Rep:Mod:2510lm2

Bonding and Molecular Orbitals in Main Group Compounds: Week 1
-Layla Malouf

BH₃

Basic calculations using small basis sets

A molecule, <chemform>BH3</chemform>, was optimised using GaussView 5.0.9, with the calculation taking 10.0 seconds to complete. A .log file containing the optimisation data is attached.

The following parameters were utilised:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: 3-21G

Yielding the following results:

Figure 1: Hartree energy of the 3-21G optimised <chemform>BH3</chemform> molecule.

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.

Figure 2: Graph showing the root mean squared gradient of the energy of the 3-21G optimised <chemform>BH3</chemform> molecule.

The total energy plot (fig. 1) shows how the energy of the <chemform>BH3</chemform> molecule falls as subsequent optimisation steps are run, plateauing out at the minimum energy structure. The RMS gradient (fig. 2) indicates the position of the molecule on its Potential Energy Surface (PES). The smallest value, at step 4, shows that it has reached the minimum of the surface and so is at that point that the <chemform>BH3</chemform> molecule has a stable structure.

• Final Energy: -26.46226338 a.u.
• RMS Gradient Norm: 0.00020672 a.u.
• Dipole Moment: 0.00 Debye
• Point Group: D_3h

Optimisation using better basis sets

A larger basis set, in this case 6-31G (d,p), produces more accurate results for final energy, etc. In this case, compared to optimisations run using the 3-21G basis set, the final energy is smaller (more negative), as is the RMS gradient, indicating that the energy calculated this time is closer to the true stable state equilibrium position on the PES. The calculations were run again on the previously optimised <chemform>BH3</chemform> molecule, with the job taking 6.0 seconds to process, producing the .log file attached.

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.

Gaussian Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: 6-31G (d,p)
• Charge: 0
• Spin: Singlet
• Final Energy: -26.61532363 a.u.
• RMS Gradient Norm: 0.00000235 a.u.
• Dipole Moment: 0.00 Debye
• Point Group: D_3h
• Optimised B-H Bond Distance: 1.19Å cf. lit. value of 1.1901Å
• Optimised H-B-H Bond Angle: 120.0°

TlBr₃

Using pseudo-potentials

Pseudo-potentials are used in calculations involving molecules which contain heavy atoms (mainly 3^rd row elements and below). They simplify the calculations involved by essentially "ignoring" the core electrons in an atom, assuming they are tightly bound to the nucleus, and so running the calculations based only on the valence electrons. A trigonal planar TlBr₃ molecule was created in GaussView. Its symmetry was set, with the point group and tolerance restricted to D_3h and "very tight (0.0001)". A Gaussian input file (.gjf) was then created and submitted to the SCAN HPC service, which ran the calculations in 29.6 seconds and produced a Gaussian output (.log) file, attached here. This data was then exported to the Chemical Database "D-space", linked here: DOI:10042/21629 .

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=-6.084055D-11 Optimization completed. -- Stationary point found.

Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: LANL2DZ
• Charge: 0
• Spin: Singlet
• Final Energy: -91.21822851 a.u.
• RMS Gradient Norm: 0.00000090 a.u.
• Dipole Moment: 0.00 Debye
• Point Group: D_3h
• Optimised Tl-Br Bond Distance: 2.65Å cf. lit. value of 2.51Å (for TlBr₃•4H₂O)
• Optimised Br-Tl-Br Bond Angle: 120.0°

BBr₃

Using a combination of a pseudo-potential and a basis set to carry out calculations

<chemform>BBr3</chemform> contains a mixture of a light and heavy atoms, as such there is a need for both a pseudo-potential to treat the Br atoms and a full basis set for the B atom. This molecule was therefore modeled in GauusView and pseudo-potentials were individually specified for each atom (LANL2DZ for bromine and the 6-31G(d,p) basis set for boron). The input file produced from this was submitted to the SCAN HPC service, which ran the calculation in 18.0 seconds to produce a .log file. The data was then exported to D-space: DOI:10042/21684 .

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.

Gaussian Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: Gen
• Charge: 0
• Spin: Singlet
• Final Energy: -64.43645296 a.u.
• RMS Gradient Norm: 0.00000382 a.u.
• Dipole Moment: 0.00 Debye
• Point Group: D_3h
• Optimised B-Br Bond Distance: 1.93Å cf. lit. value of 1.8986Å
• Optimised Br-B-Br Bond Angle: 120.0°

Structure comparison

The calculated bond distances are all reasonably close to reported experimental values and as such any discussion made can be done so with some confidence.

