Introduction

Computational chemistry can be very useful in allowing molecules that can't be characterised by experimental methods, to be analysed. It enables the location of transition states, and can provide important information about molecular orbitals, atomic interactions and dipole moments. In the following study, the program GaussView 5.0 was used to create and analyse molecules, using a variety of different basis sets and methodologies. In cases where more complex calculations were required, files were submitted to the HPC.

BH₃ Optimisation

A BH₃ molecule with trigonal planar geometry was drawn and the lengths of the B-H bonds were changed from the original 1.18A to 1.50A.

The H-B-H bond angle was 120.0 degrees.

Two different basis sets were used to optimise the borane molecule : 3-21G and 6-31G (d,p). Both were B3LYP

3-21G Basis Set

File:BH3OPTIMISATION.LOG

BH₃
File Type	.log
Calculation Type	FOPT
Calculation Method	B3YLP
Basis Set	3-21G
Final Energy	-26.46 a.u.
Gradient	0.00020672 a.u.
Dipole Moment	0.00 Debye
Point Group	D₃h
CPU Time	9.0 seconds
B-H Bond Length	1.19 a.u.
H-B-H Bond Angle	120.0

  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.
   -- Stationary point found.

The optimisation of a molecule involves solving the Schrodinger equation for varying positions of the nuclei. The Total Energy graph is formed from Gaussview iteratively searching for the minimum energy structure, where the gradient (dE/dx) of the potential energy surface equals 0. The results from the calculation tabulate that the iterations have converged at dE/dx=0, showing that the molecule has been successfully optimised. The graph of the Root Mean Square (RMS) Gradient approaches zero as Gaussview gets closer to the energy minimum. The final structure has the lowest energy, corresponding to the smallest RMS gradient.

The above graphs and values of dE/dx won't be included for the rest of the calculations in this study.

6-31G Basis Set

File:BH3OPTIMISATION631G.LOG

BH₃
File Type	.log
Calculation Type	FOPT
Calculation Method	B3YLP
Basis Set	6-31G(d,p)
Final Energy	-26.61 a.u.
Gradient	0.00000235 a.u.
Dipole Moment	0.00 Debye
Point Group	D₃h
CPU Time	10 seconds.
B-H Bond Length	1.19 a.u.
H-B-H Bond Angle	120.0

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=-1.304899D-10
Optimization completed.
   -- Stationary point found.

TlBr₃ Optimisation

TlBr₃ was optimised with a medium level basis set. The high electron count of this molecule means that it displays relativistic effects. To account for this, a pseudo-potential has to be used, which implements the approximation that only valence electrons are involved in bonding interactions.

File:Tlbr3optoutput.log

TlBr₃
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3YLP
Basis Set	LANL2DZ
Final Energy	-91.22 a.u.
Gradient	0.00275003 a.u.
Dipole Moment	0.00 Debye
Point Group	D₃h
CPU Time	29.5 seconds
Tl-Br Bond Length	2.65 a.u.
Br-Tl-Br Bond Angle	120.0

The calculated bond length is fairly close to literature value of 2.52Å [1], which shows that the models used by the program are good approximations.

        Item               Value     Threshold  Converged?
Maximum Force            0.000002     0.000450     YES
RMS     Force            0.000001     0.000300     YES
Maximum Displacement     0.000022     0.001800     YES
RMS     Displacement     0.000014     0.001200     YES
Predicted change in Energy=-6.084017D-11
Optimization completed.
   -- Stationary point found.

BBr₃ Optimisation

The calculation was published in D-space.

File:Bbr3outpuopt.log

BBr₃
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3YLP
Basis Set	GEN
Final Energy	-64.43 a.u.
Gradient	0.01418127 a.u.
Dipole Moment	0.00 Debye
Point Group	D₃h
CPU Time	18.1 seconds
B-Br Bond Length	1.93 a.u.
H-B-H Bond Angle	120.0

The calculated bond length is fairly close to literature value of 1.88Å [2], which shows that the models used by the program are good approximations.

        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=-4.026911D-10
Optimization completed.
   -- Stationary point found.

