis set for this experiment is not the most accurate one, therefore the result is not expected to have a high accuracy.

BBr₃

The BBr₃ optimisation file is linked to here

BBr₃ info.
Q	A
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	Gen
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-64.43645296 ±0.003808780 a.u.
Gradient	0.00000382 a.u.
Dipole Moment	0.00 ±0.01 Debye
Point Group	D_3h
Job Time	0 days 0 hours 0 minutes 16.5 seconds

The corresponding "Item" table:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000036     0.001800     YES
 RMS     Displacement     0.000023     0.001200     YES
 Predicted change in Energy=-4.026916D-10
 Optimization completed..

The optimised B-Br bond distance: 1.93 ±0.01 Å

The optimised Br-B-Br bond angle: 120.0^ο ±0.1^ο

Analysis

Bond Distance Info.
Molecule	Bond Distance /Å
BH₃	1.19232
GaBr₃	2.26286
BBr₃	1.93396

Bond becomes longer when the H atom from B-H bond is replaced by the Br atom. The B-Br bond is 0.74164 Å longer than the B-H bond. Also, the BBr₃ has an energy of -64.43645296 a.u. which means the energy of the molecule has increased, comparing to the original molecule (BH₃) which has an energy of -26.61532363 a.u.. In terms of similarity, both H and Br atoms have one unpaired electron in their valence shells and they are both X-type ligands. However, the Br atom have a electron configuration of [Ar] 3d¹⁰4s²4p⁵, which is much larger in size than the H atom (1S¹). It is also reflected in the increased bond length. In addition to that, the electronegativity of Br atom is higher than that of H atom, leading to a more polarised B orbital, which makes bond longer.

Both B atom and Ga atom are from group 13, having a valence electron number of 3. But the valence orbitals of Ga are 4s4p while the valence orbitals of B are 2s2p. When the central element of BBr₃ is changed from B atom to Ga atom, the bond length is increased from 1.93396 Å of B-Br to 2.26286 Å of Ga-Br. This is because the Ga atom is larger in size. However, the energy is increased significantly from -26.61532363 a.u. to -9638.24603597 a.u.. The reason for that is the poor orbital overlap between Ga valence orbitals (4s4p) and Br valence orbitals(4s4p). The 4s and 4p orbitals are more diffuse than the 2s and 2p orbitals of B atom, resulting in a weaker Ga-Br covalent bond and higher in energy.

In some cases, no bonds are shown on the gaussview, but it does not mean there is no bond. Gaussview only displays bonds when the length of the bond is within the range of pre-defined value. ^[2] A chemical bond is the attraction between atoms that holds two or more atoms together to form a new chemical substance. The attraction exists between two opposite charges (electrostatic attraction). Chemical bonds are divided into various categories based on the strength of the interaction. For example, an ionic bond implies a strong interaction between atoms, usually with an electronegativity difference larger than 1.7.

Day Three

BH₃ Frequency Analysis

The BH₃ frequency analysis file is linked to here

BH₃ Frequency Summary
Q	A
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-26.61532363 ±0.003808780 a.u.
Gradient	0.00000237 a.u.
Imaginary Frequency	0
Dipole Moment	0.00 ±0.01 Debye
Point Group	D_3h
Job Time	0 days 0 hours 0 minutes 16.0 seconds

The corresponding "Item" book:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000019     0.001800     YES
 RMS     Displacement     0.000009     0.001200     YES
 Predicted change in Energy=-1.323376D-10
 Optimization completed.