Table 1: Optimised bond distances

Molecule	BH3	BBr3	TlBr3
Bond Length/Å	1.19	1.93	2.65

Table 2: Table of atomic radii

Atom	B	H	Br	Tl
Atomic Radius/Å	0.85	0.25	1.15	1.90

BH₃ has the smallest bond length- this is expected due to the small atomic radii of both the boron and the hydrogen atoms. Changing the ligand (for BBr₃) leads to an expected increase in bond distance as bromine is a much bigger atom than hydrogen, and a larger ligand will lead to a larger bond length. The sum of atomic radii for B-H= 1.10Å, for B-Br= 2.00Å, and although the actual bond length is not simply the sum of the atomic radii, this method provides a ballpark figure for comparison, as experimental values are similar to the sums reported. H and Br are similar in that they both need 1 electron to complete their outer shell (although H can also lose an electron to form a bond). Br is in group 17, H in group 1.

Bromine electron configuration: 1s², 2s², 2p⁶, 3s², 3p⁶, 3d¹⁰, 4s², 4p⁵

Hydrogen electron configuration: 1s¹

Changing the central element also leads to an increase in bond length by ~0.72Å, which is close to the difference in the atomic radii of Tl and B (0.75Å). Boron and thallium are both group 13 elements, although boron is in the second period whereas thallium is much larger, and is in the 6th period.

Bond angle remains the same for all three molecules, this is because they are all trigonal planar and are in the D_3h point group.

Put simply, a bond is an attraction between atoms which brings them close enough that they start affecting each others' "behaviour" and properties- the atoms "join" together as a molecule. The bond depends on the strength of the attractive forces, the stronger the attraction, the stronger and shorter the bond. GaussView most likely assigns bonds based on the calculated distance between atoms- this does not mean that there are no interactions between them.

Frequency analysis

For BH₃

Frequency analysis was carried out on the previously optimised (using the 6-31G(d,p) basis set) BH₃ molecule. This produced an output file after 123.0 seconds, containing the data for the completed frequency analysis, linked here.

Calculation Summary:

• Calculation Type: Frequency(FREQ)
• Method: RB3LYP
• Basis Set: 6-31G(d,p)
• Charge: 0
• Spin: Singlet
• Final Energy: -26.61532363 a.u. (as before)
• RMS Gradient Norm: 0.00000237 a.u. (0.00000002 a.u. higher than previously calculated- not significant)
• Imaginary Frequency: 0
• Dipole Moment: 0.00 Debye
• Point Group: D_3h
• B-H Bond Distance: 1.19Å (as before)
• Optimised H-B-H Bond Angle: 120.0° (as before)

Also added is the list of "low frequencies" from the .log file attached above. The "3N-6" rule lists the vibrational modes of the molecule, and the first line of the low frequencies shows the "-6"; the 3 frequencies for the modes of translation (-0.9033, -0.7343, and -0.0054) and the frequencies for the modes of rotation (6.7375, 12.2491, and 12.2824) of the <chemform>BH3</chemform> molecule:

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

Table 3 shows the calculated frequencies of vibration of the molecule, the corresponding symmetry label and the vibration type as an animated gif (click through for animation).

Table 3: Calculated vibrational modes of BH₃

Frequency/cm-1	Intensity	Vibration Type	Symmetry Label and Vibration Description
1163	93		A2": wagging, H atoms move "up" whilst B atom moves "down", and vice-versa.
1213	14		E': doubly degenerate scissoring: two H atoms move towards each other and back out there is a slight shift along the B-H bond axis as the fragment moves up and down as the scissoring motion occurs.
1213	14		E': doubly degenerate scissoring/rocking motion two H atoms "rock" together whilst two H atoms scissor.
2852	0		A1': totally symmetric stretching, IR inactive, each H atom stretches away from and towards the stationary B atom simultaneously.
2715	126		E': doubly degenerate asymmetric stretching: one H atom stretches towards and away from B out of sync with the other two. B remains stationary.
2715	126		E': doubly degenerate asymmetric stretching: one H atom stretches towards and away from B out of sync with the other two. B remains stationary.

Figure 3 shows the computed IR spectrum for BH₃. Only three peaks are seen, due to the calculated stretch at 2852.26cm^-1 being IR inactive (the totally symmetric stretch does not give rise to a change in the molecular dipole moment), and the double degeneracy of the peaks at 2715.42cm^-1 and 1213.19cm^-1.

Figure 3: <chemform>BH3</chemform> infrared spectrum.

For TlBr₃

Frequency analysis was carried out on the optimised TlBr₃ molecule, the job was run using the SCAN HPC service which yielded a .log file after 15.5 seconds. The data was the published to D-space: DOI:10042/21696 .

Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: LANL2DZ
• Charge: 0
• Spin: Singlet
• Final Energy: -91.21812851 a.u.
• RMS Gradient Norm: 0.00000088 a.u.
• Dipole Moment: 0.00 Debye
• Point Group: D_3h
• Optimised Tl-Br Bond Distance: 2.65Å (as before)
• Optimised Br-Tl-Br Bond Angle: 120.0° (as before)

List of low frequencies:

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

The lowest real normal mode is the vibration at 46.43cm^-1.

Table 4 shows the calculated frequencies of vibration of the molecule, the corresponding symmetry label and the vibration type as an animated gif (click through for animation).