Structure Comparison

Atom	Electron Configuration
B	[He] 2s² 2p¹
Br	[Ar] 4s² 3d¹⁰ 4p⁵
H	1s¹
Tl	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p¹

Molecule	Bond Distance (a.u.)
BH₃	1.19
BBr₃	1.93
TlBr₃	2.65

Tl has larger, most diffuse valence orbitals than Boron, with a greater amount of shielding. This means that Tl gives poorer overlap with a substituent and so the longest bond distance is between Tl and Br. It is the same situation for Br in comparison to H. Br has more diffuse orbitals, with greater shielding than H, so the B-Br bond length is greater than that of B-H.

Both Br and H are non-metals with electronegativities of 2.96 and 2.20 respectively (Pauling Scale), compared to B with 2.04. The bonding character in BH3 will be covalent with comparatively little polarity in the B-H bonds, compared to BBr3 which is also covalently bonded but with a greater polarity in the B-Br bonds.

BH₃ Frequency Analysis

File:JULIUSGUTH BH3 FREQ.LOG

BH₃
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3YLP
Basis Set	6-31G(d,p)
Final Energy	-26.61 a.u.
Gradient	0.00000237 a.u.
Dipole Moment	0.00 Debye
Point Group	D₃h
CPU Time	12.0 seconds
B-H Bond Length	1.19 a.u.
H-B-H Bond Angle	120.0

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

        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=-1.323374D-10
Optimization completed.
   -- Stationary point found.

Mode	Frequency (cm^-1)	Infrared	Description	Point Group
1	1163.00	92.5478	3H bending in and out of plane	A2"
2	1213.19	14.0553	one H stationary, other 2H in-plane scissoring	E'
3	1213.19	14.0589	3H in-plane rocking	E'
4	2582.26	0.0000	3H symmetrical stretching	A₁'
5	2715.43	126.3307	one H stationary, other 2H asymmetrical stretching	E'
6	2715.43	126.3211	3H asymmetrical stretching	E'

Main peaks (Frequency/cm^-1): 1163, 1213, 2715

There are 6 vibrational modes, but the predicted IR spectrum only has 3 peaks. This is because modes 1 and 2 are degenerate, so they only produce one peak, because they have the same wavenumber. Mode 4 has no intensity (0.00) because it is a fully symmetrical stretch, resulting in no change of the dipole moment. Modes 5 and 6 are again degenerate, having the same wavenumber and so again only contribute 1 peak between them. This gives 3 peaks in total, as seen in the predicted spectrum.

TlBr₃ Frequency

The calculation was published in D-space.

File:Freqtlbr3 output.log

TlBr₃
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3YLP
Basis Set	LANL2DZ
Final Energy	-91.22 a.u.
Gradient	0.00000088 a.u.
Dipole Moment	0.00 Debye
Point Group	D₃h
CPU Time	15.7 seconds
Tl-Br Bond Length	2.65 a.u.
Br-Tl-Br Bond Angle	120.0

AS with BH₃, the 6 vibrational modes only equate to 3 peaks in the predicted IR spectrum, due to degeneracy and the lack of dipole moment change in mode 4.

        Item               Value     Threshold  Converged?
Maximum Force            0.000002     0.000450     YES
RMS     Force            0.000001     0.000300     YES
Maximum Displacement     0.000022     0.001800     YES
RMS     Displacement     0.000011     0.001200     YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
   -- Stationary point found.

Low frequencies ---   -3.4213   -0.0026   -0.0004    0.0015    3.9367    3.9367
Low frequencies ---   46.4289   46.4292   52.1449

Mode	Frequency (cm^-1)	Infrared	Description	Point Group
1	46.43	3.6867	One Br stationary, other 2Br in-plane scissoring	E'
2	46.43	3.6867	3Br in-plane rocking	E'
3	52.14	5.8466	3Br bending in and out of plane	A2"
4	165.27	0.0000	3Br symmetrical stretching	A₁
5	210.69	25.4830	One Br stationary, other 2 Br asymmetrical stretching	E'
6	210.69	25.4797	3Br asymmetrical stretching	E'

Main peaks (Frequency/cm^-1): 46, 52, 211

Comparison of TlBr3 and BH3 Vibrational Frequencies

Vibrational Mode	BH₃ Frequency (cm^-1)	TlBr₃ Frequency (cm^-1)
1	1163.00	46.43
2	1213.19	46.43
3	1213.19	52.14
4	2582.26	165.27
5	2715.43	210.69
6	2715.43	210.69

The vibrational frequencies can be approximated using Hooke's Law, which shows that the frequency is proportional to the square root of the bond constant and 1/square root of the reduced mass. This explains why the BH3 vibrational frequencies are all at higher wavenumbers than those of TlBr3; the more diffuse orbitals of the Tl and Br atoms gives a poorer orbital overlap, and so a smaller bond constant and the higher atomic weight of the Tl and Br atoms, gives them a higher reduced mass.