 Low frequencies ---   -0.9033   -0.7343   -0.0054    6.7375   12.2491   12.2824
 Low frequencies --- 1163.0003 1213.1853 1213.1880

BH₃ Frequency Summary
No.	Form of Vibration	Frequency / ±10 cm^-1	Intensity	Symmetry D_3h Point Group
1	All H atoms move in the same direction in a concerted motion, B atom is stationary	1163	92	A2"
2	Two H atoms move together in a concerted motion, the other H atom and B atom are stationary	1213	14	E'
3	All H atoms move in different directions in a concerted motion, B atom is stationary	1213	14	E'
4	All H atoms move in a concerted motion, B atom is stationary	2582	0	A1'
5	One H atom moves in while another H atom moves out, the third H atom and B atom is stationary	2715	126	E'
6	Two H atoms move in and the other H atom moves out in a concerted motion, B atom is stationary	2715	126	E'

IR spectrum of BH₃, click to enlarge:

As it can be seen from the diagram, only three peaks are shown on the IR spectrum while there are six vibrations in total according to the calculation. The forth vibration is totally symmetric (A1'), therefore it is IR inactive and no corresponding peak will appears on IR spectrum. The second and third vibrations have the same vibrational frequencies at 1213.19 cm^-1. Thus, the two peaks are overlapped and only one peak is shown on the IR spectrum. It is the same for the fifth and sixth vibrations, which share the vibrational frequencies at 2715.43 cm^-1.

GaBr₃ Frequency Analysis

Link to "D-space": DOI:10042/25339

GaBr₃ info.
Q	A
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d)
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-9638.24603597 ±0.003808780 a.u.
Gradient	0.00006761 a.u.
Imaginary Frequency	0
Dipole Moment	0.00 ±0.01 Debye
Point Group	D_3h
Job Time	0 days 0 hours 0 minutes 39.8 seconds

The corresponding "Item" book:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000135     0.000450     YES
 RMS     Force            0.000068     0.000300     YES
 Maximum Displacement     0.000813     0.001800     YES
 RMS     Displacement     0.000406     0.001200     YES
 Predicted change in Energy=-1.648213D-07
 Optimization completed.
    -- Stationary point found.

Low frequencies --- -5.2266 -3.2556 -3.2556 0.0104 0.0140 0.0222
Low frequencies --- 86.7293 86.7295 119.8002

The lowest "real" mode is the vibration at 0.0104

Click on the image for an enlarged IR spectrum:

Vibrational Frequency Comparison
Molecule	Vibrational Frequency / ±10 cm^-1	Mode
BH₃	1163	A2"
BH₃	1213	E'
BH₃	1213	E'
BH₃	2582	A1'
BH₃	2715	E'
BH₃	2715	E'
GaBr₃	87	E'
GaBr₃	87	E'
GaBr₃	120	A2"
GaBr₃	236	A1'
GaBr₃	366	E'
GaBr₃	366	E'

It is clear that there is a large difference between vibrational frequencies of BH₃ and vibrational frequencies of GaBr₃. Since all the bonds are single bonds, a larger value of vibrational frequency corresponds to a stronger covalent bond. In this case, the bond between B-H is stronger than the bond between Ga-Br. B-H bond is stronger because of the better 1s-2p orbital overlap. 1s orbital is the smallest orbital and therefore it has a stronger overlap with 2p orbital than another p orbital. Both of Ga and Br atoms are in the 4^th period corresponding to a larger (more diffuse) valence orbital (4p), which makes their orbital overlap weaker than the overlap between 1s and 2p orbitals.

It should be noticed that both of the IR spectra displays three peaks while there are six vibrational modes in each molecule. Corresponding explanation for GaBr₃ is the same as for BH₃.

For both spectra, A2" and E' modes lie closely together and A1' and E' modes lie closely together. However the A1' and E' modes have a higher vibrational frequencies than that of A2" and E' modes. By observing vibrations, it is clear that there are no bond stretching for A2" and E' modes, bond distance remains the same for those three vibrations (e.g. rocking). Yet for A1' and E' modes, there are bond stretching in all three vibrations. It implies that vibrational frequencies tend to be higher with the vibration mode with bond stretching.

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?

Different method and basis set represent different approximations and accuracies in solving Schrodinger equation, therefore the results cannot be compared if different method and basis set are chosen for the calculation.

What is the purpose of carrying out a frequency analysis?