Table 4: Calculated vibrational modes of TlBr₃

Frequency/cm-1	Intensity	Vibration Type	Symmetry Label and Vibration Description
46	3		E': doubly degenerate asymmetric deformation
46	3		E': doubly degenerate asymmetric deformation
52	5		A2": symmetric deformation
165	0		A1': totally symmetric, IR inactive
211	26		E': doubly degenerate asymmetric stretch
211	25		E': doubly degenerate asymmetric stretch

Figure 4 shows the computed IR spectrum for the molecule. Again, not all of the frequencies listed in the output file appear on the spectrum.

Figure 4: <chemform>TlBr3</chemform> infrared spectrum.

Frequency comparison for BH₃ and TlBr₃

Table 5: Frequencies and modes of BH₃ and TlBr₃

BH3		TlBr3
Frequency/cm-1	Symmetry Label	Frequency/cm-1	Symmetry Label
1163	A2"	46	E'
1213	E'	46	E'
1213	E'	52	A2"
2852	A1"	165	A1"
2715	E'	211	E'
2715	E'	211	E'

The most noticeable difference in recorded frequencies for TlBr₃ and BH₃ is the large difference in frequency values. This is due to bond strength; a stronger bond vibrates at a higher frequency as it requires more energy, as shown by the relationship: E=hv. Tl-Br bonds are weaker than B-Br bonds as there is poorer orbital overlap between the Br and Tl atoms (the orbitals are more diffuse), and the lower frequency of vibration is an indicator of this. The reduced mass effect also comes into play- bonds to hydrogen tend to have higher frequencies than bonds to heavier atoms.

The vibrational modes have reordered- the first stretch (lowest frequency) for BH₃ is the A₂" mode, whereas for TlBr₃ it is the first of the degenerate E' set. The second lowest frequency is the E' mode for both, the third is E' for BH₃ and A₂" for TlBr₃. For stretches 4-6, the order is the same.

The spectra are similar in that they both show only 3 peaks despite having 6 recorded stretches. This, as explained before, is due to 3 of the listed vibrational frequencies being IR inactive. The shape of the peaks differ between spectra- the spectrum for BH₃ shows peaks which are sharper, and more intense, compared to the broad, weak peaks in that of TlBr₃. The sharpness is also due to the strength of the bond; stronger bonds lead to less broad peaks.

A2" and E' modes (stretches 1-3) lie close together. This is because they have the same general type of motion; bending. For these two modes, the vibrations are "wagging", "scissoring", and "rocking". The A₁" and E' modes lie close together as they are of the same type, that is to say stretching. Stretching modes are higher in frequency than bending modes because they have higher force constants- more energy is required to stretch a molecule than to bend it, therefore the A2" and E' modes are lower in frequency.

A frequency analysis ensures a molecule is at a minimum in the PES- if, for example, one found that a calculated frequency was negative (that is to say, an imaginary frequency) then it would show that the molecule has not been optimised well and that the energy is in fact at a maximum (so it could be a transition state, or if all frequencies calculated are negative then the optimisation has either not finished or failed completely). We apply the same method and basis set for the optimisation and frequency analysis so that the "shape" of the PES doesn't change halfway through the calculation. For example, the BH₃ molecule was first optimised using the 3-21G basis set, then the 6-31G(d,p) set. These methods gave two different final energy values, with the energy reported for the latter basis set being lower than the former, showing that the shape of the PES was calculated differently each times.

As discussed above (Frequency Analysis: for BH₃), the low frequencies represent the "non-real" modes of a molecule. There are 6 listed as for a non-linear molecule, the number of vibrational modes are given by the equation n=3N-6, where the "-6" comprises of the 3 modes of translation of the centre of mass (lowest 3 values) and the 3 modes of rotation about the centre of mass of the molecule (highest 3 values).

MO Analysis for BH₃

An MO analysis was run on the .chk file from the 6-31G optimised <chemform>BH3</chemform> molecule. The method was set to "Energy", and the keyword "pop=full" switched on MO analysis. The "Full NBO" option was also selected, and the calculation was submitted to the SCAN HPC system. After 10.7 the job was compete, producing an output file and a formatted checkpoint file, all attached and also published to D space: DOI:10042/21823 .

Calculation Summary:

Fig. 5: MO diagram of BH₃

• Calculation Type: Energy (SP)
• Method: RB3LYP
• Basis Set: 6-31G
• Charge: 0
• Spin: Singlet
• Final Energy: -26.60595931 a.u. (previously: -26.61532363)
• RMS Gradient Norm: 0.00000000 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.00 Debye
• Point Group: Not reported
• B-H Bond Distance: 1.19Å (as before)
• Optimised H-B-H Bond Angle: 120.0° (as before)

The first 8 molecular orbitals were visualised (using the .fchk file), the first 4 being occupied and the last 4 empty- these appeared more diffuse than the bonding orbitals. Attached is the MO diagram for the molecule, drawn using LCAO theory.

Also attached is a comparison of the computed ("real") MOs and their corresponding LCAO- approximated MOs (as seen on the MO diagram).