The same basis set and method has to be used for the optimisation and frequency analysis calculations due to the total energy being dependent on which basis set is used. For comparison, the same number of atoms is required, with the same basis-set throughout. Non-linear molecules have 3N-6 vibrational frequencies. The low frequencies represent the '-6' part of the vibrational frequencies. The positive values from this onwards, are the 'real' vibrational frequencies.

BH₃ Population Analysis

The calculation was published in D-space.

File:Bh3popanalysis.log

BH₃
File Type	.log
Calculation Type	SP
Calculation Method	RB3YLP
Basis Set	6-31G(d,p)
Final Energy	-26.61 a.u.
Gradient	0.0000000 a.u.
Dipole Moment	0.00 Debye
Point Group	D₃h
CPU Time	10.5 seconds
B-H Bond Length	1.19 a.u.
H-B-H Bond Angle	120.0

The fragment orbitals used to create the MO diagram were H3, with a central B atom. For the H3 fragment, the lowest energy fragment orbital is bonding and symmetric, which has a1' symmetry. There are two degenerate higher energy FOs of e' symmetry. For the B atom, the lowest energy orbital is the s orbital, which has a1' symmetry. The px and py orbitals are degenerate with e' symmetry and the pz orbital has a2" symmetry. B and H have similar electronegativities and so the two a1' symmetry orbitals combine with a large splitting energy. The e' orbitals also combine, but with with a smaller splitting energy. The a2" orbitals remain non-bonding.

NH₃ NBO Analysis

NH₃ Optimisation

File:NH3OPTIMISE.LOG

NH₃
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3YLP
Basis Set	6-31G(d,p)
Final Energy	-56.56 a.u.
Gradient	0.00000885 a.u.
Dipole Moment	1.85 Debye
Point Group	C1
CPU Time	15.0 seconds
N-H Bond Length	1.02 a.u.
H-N-H Bond Angle	105.7

        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=-1.629731D-09
Optimization completed.
   -- Stationary point found.

NH₃ Frequency Analysis

File:NH3FREQUENCY1.LOG

NH₃
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3YLP
Basis Set	6-31G(d,p)
Final Energy	-56.56 a.u.
Gradient	0.00000888 a.u.
Dipole Moment	1.85 Debye
Point Group	C1
CPU Time	15.0 seconds
N-H Bond Length	1.02 a.u.
H-N-H Bond Angle	105.7

Low frequencies ---  -30.7764   -0.0019   -0.0015   -0.0011   20.3142   28.2484
Low frequencies --- 1089.5557 1694.1237 1694.1868

       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=-1.603126D-09
Optimization completed.
   -- Stationary point found.

Main peaks (Frequency/cm^-1): 1090, 1694

NH₃ Population Analysis

The calculation was published in D-space.

File:Nh3popanalysisnbo.log

NH₃
File Type	.log
Calculation Type	SP
Calculation Method	RB3YLP
Basis Set	6-31G(d,p)
Final Energy	-56.56 a.u.
Gradient	0.00000888 a.u.
Dipole Moment	1.85 Debye
Point Group	C1
CPU Time	6.5 seconds
N-H Bond Length	1.02 a.u.
H-N-H Bond Angle	105.7

 Summary of Natural Population Analysis:                  
                                                          
                                       Natural Population 
                Natural  -----------------------------------------------
    Atom  No    Charge         Core      Valence    Rydberg      Total
 -----------------------------------------------------------------------
      N    1   -1.12515      1.99982     6.11104    0.01429     8.12515
      H    2    0.37505      0.00000     0.62250    0.00246     0.62495
      H    3    0.37505      0.00000     0.62250    0.00246     0.62495
      H    4    0.37505      0.00000     0.62249    0.00246     0.62495
 =======================================================================
   * Total *    0.00000      1.99982     7.97852    0.02166    10.00000