Frequency analysis can help to confirm if the minimum structure is achieved. It corresponds to second derivative of the potential energy surface. Thus, positive frequencies stand for the minimum energy, negative frequencies represent the failure to achieve an optimisation. provides the IR and Raman modes to compare with experiment.

What do the "Low frequencies" represent?

Low frequencies represent the vibrations with minimum energy

MOs of BH₃

Link to "D-space": DOI:10042/25345

BH₃ MO Summary
Q	A
Calculation Type	SP
Calculation Method	RB3LYP
Basis Set	6-31G(d)
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-26.61532363 ±0.003808780 a.u.
Dipole Moment	0.00 ±0.01 Debye
Point Group	D_3h
Job Time	0 days 0 hours 0 minutes 6.2 seconds

LCAO MO is a approximation developed for certain types of chemical systems, it might not be applicable to the other chemical systems. The choice of basis set can be inadequate and would result in a poor accuracy. However, as an inexpensive method, MOs and population analysis are usually easy to interpret. ^[3]

MO diagram of BH₃ can be found here:

NH₃

NH₃ Summary Table
Calculation Type	FOPT	FREQ	SP
Calculation Method	RB3LYP	RB3LYP	RB3LYP
Basis Set	6-31G(d,p)	6-31G(d,p)	6-31G(d,p)
Charge	0
Spin	Singlet	Singlet	Singlet
Final Energy in Atomic Units / ±0.003808780 a.u.	-56.55776856	-56.55776856	-56.55776856
Gradient / a.u.	0.00000885	0.00000891
Imaginary Frequency
Dipole Moment / ±0.01 Debye	1.85	1.85	1.85
Point Group	C1	C1	C1
Job cpu Time	0 days 0 hours 1 minutes 5.0 seconds	0 days 0 hours 0 minutes 22.0 seconds	0 days 0 hours 0 minutes 6.5 seconds
log file Link	Optimisation here	Frequency here	MO here

"Item" book of optimisation file:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000024     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000079     0.001800     YES
 RMS     Displacement     0.000053     0.001200     YES
 Predicted change in Energy=-1.629716D-09
 Optimization completed.

"Item" book of frequency file:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000021     0.000450     YES
 RMS     Force            0.000009     0.000300     YES
 Maximum Displacement     0.000077     0.001800     YES
 RMS     Displacement     0.000039     0.001200     YES
 Predicted change in Energy=-1.610514D-09
 Optimization completed.

Low frequencies:

 Low frequencies ---  -30.6683   -0.0015    0.0008    0.0012   20.3158   28.3272
 Low frequencies --- 1089.5567 1694.1245 1694.1869

Image of charge distribution (-1.0 to +1.0),click on the image to enlarge.

Image of the specific NBO charges. As it can be seen from the graph, the nitrogen atom has a charge of -1.125 and each hydrogen atom has a charge of 0.375.

Ammonia-Borane

The NH₃BH₃ optimisation file is linked to here The NH₃BH₃ frequency file is linked to here

NH₃BH₃ Optimisation Summary
Q	A
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-83.22469007 ±0.003808780 a.u.
Gradient	0.00006839 a.u.
Dipole Moment	5.56 ±0.01 Debye
Point Group	C1
Job Time	0 days 0 hours 1 minutes 6.5 seconds

"Item" book of NH₃BH₃ optimisation file

         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.

NH₃BH₃ Frequency Summary
Q	A
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-83.22469014 ±0.003808780 a.u.
Gradient	0.00006833 a.u.
Imaginary Frequency	0
Dipole Moment	5.56 ±0.01 Debye
Point Group	C1
Job Time	0 days 0 hours 0 minutes 48.7 seconds

 Low frequencies ---   -0.0011   -0.0008    0.0002   19.1416   23.8752   42.9246
 Low frequencies ---  266.5875  632.3849  639.5915
 Diagonal vibrational polarizability:
        5.0198170       2.5459889       2.5468169
 Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
 activities (A**4/AMU), depolarization ratios for plane and unpolarized
 incident light, reduced masses (AMU), force constants (mDyne/A),
 and normal coordinates:
                      1                      2                      3
                      A                      A                      A
 Frequencies --    266.5824               632.3849               639.5914
 Red. masses --      1.0078                 4.9926                 1.0452
 Frc consts  --      0.0422                 1.1764                 0.2519
 IR Inten    --      0.0000                13.9835                 3.5494

E(BH₃)= -26.61532363 ±0.003808780 a.u.

