Rep:Mod:sl307module2
Analysis of BH3
Optimisation
A molecule of BH3 was created in GaussView and optimised using B3LYP method with 3-21G basis set. The optimised molecule had all B-H bond lengths equal to 1.19Å and the bond angles of B-H-B were 120.0°.
The log file of the optimisation:SIGNE_BH3_OPT.LOG
From the optimisation calculation run the following two graphs were produced:
From both the plots it can be seen that the calculation was done in 4 steps. With every step the energy of the system is decreased and the RMS gradient tends toward zero. When the RMS is nearly zero the calculation stops since there is no point trying to reduce the gradient even more since it is already sufficiently small.
MO and NBO
A Molecular Orbital and Natural Bond Orbital analysis was computed using the checkpoint file from the optimisation calculation from before. The obtained Mooecular Orbitals were visualised and saved as JPEG files.
Log file:SIGNE_BH3_MO.LOG
The visualised 8 MO's of BH3:
 E=-6.73023 |
 E=-0.51778 |
 E=-0.35689 |
 E=-0.35689 |
 E=-0.07455 |
 E=0.18879 |
 E=0.18879 |
 E=0.19236 |
LCAO approach:
The comparison of computed MO's and MO's from the LCAO approach:
| Computed MO's | LCAO MO's | Discussion | |
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The 1s orbital from the LCAO is identical to the computed one. | |
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The LCAO shows 4 separate orbitals, whereas the computed one shows one big orbital, but if we imagine all the 4 orbitals in the LCAO model diffusing together, thats the image we would get. | |
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Again if the LCAO orbitals would actually touch then it would just like the computed orbitals with one of the H's not involved at all. | |
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The HOMO orbital from LCAO looks much like the computed one (if diffused). | |
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Again this orbital is well represented by the LCAO if compared to the computed 3D version. | |
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This is the 1st orbital where the computed representation is much better since it shows the exact shape of the B anti-bonding interaction with the bonding H 1s orbital. | |
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The LCAO model gives the idea how the orbitals would look like but the computed MO gives and exact representation of the distorted boron py orbital. | |
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The LCAO gives a very good representation apart from the distorted shape of the boron pz orbital. |
All in all comparing the theoretical and computed approach of the MO's is quite good. The agreement in the shape of the lectron clouds is very good up to and including the LUMO orbital. The last 3 orbitals shown do correspond to the computed ones but do not show as precise form of the electronm clouds as the 3D versions do. Also in the diagram the 2e' orbitals are drawn having the highest energy, but in reality it is the 3a1' orbital that has the highest energy. In the LCAO approach it is very hard to say which of the 2 symmetries would have higher energy since theoretically it could be either. This is because s-s interactions are stronger than s-p so the 3a1' would be higher, but on the other hand a1' energy levels are lower than e' and hence the 2e' could be higher in energy. In reality they are very close and 2e' is lower in energy only by ca 0.01.
The NBO analysis is a very good way to see how exactly the charge between atoms is distributed, it is not just eg. +1 or -1 but it shows the actual realistic distribution. NBO charges of BH3:
| Atom | NBO charge |
| B | 0.332 |
| O | -0.111 |
Vibrations
The vibration calculation was computed for BH3 in GaussView.
Log file:SIGNE_BH3_FREQ.LOG
| No. | Form of the vibration | Frequency | Intensity | Symmetry D3h point group | |
|---|---|---|---|---|---|
| 1 |  |
1152.47 | 93.2590 | a2" | |
| 2 |  |
1209.45 | 13.2667 | e' | |
| 3 |  |
1209.45 | 13.2690 | e' | |
| 4 |  |
2577.47 | 0 | a1' | |
| 5 |  |
2715.85 | 135.5205 | e' | |
| 6 |  |
2715.85 | 135.5075 | e' |
The IR spectrum of BH3:
There are only 3 peaks on the spectrum although there are 6 vibrations. The a1' is totally symmetric and has intenisty of 0 and hence is not seen in the IR spectrum. This leaves us with 5peaks from which there are 2 pairs of degenarate states. From the table above it can be seen that they are not entirely degenerate since there is a difference in the frequency but it is so small that in the spectrum it cannot be seen and so they diffuse together. So this makes the IR spectrum of only 3 peaks at 1152.47, 1209.45 and 2715.85 cm-1.