Fig. 6: Comparison of real MOs with LCAO-based MOs.

In general, there is a very good agreement between the real and LCAO MOs, so, for simple molecules, qualitative MO theory is a useful tool.

Analysis of NH₃

Optimisation

A molecule of ammonia was drawn in GaussView and optimised using the 6-31G (d,p) basis set, producing a .log output file after 11.0 seconds.

Item Value Threshold Converged? Maximum Force 0.000005 0.000450 YES RMS Force 0.000003 0.000300 YES Maximum Displacement 0.000010 0.001800 YES RMS Displacement 0.000007 0.001200 YES Predicted change in Energy=-7.830780D-11 Optimization completed. -- Stationary point found.

Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: 6-31G(d.p)
• Charge: 0
• Spin: Singlet
• Final Energy: -56.55776863 a.u.
• RMS Gradient Norm: 0.00000289 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 1.85 Debye cf. lit. value of 1.47D
• Point Group: C_3v
• N-H Bond Distance: 1.02Å cf. lit. value of 1.01Å
• Optimised H-N-H Bond Angle: 105.7° cf. lit. value of 107.3°

Frequency

A frequency analysis was then carried out, producing a .log file after 7.0 seconds.

Item Value Threshold Converged? Maximum Force 0.000005 0.000450 YES RMS Force 0.000003 0.000300 YES Maximum Displacement 0.000011 0.001800 YES RMS Displacement 0.000006 0.001200 YES Predicted change in Energy=-8.408692D-11 Optimization completed. -- Stationary point found.

Calculation Summary:

• Calculation Type: Frequency (FREQ)
• Method: RB3LYP
• Basis Set: 6-31G(d.p)
• Charge: 0
• Spin: Singlet
• Final Energy: -56.55776863 a.u. (as before)
• RMS Gradient Norm: 0.00000281 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: as before
• Point Group: C₃
• N-H Bond Distance: as before
• Optimised H-N-H Bond Angle: as before

Table 5 confirms that the optimisation was successful as there are no negative frequencies reported:

Fig. 7: IR spectrum of NH₃.

Table 6: Calculated vibrational modes of NH₃

Frequency/cm-1	Intensity
1090	145
1694	14
1694	14
3461	1
3590	0
3590	0

Population Analysis

The .chk file from the optimised NH₃ molecule was used to produce the final data in this set of calculations. The method was set to "Energy", the keywords "pop=full" added and the "Full NBO" option selected. This, after 2.0 seconds of calculation, produced the attached output file.

Calculation Summary:

• Calculation Type: Energy(SP)
• Method: RB3LYP
• Basis Set: 6-31G(d.p)
• Charge: 0
• Spin: Singlet
• Final Energy: -56.55776863 a.u. (as before)
• RMS Gradient Norm: Not reported
• Imaginary Frequency: Not reported
• Dipole Moment: as before
• Point Group: C_3v

NBO Analysis

The output file from the population analysis (see above) was used to show the NBO charge distribution.

Fig. 8: Charge distribution by colour.

The colour range was from -1.125 to 1.125, from red at the most negative to green at the most positive. As expected, we can see from the image attached that the nitrogen atom is the most negative (being the most electronegative atom in the molecule), and the attached hydrogen atoms are positive.

Listed below are the specific NBO charges for each atom in ammonia (under Natural Charge):

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 0.62249 0.00246 0.62495 H 3 0.37505 0.00000 0.62249 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

NH₃BH₃

Optimisation

A molecule of ammonia-borane was modelled in GaussView. Using the 6-31G(d,p) basis set, its energy was optimised. Calculation time was 50.0 seconds, resulting in the output file linked here.

Item Value Threshold Converged? Maximum Force 0.000124 0.000450 YES RMS Force 0.000057 0.000300 YES Maximum Displacement 0.000660 0.001800 YES RMS Displacement 0.000304 0.001200 YES Predicted change in Energy=-1.649817D-07 Optimization completed. -- Stationary point found.

Gaussian Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: 6-31G (d,p)
• Charge: 0
• Spin: Singlet
• Final Energy: -83.22468957 a.u.
• RMS Gradient Norm: 0.00005842 a.u.
• Dipole Moment: 5.57 Debye
• Point Group: C₁

Frequency Analysis

This took 37.0 seconds to complete, producing the attached output file.

Low frequencies --- -0.0013 -0.0011 -0.0009 20.0767 22.9834 33.1523 Low frequencies --- 265.2464 632.2263 639.5172

Gaussian Calculation Summary:

• Calculation Type: Frequency (FREQ)
• Method: RB3LYP
• Basis Set: 6-31G (d,p)
• Charge: 0
• Spin: Singlet
• Final Energy: -83.22468985 a.u.
• RMS Gradient Norm: 0.00005842 a.u.
• Dipole Moment: 5.57 Debye
• Point Group: C₁

Table 7 confirms that the optimisation was successful as there are no negative frequencies reported:

Table 7: Calculated vibrational modes of NH₃BH₃

Frequency/cm-1	Intensity
265	0
632	14
640	4
640	4
1069	41
1070	41
1197	109
1204	3
1204	4
1330	114
1676	28
1676	28
2470	67
2530	231
2530	231
3463	3
3579	28
3579	028

Association Energy

Association energy is the standard enthalpy change when two atoms or molecules form a bond to make a new molecule. For ammonia-borane, the two species joining are, obviously, ammonia and borane.