E(NH₃)= -56.55776856 ±0.003808780 a.u.

E(NH₃BH₃)= -83.22469007 ±0.003808780a.u.

ΔE=E(NH₃BH₃)-[E(NH₃+E(BH₃)]= -0.05159788 ±0.003808780 a.u. = -140 ±10 kJ/mol

Mini Project

Optimisation

Al₂Cl₄Br₂ Isomers (Optimisation)
Name	Isomer 1	Isomer 2	Isomer 3	Isomer 4
Image
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
Final Energy in Atomic Units / ±0.003808780 a.u.	-2352.40630798	-2352.41626681	-2352.41109945	-2352.41631606
Gradient / a.u.	0.00000079	0.00000124	0.00000491	0.00001799
Imaginary Frequency
Dipole Moment / ±0.01 Debye	0.00	0.17	0.14	0.01
Point Group	C_2v	C_2v	C1	CS
Job cpu Time	0 days 0 hours 3 minutes 9.9 seconds	0 days 0 hours 2 minutes 41.8 seconds	0 days 0 hours 4 minutes 56.0 seconds	0 days 0 hours 2 minutes 13.7 seconds
D-Space Link	DOI:10042/25574	DOI:10042/25575	DOI:10042/25573	DOI:10042/25717

Al₂Cl₄Br₂ Isomers (Optimisation)
Name	Image	"Item" Book
Isomer 1		Item Value Threshold Converged? Maximum Force 0.000002 0.000450 YES RMS Force 0.000001 0.000300 YES Maximum Displacement 0.000636 0.001800 YES RMS Displacement 0.000255 0.001200 YES Predicted change in Energy=-6.076901D-10 Optimization completed.
Isomer2		Item Value Threshold Converged? Maximum Force 0.000001 0.000450 YES RMS Force 0.000001 0.000300 YES Maximum Displacement 0.000331 0.001800 YES RMS Displacement 0.000121 0.001200 YES Predicted change in Energy=-2.405196D-10 Optimization completed.
Isomer3		Item Value Threshold Converged? Maximum Force 0.000009 0.000450 YES RMS Force 0.000004 0.000300 YES Maximum Displacement 0.000140 0.001800 YES RMS Displacement 0.000062 0.001200 YES Predicted change in Energy=-2.149539D-09 Optimization completed.
Isomer4		Item Value Threshold Converged? Maximum Force 0.000046 0.000450 YES RMS Force 0.000017 0.000300 YES Maximum Displacement 0.000500 0.001800 YES RMS Displacement 0.000181 0.001200 YES Predicted change in Energy=-2.926330D-08 Optimization completed.

E(isomer1)= -2352.40630798 a.u. = -6176240 ±10 kJ/mol

E(isomer2)= -2352.41626681 a.u. = -6176260 ±10 kJ/mol

E(isomer3)= -2352.41109945 a.u. = -6176250 ±10 kJ/mol

E(isomer4)= -2352.41632893 a.u. = -6176270 ±10 kJ/mol

Isomer 4 possesses the lowest energy among all four isomers, therefore it is set to be the relative energy. The difference between the energy of each isomer and the relative energy is taken and the following table is obtained.