       (Occupancy)   Bond orbital/ Coefficients/ Hybrids
 ---------------------------------------------------------------------------------
     1. (1.99909) BD ( 1) N   1 - H   2  
                ( 68.83%)   0.8297* N   1 s( 24.87%)p 3.02( 75.05%)d 0.00(  0.09%)
                                           -0.0001 -0.4986 -0.0059  0.0000 -0.2910
                                            0.0052  0.8155  0.0277  0.0000  0.0000
                                            0.0281  0.0000  0.0000  0.0032  0.0082
                ( 31.17%)   0.5583* H   2 s( 99.91%)p 0.00(  0.09%)
                                           -0.9996  0.0000  0.0072 -0.0289  0.0000
     2. (1.99909) BD ( 1) N   1 - H   3  
                ( 68.83%)   0.8297* N   1 s( 24.86%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000  0.2910
                                           -0.0052  0.4077  0.0138  0.7062  0.0240
                                            0.0140  0.0243  0.0076  0.0033  0.0031
                ( 31.17%)   0.5583* H   3 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000 -0.0072 -0.0145 -0.0250
     3. (1.99909) BD ( 1) N   1 - H   4  
                ( 68.83%)   0.8297* N   1 s( 24.87%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000  0.2909
                                           -0.0052  0.4077  0.0138 -0.7062 -0.0239
                                            0.0140 -0.0243 -0.0076  0.0033  0.0031
                ( 31.17%)   0.5583* H   4 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000 -0.0072 -0.0145  0.0250
     4. (1.99982) CR ( 1) N   1           s(100.00%)
                                            1.0000 -0.0002  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
     5. (1.99721) LP ( 1) N   1           s( 25.38%)p 2.94( 74.52%)d 0.00(  0.10%)
                                            0.0001  0.5036 -0.0120  0.0000 -0.8618
                                            0.0505  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000 -0.0269  0.0155

 Natural Bond Orbitals (Summary):
                                                            Principal Delocalizations
           NBO                        Occupancy    Energy   (geminal,vicinal,remote)
 ====================================================================================
 Molecular unit  1  (H3N)
     1. BD (   1) N   1 - H   2          1.99909    -0.60417   
     2. BD (   1) N   1 - H   3          1.99909    -0.60417   
     3. BD (   1) N   1 - H   4          1.99909    -0.60416   
     4. CR (   1) N   1                  1.99982   -14.16768   
     5. LP (   1) N   1                  1.99721    -0.31756  24(v),16(v),20(v),17(v)
                                                    21(v),25(v)

Calculation of charge distribution between -1.000 to +1.000 was colour coordinated, with red indicating an area of negative charge region and green a positively charged region.

The relative charges were -1.125 for the central N atom and +0.375 for the H atoms.

NH₃BH₃

NH₃BH₃ Optimisation

3-21 G Basis Set

File:NH3BH3OPT321G.LOG

NH₃BH₃
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3YLP
Basis Set	2-31G
Final Energy	-82.77 a.u.
Gradient	0.00003006 a.u.
Dipole Moment	5.84 Debye
Point Group	C1
CPU Time	42.0 seconds.
N-H Bond Length	1.03 a.u.
H-N-H Bond Angle	109.4
B-H Bond Length	1.21 a.u.
H-B-H Bond Angle	113.6

        Item               Value     Threshold  Converged?
Maximum Force            0.000094     0.000450     YES
RMS     Force            0.000030     0.000300     YES
Maximum Displacement     0.000419     0.001800     YES
RMS     Displacement     0.000178     0.001200     YES
Predicted change in Energy=-5.742850D-08
Optimization completed.
   -- Stationary point found.

6-31G Basis Set

File:NH3BH3OPT631G.LOG

NH₃BH₃
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3YLP
Basis Set	6-31G(d,p)
Final Energy	-83.22 a.u.
Gradient	0.00005649 a.u.
Dipole Moment	5.56 Debye
Point Group	C1
CPU Time	50.0 seconds.
N-H Bond Length	1.02 a.u.
H-N-H Bond Angle	107.9
B-H Bond Length	1.21 a.u.
H-B-H Bond Angle	113.9

        Item               Value     Threshold  Converged?
Maximum Force            0.000132     0.000450     YES
RMS     Force            0.000037     0.000300     YES
Maximum Displacement     0.001192     0.001800     YES
RMS     Displacement     0.000531     0.001200     YES
Predicted change in Energy=-1.177617D-07
Optimization completed.
   -- Stationary point found.

