User:Ss4612

EX₃ Section

BH₃: B3LYP/3-21G(d,p)

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000217 0.000450 YES RMS Force 0.000105 0.000300 YES Maximum Displacement 0.000692 0.001800 YES RMS Displacement 0.000441 0.001200 YES Predicted change in Energy=-1.635269D-07 Optimization completed. -- Stationary point found.	optimised BH3 molecule

BH₃: B3LYP/6-31G(d,p)

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000203 0.000450 YES RMS Force 0.000098 0.000300 YES Maximum Displacement 0.000867 0.001800 YES RMS Displacement 0.000415 0.001200 YES Predicted change in Energy=-1.436238D-07 Optimization completed. -- Stationary point found.	optimised BH3 molecule

GaBr3: B3LYP/LANL2DZ

Optimisation file DOI:10042/31234

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000000 0.000450 YES RMS Force 0.000000 0.000300 YES Maximum Displacement 0.000003 0.001800 YES RMS Displacement 0.000002 0.001200 YES Predicted change in Energy=-1.307741D-12 Optimization completed. -- Stationary point found.	optimised GaBr3 molecule

BBr₃: B3LYP/6-31G(d,p)LANL2DZ

Optimisation file DOI:10042/31147

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000024 0.000450 YES RMS Force 0.000014 0.000300 YES Maximum Displacement 0.000131 0.001800 YES RMS Displacement 0.000089 0.001200 YES Predicted change in Energy=-3.306546D-09 Optimization completed. -- Stationary point found.	optimised BBr3 molecule

Geometry data

	BH3	BBr3	GaBr3
r(E-X)	1.19	1.93	2.35
θ(X-E-X)	120.0	120.0	120.0

As it can be seen from the geometry data of the EX₃ compounds, they all have the same bond angles, however the bond lengths increases in the order: BH3< BBr₃<GaBr₃. B and H are relatively small atoms (1st and 2nd row of the periodic table) therefore, they have better orbital alignment giving a stronger bond, resulting in a shorter bond length. In BBr3, Bromine is a large atom, so has poorer orbital alignment with Boron, therefore forms weaker bond represented by the longer bond length. The effect of changing the central element from Boron to Gallium can be seen when comparing the data from BBr₃ and GaBr₃. However, the relative energies of the molecules cannot be directly compared in this case as the calculations have been done using different basis sets. We could compare the bond lengths, however it is not always a good indication of the bond strength, as Ga-Br may have a larger bond length than B-Br, but since Gallium and Bromine are on the same row of the periodic table, they should have better orbital overlap giving rise to a stronger bond. Boron and Gallium are both group 13 elements, therefore have 3 valence electrons, coordinating to 3 ligands to give rise to trigonal planar compounds.

A bond is an attraction between 2 atoms due to electrostatics, giving rise to orbital overlap. The atoms involved in a bond share electron density between them. Strong chemical bonds occur when the orbital overlap is good- the atoms are from the same row of the periodic table- orbitals of similar energy. However, when the orbitals are of different sizes (different energies), orbital mismatch can occur which lead to weak bonds. Gaussian doesn’t draw bonds in some structures due to the distance between the atoms being larger than the pre-set values which are defined from the vanderwaals radii of the constituent atoms. However, it doesn’t necessarily mean that there is no electron density between the atoms so there orbital overlap may still be present.

BH₃:B3LYP/6-31G(d,p)

Frequency file: here

summary data	low modes
	Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625 Low frequencies --- 1162.9963 1213.1826 1213.1853

Vibrational spectrum for BH₃

wavenumber	Intensity	IR active?	type
1163	93	yes	bend
1213	14	very slight	bend
1213	14	very slight	bend
2582	0	no	stretch
2715	126	yes	stretch
2715	126	yes	stretch

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GaBr₃:B3LYP/6-31G(d,p)

Frequency file: DOI:10042/31174

summary data	low modes
	Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010 Low frequencies --- 76.3744 76.3753 99.6982

