Rep:Mod:splitinorganicprojectP1
The basic techniques of molecular mechanics and semi-empirical molecular orbital methods for structural and spectroscopic evaluations
BH3
The structure of BH3 was drawn in Gaussview and it was subsequently optimised by Gaussian to find the most stable conformation. The summary is shown in the table below. Frequency Analysis was then carried out. Using the simple molecule was to introduce us to using Gaussview and to become familiar with some of the calculations Gaussian can carry out. https://www.ch.imperial.ac.uk/wiki/index.php/Image:FINALYIHUAN_BH3_OPT.LOG
| Calculation method | B3LYP |
| Basis set | LANL2MB |
| B-H distance/Å | 1.86592 ± 0.01 |
| H-B-H bond angle/° | 120 ± 0.1 |
| Point group | D3H |
MO analysis of BH3
https://www.ch.imperial.ac.uk/wiki/index.php/Image:Final_BH3_pop.chk The diagram on the left the real MO calculated by Gaussian and the LCAO MOs. There is very good agreement between them for the occupied orbitals but the agreement is less so for the unoccupied orbitals. The LUMO and LUMO+1 etc show the orbitals where electrons would be found if they were to enter the system. However, when they are unfilled, they can only be considered a mathematical contrainst and their MOs are therefore not as accurate or reliable as the occupied orbitals. The 1a1 orbital is the 1s atomic orbital of B and is very low in energy. It is not involved in the bonding of BH3 so it has been left out of the MO diagram.
Frequencies of BH3
https://www.ch.imperial.ac.uk/wiki/index.php/Image:FINALFINAL_BH3_FREQ.LOG
| No | Form of the vibration | Frequency | Intensity | symmetry of D2h point group |
|---|---|---|---|---|
| 1 |  |
1146.03 | 92.87 | A2" |
| 2 |  |
1204.86 | 12.31 | E |
| 3 | .gif) |
1204.86 | 12.31 | E |
| 4 |  |
2591.65 | 0.00 | A1' |
| 5 |  |
2730.07 | 103.74 | E |
| 6 | .gif) |
2730.07 | 103.73 | E |
IR of BH3
The IR spectra is a visual way of representing the information shown in the table above. There are six peaks listed above and only three peaks in the IR spectrum. This is because there are two sets of degenerate vibrations, shown by the symmetry lable E, and because one vibration is of zero intensity.
BCl3
| Calculation method | B3LYP |
| Basis set | LANL2MB |
| B-Cl distance/Å | 1.87 |
| Cl-B-Cl bond angle/° | 120 ± 0.1 |
| Point group | D3H |
https://www.ch.imperial.ac.uk/wiki/index.php/Image:FINALFINAL_BCL3_OPT.LOG
In carrying any computational analysis, the molecule to be studied is always optimsed first. This determines the optimium position of the nuclei for a given electronic configuration. A loose optimisation using a low accuracy basis e.g. 3-21G set will speed up the subsequent optimisation using the medium level basis set LANL2MB. After optimisation, a frequency analysis is carried out to confirm that the optimisation has found the minima structure. The frequency analysis is the second derivative of the potential energy surface, and when the second derivative is positive, a minimum has been achieved. The test is to see if there are any negative frequencies, since this implies that the optimisation calculation failed to find a critical point so it did not complete. In my case, all the frequencies were positive, confirming that the optimisation had worked.
The same method and basis set has to be used for each calculation to garner meaningful results. This is because the the frequency is the second derivative of energy. Basis sets determine the number of functions used to describe the electronic structure and should be consistent for the study of each molecule.
The optimised B-Cl bond length calculated by Gaussview was given as 1.86592Å but it is only accurate to ~0.01 Å. Therefore the bond length for comparison is 1.87Å. The literature bond length is 1.75Å. The optimised Cl-B-Cl bond angle was 120°. This is identical to the literature bond angle.[1]
For certain structures the optimised structure in Gaussview does not contain all the bonds expected. This is because Gaussview has an internal list of bond distances and if the computed bonds are outside of this Gaussview does not draw them in. This is most evident for inorganic bonds since they are typically longer than those found in organic complexes and are longer than the distance criteria set by Gaussian. This does not mean that the bonds don't exist since they are not just a line. A bond is an attraction formed by two species of differing charge which leads to an interaction between their electrons. It is through the sharing of these electrons that a bond is formed.
The symmetry group of the ground state BCl3 structure is D3h and this is the same as what Gaussview used. Before the optimisation was carried out, the point group of the molecule was constrained to D3h and the tolerance was set to very high. This is to obtain accurate optimisation and frequency analysis because the atoms would be more fixed in space.
The optimisation calculation took 9seconds and the frequency analysis took 18 seconds when run on the laptop. There is a trade off between these short calculation times and the level of the basis set. For this relatively simple molecule it is acceptable to have a medium level basis set but this is not the case in the next section. https://www.ch.imperial.ac.uk/wiki/index.php/Image:YYIHUAN_BCL3_FREQ.LOG
| No | Form of the vibration | Frequency/cm-1 | Intensity | symmetry of D2h point group |
|---|---|---|---|---|
| 1 |  |
214.13 | 3.93 | E |
| 2 | .gif) |
214.13 | 3.93 | E |
| 3 |  |
376.94 | 43.78 | A2" |
| 4 |  |
417.38 | 0.00 | A1' |
| 5 |  |
939.47 | 258.69 | E |
| 6 | .gif) |
937.47 | 258.69 | E |
IR of BCl3
This IR spectra can be rationalised using the same argument as for BH3
Isomer of Mo(CO)4(L)2
In the second year inorganic lab course the cis and trans isomer of Mo(CO)4(L)2 where L=PPh3 were prepared and the IR spectra were analysed. For the computational analysis, the bulky PPh3 ligand is going to be replaced with PCl3. This is to reduce the computing time and make the calculation less expensive to run. Cl is chosen to replace Ph because it has a similar electronic contribution to bonding as pheyl groups and is still sterically quite large.