Relative Energies of Al₂Cl₄Br₂ Isomers
Highest Energy	isomer1, 26.27622 kJ/mol	isomer3, 13.69621 kJ/mol	isomer2, 0.12931 kJ/mol	isomer4, 0 kJ/mol	Lowest Energy

From the table above, it can be seen that there's a small energy difference (0.12931 kJ/mol) between two isomers with none of the bromine atoms in the bridging positions. However, when one of the bridging chlorine atom is replaced by a bromine atom, the energy is increased by 13.69621 kJ/mol. And when both of the bridging chlorine atoms are substituted by bromine atoms, energy is increased by 26.27622 kJ/mol, which is twice the increased energy when only one bromine atom is in the bridging position. This indicates that the energy of Al₂Br₂Cl₄ is highly dependent on the number of bridging bromine atoms. Cl atom and Al atom are in the same period, therefore they have a good overlap between their valence orbitals (3p), resulting in a lower energy and more stable covalent bond. Yet, Br atom has valence orbitals of 4p which is a poor overlap with 3p orbitals of Al atom, leading to a higher energy and less stable covalent bond.

Overall, bromine atoms do not favour a bridging position in Al₂Cl₄Br₂ compared to chlorine atoms, isomer 4 which has two bridging Cl atoms is the most stable isomer.

Optimisation analysis is carried out on AlBrCl₂, the following result is obtained.

AlBrCl₂ Optimisation
Image
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	Gen
Charge	0
Spin	Singlet
Final Energy in Atomic Units / ±0.003808780 a.u.	-1176.19013679
Gradient / a.u.	0.00004196
Imaginary Frequency
Dipole Moment / ±0.01 Debye	0.11
Point Group	C_2v
Job cpu Time	0 days 0 hours 0 minutes 36.8 seconds
D-Space Link	DOI:10042/25697

"Item" book of AlBrCl₂ Optimisation

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=-7.984418D-08
Optimization completed.

E(AlBrCl₂)= -1176.19013679 ±0.003808780 a.u. = -3088090 ±10 kJ/mol

Dissociation Energy = 2E(AlBrCl₂) - E(isomer4)= 2*-3088087.20414 - (-6176269.03782)= 90 ±10 kJ/mol

The dissociation energy shows a positive value which means that the dimer has a lower energy than two monomers. Therefore the product (dimer) is more stable than isolated monomers.

Frequency Analysis

Al₂Cl₄Br₂ Isomers (Frequency Analysis)
Name	Isomer 1	Isomer 2	Isomer 3	Isomer 4
Image
Calculation Type	FREQ	FREQ	FREQ	FREQ
Calculation Method	RB3LYP	RB3LYP	RB3LYP	RB3LYP
Basis Set	Gen	Gen	Gen	Gen
Charge	0	0	0	0
Spin	Singlet	Singlet	Singlet	Singlet
Final Energy in Atomic Units / ±0.003808780 a.u.	-2352.40630798	-2352.41626681	-2352.41109945	-2352.41631606
Gradient / a.u.	0.00000076	0.00000127	0.00000490	0.00001799
Imaginary Frequency	0	0	0	0
Dipole Moment / ±0.01 Debye	0.00	0.17	0.14	0.01
Point Group	C_2v	C_2v	C1	CS
Job cpu Time	0 days 0 hours 1 minutes 18.5 seconds	0 days 0 hours 1 minutes 35.3 seconds	0 days 0 hours 3 minutes 17.8 seconds	0 days 0 hours 2 minutes 5.7 seconds
IR Spectrum
D-Space Link	DOI:10042/25647	DOI:10042/25648	DOI:10042/25649	DOI:10042/25718

Different isomers have different symmetries, which implies that different number of vibrations and type of modes are expected. Some vibrational modes display no change in dipole moment, which makes them IR inactive. An IR active vibrational mode requires at least one change in dipole ^[4]. Otherwise it would not be detected by IR spectrometer.