Vibrational spectrum for GaBr₃

wavenumber	Intensity	IR active?	type
76	3	very slight	bend
76	3	very slight	bend
100	9.21	very slight	bend
197	0	no	stretch
316	57	yes	stretch
316	57	yes	stretch

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Comparison of vibrational spectra of GaBr₃ and BH₃

Molecule	Vibrational frequencies
GaBr3	1 2 3 E' E' A2" Frequencies -- 76.3744 76.3753 99.6982 Red. masses -- 77.4211 77.4212 70.9513 Frc consts -- 0.2661 0.2661 0.4155 IR Inten -- 3.3447 3.3447 9.2161 4 5 6 A1' E' E' Frequencies -- 197.3371 316.1825 316.1863 Red. masses -- 78.9183 72.2067 72.2066 Frc consts -- 1.8107 4.2531 4.2532 IR Inten -- 0.0000 57.0704 57.0746
BH3	1 2 3 A2" E' E' Frequencies -- 1162.9963 1213.1826 1213.1853 Red. masses -- 1.2531 1.1072 1.1072 Frc consts -- 0.9986 0.9601 0.9601 IR Inten -- 92.5482 14.0551 14.0587 A1' E' E' Frequencies -- 2582.2764 2715.4465 2715.4477 Red. masses -- 1.0078 1.1273 1.1273 Frc consts -- 3.9595 4.8977 4.8977 IR Inten -- 0.0000 126.3302 126.3206

The most obvious difference between the vibrational spectra of GaBr₃ and BH₃ is the reordering of the vibrational modes. GaBr₃ and BH₃ have different characteristics because in BH3, the ligands (hydrogen atoms) are lighter than the central atom (Boron) whereas in GaBr₃, the heavier atoms (bromine) are the ligands and the lighter atom is the central atom (gallium). This causes a rearrangement in energies of the modes. For example, the a2” umbrella motion for BH₃, the hydrogen atoms have the larger displacement vectors than the Boron; whereas in GaBr₃, Ga has the higher displacement vector than the Br due to the Br being heavier than the Ga.

 
BH3 a2" mode with displacement vectors 

GaBr3 a2" mode with displacement vectors

The large difference in the vibrational frequencies of BH₃ and GaBr₃ indicate that the nature of the strength of the bonding is different for the two. Vibrational frequency is related to the reduced mass of the molecule (inversely proportional). Since GaBr has a larger reduced mass of 70.95, which is due to the constituent atoms being heavier, the frequency of vibrations are much lower than that of B-H where the constituent atoms have much lower reduced mass of 1.25

The force constants give an indication of the strength of the bond (albeit being good at short displacements due to the harmonic potential being parabolic, whereas an actual bond potential is better modelled by the morse potential), it is the second derivative of the potential energy surface. For the a2" umbrella motion, the force constant for BH3 is 1.00, whereas for GaBr3 is 0.27. This suggests that the bonding between B and H in BH3 is much stronger than Ga and Br in GaBr3. Also, the intensity of the IR frequency for a2" motion differs vastly for GaBr3 and BH3, being 9.21 and 92.55 respectively which for BH3 is 10 times as large than that of GaBr3. This would indicate that for BH3, there is a much larger change in the dipole moment than in GaBr3 for this motion.

A frequency analysis is carried out for a few reasons. In particular, it gives an idea of how well the optimisation of the molecule was carried out. The better the optimisation (reaching the lowest energy in the potential surface for a particular geometry), the lower the range of the low frequencies and the closer to zero they are. As well, experimentally, only the IR modes of vibration that cause a change in the dipole moment of the molecule show up on the IR spectra, however, when we carry out a frequency analysis, we could get an idea of the frequency of the vibrations that do not cause a change in the dipole moment and hence can't be detected experimentally via IR spectroscopy.

It is crucial that the same basis sets and methods are used for the optimisation and frequency calculations as calculations using different methods and basis sets may yield meaningless values becuase a frequency analysis is carried out on an optimised molecule.