E_NH3: -56.55776863 a.u.

E_BH3: -26.61532363 a.u.

E_NH3H3: -83.22468957 a.u.

ΔE= -83.22468957 - (-56.55776863 + -26.61532363)= -0.05158731

Association energy is the same as dissociation energy: E=-135.44kJ/mol, cf. lit. value of 28.5kcal/mol (=119.24kJ/mol)

Main Group Halides: Week 2

Energy and Frequency analysis of isomers of Al₂Cl₄Br₂

Four isomeric oligomers formed from the monomer <chemform>AlCl2Br</chemform> were identified, an optimisation and a frequency job were carried out on each isomer to ensure the calculated energy was at a minimum. A mixture of basis sets and pseudo-potentials were applied, 6-31G(d,p) for Al and Cl, and LanL2DZ for Br.

Red atoms: bromine, green atoms: chlorine, pink atoms: aluminium.

Isomer 1

Fig. 9: Isomer 1

An optimisation job on this isomer was sent to the SCAN HPC service, producing an output file after 10mins 13.1 seconds. The data was then published online: DOI:10042/21906 .

Point group: D_2h.

Item Value Threshold Converged? Maximum Force 0.000011 0.000450 YES RMS Force 0.000005 0.000300 YES Maximum Displacement 0.001571 0.001800 YES RMS Displacement 0.000652 0.001200 YES Predicted change in Energy=-4.446219D-09 Optimization completed. -- Stationary point found.

Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.40630797 a.u.
• RMS Gradient Norm: 0.00000427 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.0018 Debye
• Point Group: C₁

Note: Point group assigned by Gaussian is different to actual point group- vibrational modes were assigned "manually".

Calculated bond lengths and angles:

See image 3 for corresponding labels

1. 2.09Å
2. 2.49Å
3. 3.47Å
4. 3.57Å
5. 88.3°
6. 91.7°
7. 121.8°
8. 109.8°

Frequency analysis was then carried out on the optimised dimer, the job was run using the SCAN HPC service which gave an output file after 3mins 46.7 seconds. The data was the published to D-space: DOI:10042/21978 .

Calculation Summary:

• Calculation Type: Frequency (FREQ)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.40630797 a.u. (as before)
• RMS Gradient Norm: 0.00000431 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.0018 Debye
• Point Group: C₁

List of low frequencies:

Low frequencies --- -5.1916 -5.0899 -3.2098 0.0031 0.0033 0.0036 Low frequencies --- 14.8182 63.2683 86.0740

18 vibration frequencies are recorded, but only 7 are shown on the spectrum. The other 11 frequencies have intensities of 0, meaning they are IR inactive; for a stretch to give rise to a peak in an IR spectrum, it must cause a change in the dipole moment of the molecule, the vibrations at these frequencies clearly do not and so are inactive.

Fig. 10: Infrared spectrum of isomer 1.

Table 8: Calculated vibrational modes of isomer 1

Frequency/cm-1	Intensity	Vibration Mode
15	0	B2u
63	0	Au
86	0	B3g
87	0	Ag
108	5	B1u
111	0	B1g
126	8	B3u
135	0	B2g
138	7	B2u
163	0	Ag
197	0	B2g
241	100	B3u
247	0	Ag
341	161	B1u
467	347	B3u
494	0	Ag
608	0	B1g
616	332	B2u

Isomer 2

Fig. 11: Isomer 2

An optimisation job on this isomer was sent to the SCAN HPC service, producing an output file after 8mins 48.8 seconds. The data was then published online: DOI:10042/21943 .

Point group: C_2v.

Item Value Threshold Converged? Maximum Force 0.000069 0.000450 YES RMS Force 0.000022 0.000300 YES Maximum Displacement 0.001576 0.001800 YES RMS Displacement 0.000524 0.001200 YES Predicted change in Energy=-7.464259D-08 Optimization completed. -- Stationary point found.

Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.41632880 a.u.
• RMS Gradient Norm: 0.00003248 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.1877 Debye
• Point Group: C₁

Calculated bond lengths and angles:

1. 2.28Å
2. 2.30Å
3. 3.25Å
4. 3.25Å
5. 2.09Å
6. 89.8°
7. 90.0°
8. 121.8°
9. 110.1°
10. 121.5°
11. 110.2°

Frequency analysis was carried out, producing an output file after 5mins 18.7 seconds. The data was published to D-space: DOI:10042/21980 .