The number of CO vibrational bands active is related to the symmetry of the complex, four carbonyl absorption bands are expected from the compound with cis ligands and only one band is expected from the compound with trans ligands. This was seen in the experimental IR spectra and will be analysed in the computational IR spectra as well. Additionally, the structure and stability of the cis and trans isomer will be discussed.
The first step was to optimise the structures and then frequency analysis was undertaken.
Cis Isomer
| Calculation method | B3LYP |
| Basis set | LANL2DZ |
| Point group | C1 |
Fine optimisation files: DOI:10042/to-2851
The literature found only gives information in the trans isomer. See information on the trans isomer for comparison between computed and literature values
| Bond | Computed/Å | Literature/Å |
| Mo-C | 2.06 | - |
| Mo-P | 2.51 | <2.50 |
| C=O | 1.17 | - |
| P-Cl | 2.24 | - |
| Bond | Computed/° | Literature/° |
| P-Mo-P | 94.2 | - |
| C-Mo-C | 178.4 | - |
The MO-P and P-Cl bonds are not present in the vibration aminations because upon optimisation, Gaussview did not draw in the physical bonds and the vibrations can only be seen on the unaltered molecule. Frequency calculation files DOI:10042/to-2604
| vibration | Computated frequency/cm-1 | Literature frequency/cm-1[2] |
|---|---|---|
 |
1945 | 1882 |
 |
1948 | 1903 |
 |
1958 | 1917 |
 |
2023 | 2022 |
|
The IR spectrum shows all four peaks but since the vibrations occur at such similar frequencies, they cannot be properly distinguished. |
Trans Isomer
| Calculation method | B3LYP |
| Basis set | LANL2DZ |
| Point group | C1 |
Trans optimisation files DOI:10042/to-2853
Frequency calculation files DOI:10042/to-2854
| vibration | Computed frequency/cm-1 | intensity | Literature frequency/cm-1[3] |
|---|---|---|---|
 |
1950.29 | 1475 | 1890 |
 |
1950.93 | 1467 | Not seen |
| Not shown due to very low intensity | 1977 | 0.64 | Not seen |
| Not shown due to very low intensity | 2030 | 3.78 | Not seen |
Only one peak in the IR spectra is expected, but there are four frequencies shown in the table. This is due to the fact that Gaussview did not consider the correct point group of the molecule, . It considered the point group to be C1 so therefore all the CO ligands were not considered equivalent. However, the two vibrations at 1977 and 2030cm-1 are of very low intensities and are not visible in the IR spectrum. The other two vibrations occur at near equivalent wavenumber, Gaussview has considered the axial and equatorial CO stretches to be inequivalent which is incorrect. This is because the point group C2v was not set.
| Bond | Computed/Å | Literature/Å[4] |
| Mo-C | 2.06 | 2.01, 2.06 |
| Mo-P | 2.44 | 2.50 |
| C=O | 1.17 | 1.16 |
| P-Cl | 2.24 | - |
| Bond | Computed/° | Literature/° |
| P-Mo-P | 171.4 | 180.0 |
| C-Mo-C | 89.5 | 92.1 |
There is good agreement between the literature and computed values for bond lengths and bond angles. The small discrepancies between the two sets of data could be due to the accuracy of the computed method which is ~0.1Å and once this is considered, the bond lengths are in greater agreement.Therefore, Gaussian has successfully optimised the structures to get the bond lengths and bond angles. An improvement to make to the computational results would be to constrict the point group of the trans isomer to D4h.
Discussion of cis and trans isomer
|
Both the cis and the trans isomer had vibrations at very low frequencies. For the cis isomer, there were vibrations at 10 and 17cm-1 and for trans there were vibrations at 5 and 6cm-1. The cis vibration at 5cm-1 is shown and it is representative of all four low frequency vibrations. Since they occur at such low wavenumbers, these vibrations required very little energy to take place. Therefore at room temperature, the cis and trans isomers are constantly undergoing these vibrations. |
The energy of the cis isomer was calculated to be -623.57707195 a.u. the energy of the trans isomer as -623.57603109 a.u., giving a small energy difference of -2.7kJ/mol. This implies that the cis isomer is more stable. However, the energies calculated by Gaussian have an error of ~10kJ/mol and once this is taken into account, the greater stability of one isomer over the other cannot be inferred. The cis isomer might be the more stable because two of the CO ligands are 90° apart from one another. Bonding in metal carbonyl complexes arise from donation of electron density from the metal filled d orbitals to the empty anti-bonding CO orbital. Since the CO are 90°, they do not compete with eachother for backbonding from the same MO d orbitals.
On the other hand, I predict that as the size of L ligand increases, the trans isomer will be more stable. In the case of Mo(CO)4L2 where L=PPh3, steric effects between the PPh3 ligands would destabilise the cis isomer. The larger the L group, the greater the steric clash until a limit is reached when steric effects outweigh the electronic effects. This was proved in the 2nd Year Synthesis Lab, experiment 5S, in which both isomers of Mo(CO)4(PPh3)2were made and the higher melting point of the trans isomer confirmed its greater thermal stability.
References and citations