MO analysis of BH₃

Energy MO file DOI:10042/31175

LCAO MOs and “real” MOs look quite similar. LCAO gives a good indication of the shape of the molecular orbital. The “real” MOs shows the overall orbital as a result of the atomic orbital contribution and also portrays well the extent of delocalisation of the orbitals of the molecule which from the LCAO approach can prove difficult to visualise. The bonding MO orbital has more contribution from the lower energy atomic orbital, where as the anti bonding orbital will have larger contribution from the contributing higher energy atomic orbital. It is useful to see the 3D computed MOs and derive the energies of the MOs. Qualitative analysis provides a quick and easy way of getting an idea of the MO and the relative energy levels, however it can prove difficult to judge the energies of the Molecular orbitals and thus the contributions from the atomic orbitals, through qualitative means.

NH₃: B3LYP/6-31G

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000000 0.000450 YES RMS Force 0.000000 0.000300 YES Maximum Displacement 0.000004 0.001800 YES RMS Displacement 0.000002 0.001200 YES Predicted change in Energy=-2.495686D-12 Optimization completed. -- Stationary point found.	optimised NH3 molecule

NH₃:B3LYP/6-31G(d,p)

Frequency log file here

summary data	low modes
	Low frequencies --- -7.8755 -7.7311 -7.7308 0.0013 0.0021 0.0116 Low frequencies --- 1089.2805 1693.9179 1693.9180

Vibrational spectrum for NH₃

wavenumber	Intensity	IR active?	type
1089	145	yes	bend
1694	14	very slight	bend
1694	14	very slight	bend
3461	1	very slight	stretch
3590	0	yes	stretch
3590	0	yes	stretch

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NH3 population analysis: DOI:10042/31235

Charge Distribution of NH₃

The following charge distribution is for NH3 molecule within the range -1.000 to +1.000. The colour red represents negative charge which sits on the Nitrogen atom due to it's high electronegativity; whilst green represents positive charge and sits on the Hydrogen atoms.

NBO charges on NH3

NH₃BH₃: B3LYP/6-31G(d,p)

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000006 0.000015 YES RMS Force 0.000002 0.000010 YES Maximum Displacement 0.000054 0.000060 YES RMS Displacement 0.000016 0.000040 YES Predicted change in Energy=-4.309418D-10 Optimization completed. -- Stationary point found.	optimised NH3BH3 molecule

NH₃BH₃ frequency analysis

Frequency log file here

summary data	low modes
	Low frequencies --- -6.2135 -0.1864 -0.0266 -0.0007 2.0267 2.0570 Low frequencies --- 263.2686 632.9065 638.4482

Vibrational spectrum for NH₃BH₃

wavenumber	Intensity	IR active?	type
263	0	no	H-N-B-H bend
633	14	very slight	N-B stretch
638	4	very slight	H3N-BH3 bend
638	4	very slight	H3N-BH3 bend
1069	41	yes	H3N-BH3 bend
1069	41	yes	H3N-BH3 bend
1196	109	yes	B-H bend
1204	3	very slight	B-H bend
1204	4	very slight	B-H bend
1329	114	yes	N-H bend
1676	28	yes	N-H bend
1676	28	yes	N-H bend
2472	67	yes	B-H stretch
2532	231	yes	B-H asymmetric stretch
2532	231	yes	B-H asymmetric stretch
3464	2.5	very slight	N-H symmetric stretch
3581	28	yes	N-H asymmetric stretch
3581	28	yes	N-H symmetric stretch

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Relative energy of NH₃BH₃:

• E(NH₃)=-56.5577686 a.u.
• E(BH₃)=-26.6153235 a.u.
• E(NH₃BH₃)=-83.2246891 a.u.

• ΔE=E(NH₃BH₃)-[E(NH₃)+E(BH₃)]= -0.0515970 a.u. = -135.47 kJ/mol

Since the relative energy is negative, it indicates that NH₃BH₃ is more stable than the starting materials, hence the formation of NH₃BH₃ from NH₃ and BH₃ is favourable.