Frequency Analysis

File:JULIUSGUTH NH3BH3FREQ.LOG

NH₃BH₃
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3YLP
Basis Set	6-31G(d,p)
Final Energy	-83.22 a.u.
Gradient	0.00005654 a.u.
Dipole Moment	5.56 Debye
Point Group	C1
CPU Time	69.0 seconds
N-H Bond Length	1.018 a.u.
H-N-H Bond Angle	107.9
B-H Bond Length	1.21 a.u.
H-B-H Bond Angle	113.9

Low frequencies ---   -0.0012   -0.0010   -0.0009    3.5300   15.6870   20.3924
Low frequencies ---  263.3630  631.3094  638.1307

       Item               Value     Threshold  Converged?
Maximum Force            0.000254     0.000450     YES
RMS     Force            0.000057     0.000300     YES
Maximum Displacement     0.001412     0.001800     YES
RMS     Displacement     0.000694     0.001200     YES
Predicted change in Energy=-2.141505D-07
Optimization completed.
   -- Stationary point found.

Main peaks (Frequency/cm^-1): 638, 1069, 1204, 1329, 1676, 2472, 2533, 3581

Association Energy of NH3BH3

E(BH3) = -26.61 a.u.

E(NH3) = -56.56 a.u.

E(BH3NH3) = -83.22 a.u.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE = -83.22 a.u. - -83.17

ΔE = -0.05 a.u.

1 a.u. = 2625.5 kJ mol-1

Enthalpy of formation of ammonia-borane ΔHf = -0.05 a.u. * 2625.5 = -131.3 kJ mol-1

This value is lower than the literature value of -172.1 kJ mol-1

Lewis Acid Mini project

Cl2Al(μ-Br2)AlCl2 isomer

Optimisation and pseudo-potential

File:Al2br2cl4optimised631gpseudo.log

Al₂Br₂Cl₄
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	GEN
Final Energy	-2352.40630798 a.u.
Gradient	0.00000396 a.u.
Dipole Moment	0.00 Debye
Point Group	D₂h
CPU Time	3 minutes 21.0 seconds

      Item               Value     Threshold  Converged?
 Maximum Force            0.000007     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000154     0.001800     YES
 RMS     Displacement     0.000058     0.001200     YES
 Predicted change in Energy=-1.207258D-09
 Optimization completed.
    -- Stationary point found.

Frequency Analysis

File:Alisomer1freq.log

 Low frequencies ---   -5.1810   -5.0302   -3.2289   -0.0003    0.0012    0.0031
 Low frequencies ---   14.8284   63.2817   86.0839

        Item               Value     Threshold  Converged?
 Maximum Force            0.000013     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000209     0.001800     YES
 RMS     Displacement     0.000099     0.001200     YES
 Predicted change in Energy=-2.119810D-09
 Optimization completed.
    -- Stationary point found.

Main peaks (Frequency/cm^-1): 241, 341, 467, 616

BrClAl(μ-Br,Cl)AlCl2

Optimisation and pseudo-potential

File:Al2br2cl4 2ndisomerpseudoout.log

Al₂Br₂Cl₄
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	GEN
Final Energy	-2352.41109944 a.u.
Gradient	0.00001557 a.u.
Dipole Moment	0.1386 Debye
Point Group	D₂h
CPU Time	4 minutes 16.8 seconds

  Item               Value     Threshold  Converged?
 Maximum Force            0.000035     0.000450     YES
 RMS     Force            0.000014     0.000300     YES
 Maximum Displacement     0.000509     0.001800     YES
 RMS     Displacement     0.000182     0.001200     YES
 Predicted change in Energy=-2.015419D-08
 Optimization completed.
    -- Stationary point found.

Frequency Analysis

File:Alisomer2freq.log

 Low frequencies ---   -2.2907    0.0011    0.0016    0.0019    1.2447    3.3231
 Low frequencies ---   17.1610   55.9531   80.0563

   Item               Value     Threshold  Converged?
 Maximum Force            0.000034     0.000450     YES
 RMS     Force            0.000016     0.000300     YES
 Maximum Displacement     0.001349     0.001800     YES
 RMS     Displacement     0.000527     0.001200     YES
 Predicted change in Energy=-3.663910D-08
 Optimization completed.
    -- Stationary point found.