Calculation Summary:

• Calculation Type: Frequency(FREQ)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.41632880 a.u. (as before)
• RMS Gradient Norm: 0.00003245 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.1877 Debye
• Point Group: C₁

List of low frequencies:

Low frequencies --- -4.1127 -2.6896 -1.5352 -0.0023 -0.0020 -0.0010 Low frequencies --- 17.6511 50.9231 72.1585

Again, 18 vibrations are reported but only 10 significant ones are seen- the other 8 are either completely IR inactive or lead to such a small change in dipole moment that the intensities are very small (≤2).

Figure 12: Infrared spectrum of isomer 2.

Table 9: Calculated vibrational modes of isomer 2

Frequency/cm-1	Intensity	Vibration Mode
18	0	B2
51	0	A2
72	1	A1
98	0	B2
112	6	B1
112	2	A2
120	11	A1
160	1	B1
166	7	B2
187	2	A1
264	0	B1
271	13	A1
323	41	A1
413	150	B1
418	309	A1
496	134	B2
503	105	A1
615	177	B2

Isomer 3

Fig. 13: Isomer 3

An optimisation job on this isomer was sent to the SCAN HPC service, producing an output file after 7mins 14.1 seconds of calculation. The data was also published to D-space, accessible here: DOI:10042/21912 .

Point group: C_2v.

Item Value Threshold Converged? Maximum Force 0.000056 0.000450 YES RMS Force 0.000014 0.000300 YES Maximum Displacement 0.001350 0.001800 YES RMS Displacement 0.000455 0.001200 YES Predicted change in Energy=-2.906554D-08 Optimization completed. -- Stationary point found.

Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.41626676 a.u.
• RMS Gradient Norm: 0.00002310 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.1664 Debye
• Point Group: C₁

Calculated bond lengths and angles:

1. 2.09Å
2. 2.30Å
3. 3.25Å
4. 3.25Å
5. 2.27Å
6. 89.8°
7. 90.2°
8. 121.5°
9. 110.5°

After running a frequency analysis, an output file after 4mins 42.6 seconds. The data was published to D-space: DOI:10042/21985 .

Calculation Summary:

• Calculation Type: Frequency(FREQ)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.41626676 a.u.
• RMS Gradient Norm: 0.00002309 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.1664 Debye
• Point Group: C₁

List of low frequencies:

Low frequencies --- -4.3883 -2.5246 0.0032 0.0040 0.0041 1.0099 Low frequencies --- 17.1336 50.9061 78.5303

In this spectrum, there are again the very weak/non-existent peaks from IR inactive stretches, but there are also peaks which are broad enough to encompass two reported frequencies (eg: 413 and 420cm^-1).

Fig. 14: Infrared spectrum of isomer 3.

Table 10: Calculated vibrational modes of isomer 3

Frequency/cm-1	Intensity	Vibrational mode
17	0	A1
51	0	A2
79	0	A1
99	0	B2
103	3	B1
121	13	B2
123	6	B1
157	0	A2
158	5	A1
194	2	A1
264	0	A2
279	25	B2
309	2	A1
413	149	B1
420	411	B2
461	35	A1
570	32	B2
582	278	A1

Isomer 4

Fig. 15: Isomer 4

An optimisation job on this isomer was sent to the SCAN HPC service, producing an output file after 6mins 16.0 seconds of calculation. Results were published online: DOI:10042/21913 .

Actual Point group: C_2h.

Item Value Threshold Converged? Maximum Force 0.000119 0.000450 YES RMS Force 0.000037 0.000300 YES Maximum Displacement 0.001539 0.001800 YES RMS Displacement 0.000595 0.001200 YES Predicted change in Energy=-2.047282D-07 Optimization completed. -- Stationary point found.

Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.41629828 a.u.
• RMS Gradient Norm: 0.00005819 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.0095 Debye
• Point Group: C₁

Calculated bond lengths and angles:

1. 2.09Å
2. 2.30Å
3. 3.25Å
4. 3.26Å
5. 2.27Å
6. 89.8°
7. 90.2°
8. 121.5°
9. 109.8°
10. 110.5°

Frequency analysis produced an output file after 3mins 25.0 seconds. Data was then published online: DOI:10042/21989 .

Calculation Summary:

• Calculation Type: Frequency (FREQ)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.41629828 a.u. (as before)
• RMS Gradient Norm: 0.00005822 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.0095 Debye
• Point Group: C₁

List of low frequencies:

Low frequencies --- -5.0609 0.0032 0.0042 0.0046 1.1152 2.3756 Low frequencies --- 18.1039 49.1130 72.9906

7 peaks in the spectrum correspond to the 7 IR active vibrations.

Fig. 16: Infrared spectrum of isomer 4.