Project Section: Lewis Acids and Bases

Al₂Cl₄Br₂: BL3YP; Al, Cl: 6-31G(d,p); Br: PP LANL2DZdp

Al₂Cl₄Br₂: Bridging Bromine (isomer 1)

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000003 0.000450 YES RMS Force 0.000001 0.000300 YES Maximum Displacement 0.000057 0.001800 YES RMS Displacement 0.000015 0.001200 YES Predicted change in Energy=-2.941357D-10 Optimization completed. -- Stationary point found.	optimised Al2Cl4Br2 bridging bromine molecule

Frequency analysis

Frequency log file here

summary data	low modes
	Low frequencies --- -5.1748 -5.0353 -3.1463 -0.0039 -0.0038 -0.0035 Low frequencies --- 14.8261 63.2702 86.0770

Vibrational spectrum

wavenumber	Intensity	IR active?	type
15	0	no	bend
63	0	no	bend
86	0	no	bend
87	0	no	bend
108	5	very slight	bend
111	0	no	bend
126	8	very slight	bend
135	0	no	bend
138	7	very slight	bend
163	0	no	bend
197	0	no	stretch
241	100	yes	stretch
247	0	no	symmetric stretch
341	161	yes	stretch
467	347	yes	stretch
494	0	no	stretch
608	0	no	stretch
616	332	yes	stretch

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Al₂Cl₄Br₂: Bridging Br,Cl (isomer 2)

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000105 0.000450 YES RMS Force 0.000026 0.000300 YES Maximum Displacement 0.001371 0.001800 YES RMS Displacement 0.000597 0.001200 YES Predicted change in Energy=-1.135980D-07 Optimization completed. -- Stationary point found.	optimised Al2Cl4Br2 bridging BrCl molecule

Frequency analysis

Frequency log file here

summary data	low modes
	Low frequencies --- -2.9949 -1.4967 -0.0018 -0.0009 0.0009 3.0905 Low frequencies --- 17.0179 55.9576 80.0483

Vibrational spectrum

wavenumber	Intensity	IR active?	type
17	0	no	bend
56	10	no	bend
80	0	no	bend
92	1	no	bend
107	0	no	bend
110	5	very slight	bend
121	8	very slight	bend
149	5	very slight	bend
154	6	very slight	bend
186	1	no	bend
211	21	yes	stretch
257	10	very slight	stretch
289	48	yes	stretch
384	154	yes	stretch
424	274	yes	stretch
493	107	yes	stretch
574	122	yes	stretch
615	197	yes	stretch

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Al₂Cl₄Br₂: Trans-terminal-Bromine (isomer 3)

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000004 0.000450 YES RMS Force 0.000002 0.000300 YES Maximum Displacement 0.000052 0.001800 YES RMS Displacement 0.000022 0.001200 YES Predicted change in Energy=-5.709023D-10 Optimization completed. -- Stationary point found.	optimised Al2Cl4Br2 trans-terminal-bromine molecule

Frequency analysis

Frequency log file here

summary data	low modes
	Low frequencies --- -4.2788 -2.4941 -0.0035 -0.0028 -0.0025 0.9634 Low frequencies --- 17.7201 48.9826 72.9516

Vibrational spectrum

wavenumber	Intensity	IR active?	type
18	0	no	bend
49	0	no	bend
73	0	no	bend
105	0	no	bend
110	0	no	bend
117	9	very slight	bend
120	13	very slight	bend
157	0	no	bend
160	6	very slight	bend
192	0	no	bend
264	0	no	stretch
289	29	yes	stretch
308	0	yes	stretch
413	149	yes	stretch
421	439	yes	stretch
459	0	no	stretch
574	0	no	stretch
580	316	yes	stretch

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Al₂Cl₄Br₂: Cis-terminal-Bromine (isomer 4)

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000022 0.000450 YES RMS Force 0.000012 0.000300 YES Maximum Displacement 0.000812 0.001800 YES RMS Displacement 0.000297 0.001200 YES Predicted change in Energy=-2.336370D-08 Optimization completed. -- Stationary point found.	optimised Al2Cl4Br2 cis-terminal-bromine molecule