Main peaks (Frequency/cm^-1): 289, 384, 424, 493, 574, 614

Trans-BrClAl(μ-Cl2)AlClBr

Optimisation and pseudo-potential

File:Al isomer3outputpseudo.log

Al₂Br₂Cl₄
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	GEN
Final Energy	-2352.41629858 a.u.
Gradient	0.00001567 a.u.
Dipole Moment	0.00 Debye
Point Group	D₂h
CPU Time	4 minutes 6.2 seconds

         Item               Value     Threshold  Converged?
 Maximum Force            0.000039     0.000450     YES
 RMS     Force            0.000015     0.000300     YES
 Maximum Displacement     0.000467     0.001800     YES
 RMS     Displacement     0.000168     0.001200     YES
 Predicted change in Energy=-2.435287D-08
 Optimization completed.
    -- Stationary point found.

Frequency Analysis

File:Alisomerfreqisomer3 .log

 Low frequencies ---   -4.7965    0.0020    0.0024    0.0030    1.4551    2.2602
 Low frequencies ---   18.1749   49.1211   73.0074

        Item               Value     Threshold  Converged?
 Maximum Force            0.000050     0.000450     YES
 RMS     Force            0.000016     0.000300     YES
 Maximum Displacement     0.000576     0.001800     YES
 RMS     Displacement     0.000258     0.001200     YES
 Predicted change in Energy=-3.235482D-08
 Optimization completed.
    -- Stationary point found.

Main peaks (Frequency/cm^-1): 421, 579

Cis-BrClAl(μ-Cl2)AlClBr

Optimisation and pseudo-potential

File:Al pseudooutputisomer4.log

Al₂Br₂Cl₄
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	GEN
Final Energy	-2352.41626677 a.u.
Gradient	0.00001470 a.u.
Dipole Moment	0.1658 Debye
Point Group	D₂h
CPU Time	4 minutes 8.1 seconds.

        Item               Value     Threshold  Converged?
 Maximum Force            0.000040     0.000450     YES
 RMS     Force            0.000016     0.000300     YES
 Maximum Displacement     0.001359     0.001800     YES
 RMS     Displacement     0.000424     0.001200     YES
 Predicted change in Energy=-2.577003D-08
 Optimization completed.
    -- Stationary point found.

Frequency Analysis

File:Alisomer4freq .log

 Low frequencies ---   -3.8191   -2.2355   -0.0023   -0.0015    0.0007    1.3869
 Low frequencies ---   17.2012   50.9457   78.5393

        Item               Value     Threshold  Converged?
 Maximum Force            0.000048     0.000450     YES
 RMS     Force            0.000015     0.000300     YES
 Maximum Displacement     0.001464     0.001800     YES
 RMS     Displacement     0.000541     0.001200     YES
 Predicted change in Energy=-4.001091D-08
 Optimization completed.
    -- Stationary point found.

Main peaks (Frequency/cm^-1): 420, 582

Disssociation Energy of trans isomer

E(monomer) = -1176.19013697 a.u.

E(adduct) = -2352.41629858 a.u

ΔE = E(adduct)-[2x(monomer)]

ΔE = -2352.41629858 - -(2x-1176.19013697)

ΔE = -0.03602464 a.u.

1 a.u. = 2625.5 kJ mol-1

Enthalpy of dissociation = -0.03602464 a.u. * 2625.5 = -94.6 kJ mol-1

Relative Energies

Energy Comparison
Molecule	Energy (a.u.)	Energy (kJ/mol)	Relative Energy (kJ/mol)
Cl2Al(μ-Br2)AlCl2	-2352.40630798	-6176242.762	26.23
BrClAl(μ-Br,Cl)AlCl2	-2352.41626677	-6176268.908	0.08
Trans-BrClAl(μ-Cl2)AlClBr	-2352.41629858	-6176268.992	0.00
Cis-BrClAl(μ-Cl2)AlClBr	-2352.41109944	-6176255.342	13.65

Trans-BrClAl(μ-Cl2)AlClBr has the lowest energy and so is the most stable isomer. This is because when broken into the two constituent monomers, there is an electron acceptor (acting as the lewis acid) and an electron donor (acting as a lewis base)in each of the fragments. The trans isomer was therefore assigned an energy of zero, so that the relative energies of the other isomers could be more easily compared to this.

The Cl2Al(μ-Br2)AlCl2 isomer has the highest relative energy and so is the least stable. This is because Br has more diffuse orbitals than Cl, so the orbital overlap of the Al atoms with the bridging Br atoms is less effective than with Cl atoms.