Table 11: Vibrational modes of isomer 4

Frequency/cm-1	Intensity	Vibration Mode
18	0	Bu
49	0	Au
73	0	Ag
105	0	Ag
109	3	Bg
117	9	Au
120	13	Bu
157	0	Bg
160	6	Bu
192	0	Ag
264	0	Bg
280	29	Bu
308	0	Ag
413	150	Au
421	438	Bu
459	0	Ag
574	0	Ag
579	316	Bu

Discussion

Frequency:

For an IR band to be active, the vibration must lead to a change in the dipole moment of the molecule. Point group clearly affects the dipole moment of the dimers, and we can expect dimers with the same point group to have similar IR spectra. Isomers 2 and 3 have the same point group (C_2v), and, looking at their frequency tables, both have the same number (10) of significantly intense stretches (intensity >2). Isomer 4 (of C_2h symmetry) only has 7 significant peaks in its IR spectrum. Isomer 1 (D_2h) also has 7 peaks. This shows that the higher the symmetry of the molecule, the more degenerate peaks there are.

Table 12: Key vibrations relating to Al-Br bond stretches

Dimer 1		Dimer 2		Dimer 3		Dimer 4
Frequency/cm-1	Symmetry Label	Frequency/cm-1	Symmetry Label	Frequency/cm-1	Symmetry Label	Frequency/cm-1	Symmetry Label
241	B3u	271	A1	420	B2	421	Bu
341	B1u	413	B1	461	A1	459	Ag
467	B3u	418	A1	570	B2	574	Ag
		496	A2	582	A1	579	Bu

Isomers 2 and 3 are in the same point group so it is only possible to compare modes for those two. Unfortunately there does not seem to be much of a correlation between the two. There are fewer Al-Br stretching modes for dimer one, which is when they are bridging, rather than the modes for the terminal bromines. The bridging atoms also require less energy to stretch (they have a lower frequency) compared to the other three isomers (with some exception for isomer 2, incidentally the most stable isomer). This is because the bromine atom is more coordinated when bridging, and as is known, the stretching frequency falls with increasing coordination number. This is because by coordinating, the electron density of bromine is shared across two atoms, weakening the bonds relative to when it is not bridged, making it easier to stretch the Al-Br bond.

Table 13: Comparison of isomer energies

Isomer	Energy in a.u.	Energy in kJ/mol	Energy difference relative to lowest E isomer
1	-2352.40630797	-6176242.759	26.31
2	-2352.41632880	-6176269.069	0
3	-2352.41626676	-6176268.906	0.163
4	-2352.41629828	-6176268.99	0.079

Highlighted box is lowest energy (most stable) isomer of <chemform>Al2Cl4Br2</chemform>. Least stable isomer is the first by far, where two Br atoms bridge. Isomers 2, 3 and 4 all have bridging Cl atoms, and are much lower in energy than isomer 1. This shows that a terminal Al-Br bond is preferred. Cl and Al are in the same period and so an Al-Cl bond has better orbital overlap than and Al-Br bond, making it stronger. As bromine is larger than chlorine, having it as a bridging atom would cause some strain in the molecule which is minimised when chlorine bridges.

There is also an energy difference for the isomers 3 and 4 relative to 2. However, these are very small, and considering the inherent error brought about by using a less accurate basis set/pseudo-potential (~10kJ/mol), the effect of the position of terminal bromines on energy cannot be discussed properly.

MO Analysis

A population analysis was run on the lowest energy isomer of <chemform>Al2Cl4Br2</chemform>. The .fchk from the optimisation of the dimer (accessible from D-space, also attached here) was used for this calculation. The method was set to "energy", and both keywords "pseudo=read gfinput" and "pop=full" included to ensure the specified pseudo-potentials and basis sets (as before) were used and to switch on MO analysis. The "full NBO" option was selected, and the file submitted to the SCAN HPC service. This gave a .log output file, a formatted checkpoint (.fchk) file and more data, all accessible from D-space: DOI:10042/22031 . The calculation took 53.6 seconds to complete.

Fig. 16: MO 32 of dimer 2

Fig. 17: MO 37 of dimer 2

Fig. 18: Orbital diagram of fragments

Fig. 19: HOMO of dimer 2

Fig. 20: LUMO of dimer 2

Fig. 21: MO 57 of dimer 2

Calculation Summary:

• Calculation Type: Energy (SP)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -2352.41632880
• RMS Gradient Norm: Not reported
• Imaginary Frequency: Not reported
• Dipole Moment: 0.19 Debye
• Point Group: C₁

Using the .fchk file from the energy analysis, the molecular orbitals of the dimer were visualised. There are 56 core electrons, so the first 28 orbitals are core orbitals (their energy is too low to have an effect on the reactivity of the molecule).

5 MOs are shown below, ranging from highly bonding to highly antibonding.

• First shown is a highly bonding MO:

MO number 32, energy: -0.88765. The s orbitals on each bridging Cl are out of phase and so cannot interact in the centre of the molecule, leading to the one nodal area shown. The orbitals are quite large (especially compared to some orbitals in the following images), which is an indicator that the chlorine atoms contribute very strongly towards the bonding character of the MO- this makes sense as of the three atoms in the molecule, chlorine is the most electronegative. AO interactions are quite strong, and the orbitals on the terminal atoms are not shown because no matter what phase they are, there will be an equal amount of bonding and antibonding interactions so they "cancel out" and the energy of this molecular orbital remains unchanged.