Frequency analysis

Frequency log file here

summary data	low modes
	Low frequencies --- -4.2142 -2.4692 -0.0045 -0.0039 -0.0032 0.9511 Low frequencies --- 17.0927 50.8321 78.6205

Vibrational spectrum

wavenumber	Intensity	IR active?	type
17	0	no	bend
51	0	no	bend
79	0	no	bend
99	0	no	bend
104	3	very slightly	bend
121	13	very slight	bend
123	6	very slight	bend
157	0	no	bend
159	0	no	bend
194	1.5	very slight	stretch
264	0	no	stretch
279	26	yes	stretch
309	2	very slight	stretch
413	149	yes	stretch
420	409	yes	stretch
461	36	yes	stretch
570	34	yes	stretch
582	277	yes	stretch

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Relative energies of Al₂Cl₄Br₂ isomers

• E(isomer1)= -2352.4063080 a.u.
• E(isomer2)= -2352.4110993 a.u.
• E(isomer3)= -2352.4162882 a.u. (lowest energy conformer)
• E(isomer4)= -2352.4162658 a.u.

Therefore the relative energies of the isomers:

• E(isomer1)= E(isomer1)-E(isomer3)= 0.0099802 a.u. = 26.20 kJ/mol
• E(isomer2)= E(isomer2)-E(isomer3)= 0.0051889 a.u. = 13.62 kJ/mol
• E(isomer3)= E(isomer3)-E(isomer3)= 0 a.u. = 0 kJ/mol
• E(isomer4)= E(isomer4)-E(isomer3)= 0.0022400 a.u. = 5.88 kJ/mol

Bridging ligands form 2 2c-2e bond with both metal centres. One being a covalent bond, the other is a donation of one of it's lone pairs to the other metal centre (dative covalent bond). As is reflected from the data, the most stable isomer of Al₂Cl₄Br₂ is isomer 3 where the Bromine atoms are the furthest from each other, as they are terminal and trans. Isomer 4 is very similar in energy to isomer 3, but slightly higher in energy due to the configuration of the Bromine atoms being cis-terminal. Isomer 1 has the highest energy, and therefore the least stable due to the both the Bromine atoms being bridging. Bromine atoms are much larger than Chlorine, therefore has a larger van der waals radius, which are: 1.76 and 1.87 for Chlorine and Bromine respectively.. Since in isomer 1, both the Br atoms are bridging, this would mean that they are very close to each other, which would make the structure strained.

AlCl₂Br

Optimisation log file here

summary data	convergence	Jmol
	Item Value Threshold Converged? Maximum Force 0.000136 0.000450 YES RMS Force 0.000073 0.000300 YES Maximum Displacement 0.000760 0.001800 YES RMS Displacement 0.000497 0.001200 YES Predicted change in Energy=-7.984435D-08 Optimization completed. -- Stationary point found.	optimised AlCl2Br molecule

Frequency analysis

Frequency log file here

summary data	low modes
	Low frequencies --- -0.0025 0.0006 0.0027 1.3569 3.6367 4.2604 Low frequencies --- 120.5042 133.9178 185.8950

Vibrational spectrum

wavenumber	Intensity	IR active?	type
121	5	very slight	bend
134	6	very slight	bend
186	33	yes	bend (umbrella)
313	7	very slight	stretch
552	174	yes	stretch
613	186	yes	asymmetric stretch

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Dissociation energy of Isomer 3 into 2AlCl₂Br

• E(isomer3)= -2352.4162882 a.u.
• E(AlCl₂Br)= -1176.1901368 a.u.

Dissociation:

Al₂Cl₄Br₂--> 2AlCl₂Br

Dissociation energy:

ΔE= 2E(AlCl₂Br) - E(isomer3)= 0.0360146 a.u. = 94.56 kJ/mol

Since the Dissociation energy is positive, energy needs to be put into the system in order for the Al2Cl4Br2 dissociation to occur into its monomers. Aluminium is a group 13 element, so has 3 valence electrons. Upon bonding to 3 ligands, it still has an incomplete octet, which makes the Aluminium centres electron deficient, therefore it acts as a lewis acid. Upon dimerisation, this electron deficiency is reduced by the electron rich bridging halide atoms.