Analysis of BCl3
Optimisation
The boron trichloride molecule was drawn in GaussView and an input file was created to perform the optimisation of the molecule. The point group for the molecule was set to D3h with very tight tolerance. The 1st optimisation was run with the standard B3LYP method, but the basis set used was set to LanL2MB. The bond legth of the optimised molecule was 1.87Å with the bond angles being 120.0°.
The log file of the optimisation:SIGNE_BCL3_OPT.LOG
Vibrations
The basis set used was the same as for the optimisation calculation. It has to be the same so that the energy curves do not change by the use of different basis sets for the calculation.
The log file:SIGNE_BCL3_FREQ.LOG
The frquency analysis has to be done in order to confirm that the molecule is at its lowest energy state.
| # | Frequency/cm-1 | Intensity |
| 1 | 214.13 | 3.93 |
| 2 | 214.13 | 3.93 |
| 3 | 376.94 | 43.78 |
| 4 | 417.38 | 0.00 |
| 5 | 939.47 | 258.69 |
| 6 | 939.47 | 258.69 |
All the vibrations are similar in nature to BH3, having two pairs of degenerate frequencies and one vibration with zero intensity. All the vibratiuons have positive values and therefore we can assume that this structure is the one with the minimum energy.
GaussView has omitted some bonds in the molecule, this does not mean that the bonds are not there. GaussView has been set to certain parameters and so if the bonds are longer that what has been set it simply will not display them because it thinks that they are too weak and that the structure of the molecule is actually not the optimum structure. One example is the BH3 structure, where the optimisation happened in 4 stages and the 1st and 2nd stage had no bondes shown between the B atom and the H's since the bonds were too long but in the final optimised structure the bonds were shown.
A bond can be defined as an attraction between atoms or ions in such way that the forces acting between them lead to the formation of an aggregate with sufficient stability.
The optimisation calculation took 8 seconds to run and the frequency calculation took 20 seconds to run which is an insifigant time for such calculation as for more complicated structures these calculations can take even several days.
Cis and Trans isomers of Mo(CO)4(PCl3)2
Optimisation
The optimisation was computed with the basis set as in the instructions. After the 1st optimisation the cis-isomer came back with no P-Cl or Mo-P bonds and the trans-isomer had no P-Cl bonds. After the 2nd isomerisation it was still the case although checking if the optimisation has worked it confirmed that it did. The reason for the missing bonds is the restricted pre-set parameters in GaussView.
The log file for cis-isomer after 2nd optimisation:DOI:10042/to-3374
The log file for trans-isomer after 2nd optimisation:DOI:10042/to-3375
The cis isomer took longer to run compared to trans isomer, but if the time taken shown in summary is compared to the time given in SCAN, the time SCAN shows is half of that in summary. Since the time taken for cis-isomer to optimise is longer than for the trans-isomer, we can assume that the trans-isomer was closer to its lower energy form that cis-isomer before the optimisation.
Structure comparison
Shown below are the two isomers with their atoms numbered.
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| ' | Mo-P/Å | P-Cl/Å | C2-Mo-P10/° | C3-Mo-P10/° | C4-Mo-P10/° | C5-Mo-P10/° |
| Cis | 2.51 | 2.24 | 91.9 | 89.4 | 176.1 | 89.2 |
| Trans | 2.44 | 2.24 | 90.0 | 91.3 | 88.7 | 90.0 |
Note: The Mo-P bond lengths are the same for both the P atoms and also the bond lengths for all P-Cl groups are considered the same since the first 2 digits after the decimal were the same. Also in the table all the C atoms have the same numbering for both the isomers but it is actually not true from the images so here is the conversion: C2 cis=C5 trans, C3 cis=C2 trans, C5 cis=C3 trans.
From the table it can be seen that the Mo-P bond in cis- is slightly longer than the corresponding bond in the trans-isomer, which explains why in the images the Mo-P bonds for trans- are shown but for cis-isomer they are missing. All the P-Cl bonds in both the isomers are the same. All the bond angles are quite close to each other and not far off 90° apart from the C4-Mo-P10 bond angle in the cis isomer which is 176.1° instead of 180°.
Relative energies
Below is the table of the energies of both the isomers:
| ' | E/Eh | E/kJmol-1 |
| Cis | -623.577 | -1637201 |
| Trans | -623.576 | -1637199 |
1Hartree=2625.5kJmol-1 [1]
From the table it can be seen that the trans-isomer has a lower energy meaning that it is the more stable isomer. This could be due to the C=O backbonding.
The energy difference between the isomers is 2.6kJmol-1, which compared to the energies of the isomers that are millions of kJmol-1 is extremely small.