Monomer

Optimisation and pseudo-potential

File:Monomer631.log

AlBrCl₂
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	GEN
Final Energy	-1176.19013697 a.u.
Gradient	0.00000291 a.u.
Dipole Moment	0.1134 Debye
Point Group	C₂v
CPU Time	46.6 seconds

     Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000022     0.001800     YES
 RMS     Displacement     0.000012     0.001200     YES
 Predicted change in Energy=-1.397817D-10
 Optimization completed.
    -- Stationary point found.

Frequency Analysis

File:Monomerfreq .log

 Low frequencies ---   -2.4223   -0.0067   -0.0065   -0.0059    2.7464    2.9629
 Low frequencies ---  120.5194  133.8347  185.7791

       Item               Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000021     0.001800     YES
 RMS     Displacement     0.000009     0.001200     YES
 Predicted change in Energy=-1.460239D-10
 Optimization completed.
    -- Stationary point found.

Orbital representation	Energy	Description
	-0.42931	The high level of delocalisation shown in these molecular orbitals implies that there is significant aromatic character. A combination of the p orbitals of the terminal halides contributing to the electron density and alignment of the py orbitals of the Al atoms and bridging chlorides causes this aromaticity.
	-0.50714	The p orbitals of the terminal halides bond end-on with the Al atoms in sigma bonding interactions. There is antibonding character with respect to the bridging chlorine atoms. There are 5 nodal planes, with 4 of them bisecting the bonds between the Al atoms and terminal halides and the other bisecting the bridging Cl atoms.
	-0.45914	The pz orbitals of the terminal chlorine atoms are involved in pi bonding interactions, whereas the bridging chlrorines display pi antibonding characteristics. There are 6 nodes, 4 perpendicular to the bonds between the Al and terminal halides and one above and below the plane of the terminal halides.
	-0.32163	As Br is a bigger atom than Cl, it has larger, more diffuse orbitals. This is represented in the molecular orbitals, where the Br pz orbitals are visibly much larger than the Cl pz orbitals, with pi antibonding interactions between them. There are 6 nodes in total, with one between each of the terminal halide pairs.
	-0.31462	These molecular orbitals represent the HOMO of the molecule, which shows overall antibonding character. As with the previous molecular orbitals, the larger, more diffuse nature of the Br orbitals in comparison to Cl can clearly be seen. There are several weak through-space bonding interactions. There are 4 nodes, with one going through the plane of the aluminium atoms and terminal halides, and the other remaining three nodal planes perpendicular to this.

1.↑ M. Schuurman, W. Allen, H. Schaefer, Journal of Computational Chemistry, 2005, 26, 1106

2.↑ J. Blixt et al., J. Am. Chem. Soc. , 117, 1995, pp 5089 - 5104

3.↑ Bondi (1964) J. Phys. Chem. 68, 441

4.↑ Paula, Peter Atkins, Julio de (2009). Elements of physical chemistry (5th ed. ed.). Oxford: Oxford U.P. pp. 459. ISBN 978-0-19-922672-6.

Introduction

BH3 Optimisation

3-21G Basis Set

6-31G Basis Set

TlBr3 Optimisation

BBr3 Optimisation

Structure Comparison

BH3 Frequency Analysis

TlBr3 Frequency

Comparison of TlBr3 and BH3 Vibrational Frequencies

BH3 Population Analysis

NH3 NBO Analysis

NH3 Optimisation

NH3 Frequency Analysis

NH3 Population Analysis

NH3BH3

NH3BH3 Optimisation

3-21 G Basis Set

6-31G Basis Set

Frequency Analysis

Association Energy of NH3BH3

Lewis Acid Mini project

Cl2Al(μ-Br2)AlCl2 isomer

BrClAl(μ-Br,Cl)AlCl2

Trans-BrClAl(μ-Cl2)AlClBr

Cis-BrClAl(μ-Cl2)AlClBr

Relative Energies

Monomer

BH₃ Optimisation

TlBr₃ Optimisation

BBr₃ Optimisation

BH₃ Frequency Analysis

TlBr₃ Frequency

BH₃ Population Analysis

NH₃ NBO Analysis

NH₃ Optimisation

NH₃ Frequency Analysis

NH₃ Population Analysis

NH₃BH₃

NH₃BH₃ Optimisation