Symmetry and IR bands

The 4 isomers of Al₂Cl₄Br₂ have the following point groups:

• Isomer1: d2h; IR active modes: b_1u, b_3u, b_2u
• Isomer2: c1; IR active modes: a
• Isomer3: c2h; IR active modes: a_u, b_u
• Isomer4: c2v; IR active modes: a₁, b₁, b₂

D_2h point group has 3 IR active symmetry labels: b_1u, b_3u and b_2u, all of which have translational motion that causes a change in the dipole moment of the molecule giving rise to IR bands. Isomer 2 has a C₁ point group which have no symmetry elements, therefore most vibrations result in a change of dipole moment of the molecule, therefore it has the highest number of IR active vibrational modes. Isomer 3 has a C_2h point group which has 2 IR active translational labels, giving rise to 2 main IR active bands. Isomer 4 has a C_2v symmetry, with 3 IR active translational labels, giving 3 main IR active bands.

The more symmetrical a molecule, the lower the number of IR active bands due to the lower number of IR vibrational modes resulting in change of the dipole moment of the molecule.

Vibrational analysis of Al₂Cl₄Br₂

Mode	Isomer	Details
Mode 18	Isomer 1	Frequency: 616 cm-1 Intensity: 331
Modes 17 and 18	Isomer 2	Mode 17: Frequency: 574 cm-1 Intensity: 122 Mode 18: Frequency: 615 cm-1 Intensity: 197
	Isomer 3	Frequency: 579 cm-1 Intensity: 316
	Isomer 4	Frequency: 582 cm-1 Intensity: 277

Similar vibrational mode for the 4 isomers are tabulated above. As it can be seen from the table above, isomer 2 with a point group of C1 is the least symmetrical. The two Al atoms carry different substituent atoms hence the spitting of the vibrational mode in two. Isomer 1 has all the Br atoms as bridging ligands. For this mode of vibration, Isomer 1 has the highest frequency. It involves the Al atoms bending around Br atoms, and the stretching of Al-Cl bonds. Here, all 4 bond stretches are Al-Cl bonds, and since Al-Cl bonds are stronger than Al-Br bonds, isomer 1 has the highest frequency. In mode 17 for isomer 2, it involves terminal asymmetrical stretches of Cl-Al-Br , compared to mode 18 where it is Cl-Al-Cl stretch. The frequency for mode 17 is lower than for mode 18, which reflects the weaker bonding in Cl-Al-Br, as well as the higher reduced mass of this component, reducing the frequency.

Mode	Isomer	Details
Mode 10	Isomer 1	Frequency: 163 cm-1 Intensity: 0
Mode 10	Isomer 2	Frequency: 186 cm-1 Intensity: 1
Mode 10	Isomer 3	Frequency: 192 cm-1 Intensity: 0
Mode 10	Isomer 4	Frequency: 194 cm-1 Intensity: 2

From the table presented above, the highest frequency for this mode is for isomer 4 where all the bridging atoms are Cl, and the Bromines are terminal and cis. A few interesting points are that there is a visible trend in the change in frequency of the isomers for this mode of vibration as the bridging substituents are changed from Cl to Br. Al-Cl bond in stronger, consequently, isomers 3 and 4 where all the bridging atoms are Cl, the frequency is higher. There is gradual shift to lower frequencies as the bridging ligands are replaced from Cl to Br which can be seen moving from isomers 3 to 1, where the stretching frequencies are: 192, 186 and 163 cm-1 respectively. The possible contributing factors could be the difference in the force constants of the Al-Cl and Al-Br bonds, as well as the change in the reduced mass of the mode due to Br being heavier than Cl.

MO analysis of Isomer 3

Orbital 37

Orbital 41

Orbital 43

Orbital 46

Orbital 49

Orbital 54