MO

Isomer 4 MO Summary
Q	A
Calculation Type	SP
Calculation Method	RB3LYP
Basis Set	GEN
Charge	0
Spin	Singlet
Final Energy in Atomic Units	-2352.41631606 ±0.003808780 a.u.
Gradient	0.00000000 a.u.
Dipole Moment	0.01 ±0.01 Debye
Point Group	CS
Job Time	0 days 0 hours 0 minutes 19.6 seconds
D-Space Link	DOI:10042/25730

Al₂Cl₄Br₂ Isomers (Optimisation)
	Image	Description
Highly Bonding		There are through-space interactions, the only exception is the strong anti-bonding interaction in the middle. Two nodes present in total, there is one angular node as a flat plane in the middle, and one radial node as a circular ring outside. Delocalisation is strong is this MO.
		Through-space interactions exist between the orbitals of bridging atom and orbitals of terminal atom. All through-space interactions are bonding orbitals in this molecular orbital and only one radial node exists. It can be seen that the green orbital in the middle is greatly delocalised.
		The strong bonding interactions in this molecular orbital shown in the diagram are through-space interactions. There are two angular nodes sit in the middle. There is weak delocalisation between orbitals of terminal chlorine atom and bridging chlorine atom.
		There are four weak through-space interactions in this MO, two of which are bonding interactions and the other two are anti-bonding interactions. There is one angular node between two bridging chlorine atoms and one radial node outside. It can be seen from the diagram that delocalisation is strong between bridging chlorine atom and two separate terminal atoms.
Highly Anti-bonding		Through-space interactions present in this MO. There are two radial nodes and four angular nodes. MO is not well delocalised.

Further Study

There is a possibility should be considered which is the presents of the fifth isomer. Al₂Cl₄Br₂ could undergo interchange, resulting in the attachment of both bromine atoms to the same aluminum atom on terminal positions. The fifth isomer is being optimised and the following summary is obtained.

isomer 5 Optimisation
Image
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	Gen
Charge	0
Spin	Singlet
Final Energy in Atomic Units / ±0.003808780 a.u.	-2352.41632893
Gradient / a.u.	0.00000939
Imaginary Frequency
Dipole Moment / ±0.01 Debye	0.19
Point Group	CS
Job cpu Time	0 days 0 hours 3 minutes 13.2 seconds
D-Space Link	DOI:10042/25656

"Item" book of isomer 5 Optimisation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000021     0.000450     YES
 RMS     Force            0.000009     0.000300     YES
 Maximum Displacement     0.000285     0.001800     YES
 RMS     Displacement     0.000115     0.001200     YES
 Predicted change in Energy=-7.918666D-09
 Optimization completed.

When it is compared to the other four isomers, isomer 5 shows a lower energy than the energies of other four isomers, meaning it is more stable. Therefore, based on the calculations, there is a high chance of the existence of isomer 5.

References

↑ 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.
↑ Hunt Research Group, Understanding optimisation part a., http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year3/3a_understand_opt.html
↑ B. E. Bursten, Some comments on approximate LCAO molecular orbital theory in organometallic chemistry: Getting more by doing less?, Pure & Appl. Chem., 1991, 63, 841.
↑ J. D. Paula, P. Atkins, Elements of physical chemistry, 2009, 5, 459

[GaBr-1] 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.

[Hunt-2] Hunt Research Group, Understanding optimisation part a., http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year3/3a_understand_opt.html

[LCAO-3] B. E. Bursten, Some comments on approximate LCAO molecular orbital theory in organometallic chemistry: Getting more by doing less?, Pure & Appl. Chem., 1991, 63, 841.

[IR_active-4] J. D. Paula, P. Atkins, Elements of physical chemistry, 2009, 5, 459

[1]

[2]

[3]

[4]

Week One

Day One

3-21G

6-31G(d,p)

Day Two

GaBr3

BBr3

Analysis

Day Three

BH3 Frequency Analysis

GaBr3 Frequency Analysis

MOs of BH3

NH3

Ammonia-Borane

Mini Project

Optimisation

Frequency Analysis

MO

Further Study

References

GaBr₃

BBr₃

BH₃ Frequency Analysis

GaBr₃ Frequency Analysis

MOs of BH₃

NH₃