• The next MO chosen is also a bonding one:

MO number 37, energy: -0.40132. The orbitals around the terminal Cl are larger than those around the terminal Br, confirming that chlorine contributes more strongly towards a bonding combination of AOs. Judging by the shape, the p orbitals of the chlorine atoms and the s orbital of the Al atom combine to form the large red orbital centred around the aluminium atom (see figure 3). The same combination occurs on the other "side" of the molecule, the AlBl₂ fragment. The p-orbitals of the bromine combine with the s orbital of the aluminium to form the smaller green area around the other Al. As discussed above, this combination results in smaller orbitals as the less electronegative Br contributes less to the bonding character.

• This MO is the HOMO:

MO number 54, energy: -0.31309. The orbitals around the bromine atoms are now larger than those around the bridging Cl and also much larger than previously seen, showing that Br is starting to contribute more towards the bonding character of the MO, destabilising it and causing a rise in energy. Only the p orbitals on the Br and the bridging Cl atoms are seen- the others aren't shown because no matter what their phase, the bonding/anti-bonding interactions will balance out. The orbitals are also becoming more diffuse as the MO energy rises, and now we can see a through space anti-bonding interaction between the opposite phases of the orbitals on Br and Cl, causing a further destabilisation.

• Next, the LUMO:

MO number 55, energy: -0.06639. The LUMO has a very large number of nodes, and the more there are, the less stable the orbital is. Again, the Br- based orbitals are larger than those centred around the Cl. The orbitals around the Al atoms have stron s character, and these interact with the opposite phases of the orbitals around the terminal ligands. The bridging Cl contributes a p orbital which interacts constructively through space with the orbital centred on the AlCl₂ fragment.

• An antibonding MO is shown:

MO number 57, energy: 0.01245. There is an even greater number of nodes in this MO, indicating further instability. The orbitals around Br are larger than those of Cl, but those of Al are even larger and more diffuse, meaning they contribute most strongly towards the anti-bonding character of the orbital.

Bond Dissociation Energy, Counterpoise Correction and the Basis Set Superposition Errors

Fig. 22: <chemform>AlCl2Br</chemform> monomer, labelled.

The monomer AlCl₂Br was modelled and optimised using a mixture of the 6-31G(d,p) basis set for Al and Cl and the pseudo-potential LanL2Dz for Br. The job was submitted to the SCAN HPC service, which produced an output file after 48.4 seconds. Results were also published online: DOI:10042/21968 .

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=-7.984477D-08 Optimization completed. -- Stationary point found.

Calculation Summary:

• Calculation Type: Optimisation (FOPT)
• Method: RB3LYP
• Basis Set: GEN
• Charge: 0
• Spin: Singlet
• Final Energy: -1176.19013679 a.u.
• RMS Gradient Norm: 0.00005819 a.u.
• Imaginary Frequency: Not reported
• Dipole Moment: 0.1075 Debye
• Point Group: C_2v

Calculated bond lengths and angles:

1. 2.67Å
2. 2.09Å
3. 119.8°
4. 120.1°

The reported final energy is -1176.19013679 a.u.

Final energy in kJ/mol: -3088087.202kJ/mol

Bond dissociation energy of dimer 2:

ΔE= -2352.41632880 - (2*-1176.19013679) = -0.036056 a.u.

ΔE= -94.665kJ/mol

The product (<chemform>Al2Cl4Br2</chemform>) is more stable than the energy of two equivalents of monomer, so forming the dimer is preferred. However, this is not a very accurate way of calculating dissociation energy. Gaussian calculates energies using discrete basis sets/pseudo-potentials which are centred on the nuclei of each atom in the monomer, giving rise to a basis set superposition error (BSSE) . This error overestimates how much the dimer is stabilised when it is formed from the two AlCl₂Br fragments, as in, ΔE calculated is more negative than it should be. It happens because when Gaussian calculates the energy for the dimer, each "half" can interact with the 6-31G(d,p) basis sets and the LanL2DZ pseudo-potential on the other "half" of the molecule, causing the programme to include these intramolecular interactions. This, in itself, is not an error ; the BSSE comes about because the two monomers which join together to make the dimer are not modeled in the same way- these interactions aren't taken into account when we simply calculate the energy of one monomer and double it.

The BSSE is a significant error, its size is comparable to ΔE, so in order to obtain a more correct value for the bond dissociation/association energy one must either use the Chemical Hamiltonian approach or apply counterpoise correction.

This was attempted for the AlCl₂Br monomer- the optimised monomer was duplicated in the builder, and the "atom group editor" and "select atoms by rubberband" tools used to define each monomer as a separate fragment. The optimisation job was then sent to the SCAN HPC service, with the "Use Counterpoise" option under the "General" tab checked. The basis set 6-31G(d,p) was again applied to the Al and Cl atoms, and the pseudo-potential LanL2DZ applied to Br. Unfortunately, the job did not converge so the error cannot be accounted for.