IR spectra
The log file for cis-isomer for frequency:DOI:10042/to-3440
The log file for trans-isomer for frequency:DOI:10042/to-3441
Below are the IR spectra for both the isomers:
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None of the produced frequencies are negative but there are quite few that have very low frequencies. Since there are no negative frequencies, it means that both the isomers are at their lowest energy state.
Table with the lowest 5 frequencies of the cis-isomer with C2v point group:
| #. | Form of the vibration | Frequency | Intensity | |
|---|---|---|---|---|
| 1 |  |
10.74 | 0.0264 | |
| 2 |  |
17.60 | 0.0073 | |
| 3 |  |
42.04 | 0.0048 | |
| 4 |  |
44.42 | 0.1030 | |
| 5 |  |
56.22 | 0.8282 |
All the motions are very random and some of the displacements are so small it is very hard to see the displacement vectors.
Table with the lowest 5 frequencies of the trans-isomer with D4h point group:
| #. | Form of the vibration | Frequency | Intensity | |
|---|---|---|---|---|
| 1 |  |
4.93 | 0.0941 | |
| 2 |  |
6.12 | 0 | |
| 3 |  |
37.20 | 0.4187 | |
| 4 |  |
40.22 | 0.3116 | |
| 5 |  |
72.25 | 0 |
Again all the motions are fairly random and it is very hard to see the dislpacement vectors for some of the vibrations. It is worth mentioning that for the first two vibration I have not drawn the displacement vectors since only the Cl atoms were slightly wiggling and it was hard to represent that in a form of a vector and also at the lowest frequency - 4.93 - the C=O bonds were rotating.
In general all the the low frequencies for both the isomers were quite random although since the trans-isomer is more symmetric than the cis-isomer the displacements were symmetric as can be seen from the displacement vectors.
The vibrations/rotations that have a very low energy, their stretches are very assymetric and the displacements are very small. At room temperature these vibrations would not be occuring since in the air has all frequencies in different probabilities so the source inducing these vibrations would be weaker and hence these vibrations would not be happening.
A table of computed C=O stretches are shown below:
Note: a=assymetric, s=symmetric
| ' | C=O stretches/cm-1 | Intensity |
| Cis | 1945.29 a | 762.6641 |
| 1948.68 a | 1498.7409 | |
| 1958.36 a | 633.0221 | |
| 2023.33 s | 597.6577 | |
| Trans | 1950.47 a | 1475.4447 |
| 1951.11 a | 1466.7534 | |
| 1977.38 a | 0.6388 | |
| 2031.16 s | 3.7680 | |
Below are the values for the C=O stretches from my 2nd year experiment and the literature value that I compared to the values:
| ' | C=O stretch/cm-1 | Literature/cm-1 |
| Cis | 1888.96 and 2012.75 | ~1900 |
| Trans | 1890.17 | ~1900 |
The computed values are quite far off the values produced in my 2nd year lab experiment and also if compared to literature these values are much higher. But the symmetric stretch in cis-isomer compares very well with the 2nd C=O stretch from the experiment. The vast difference between the computed and experimental values is due to the other substituents which in the experiment are PPh3 but in the computed these are PCl3. Although Ph is kind of similar in size with Cl the electronegativities are different hence the different C=O stretches.
Comapring the intesities of C=O stretches of the ci- and trans-isomers it can be seen that all cis-isomer stretches are significant, but for the trans-isomer we can see that only two have high intesities the other two have intensities under 10 and hence are insignificant. The two significant trans-isomer stretches are very close in frequency and hence are degenerate in energy. Also all the trans-isomer stretches have slightly higher frequencies than the corresponding cis-isomer frequencies suggesting that the C=O bonds in trans-isomer are slightly stronger.
Mini project
Introduction
In my mini-project I have decided to study a disilicon compound with two H's and two F's attached to it in cis- and trans-isomer form and compare their energies. Then do the same for Ge two isomers and then look at the trend going down group 14 since both - Si and Ge - are in group 14. And also compare the energies of another 2 molecules: Ge=Si with 2 F's attached to Ge and 2 H's attached to Si and vice versa. Si has less electrons than Ge but Ge is more diffused so Si is more electronegative. So it would be interesting to compare these compounds to see the influnce on the energies and also on the relative double bond strengths.
1st optimisation
For the 1st optimisation I used the B3LYP method with 3-21G basis set just to get a general optimisation and also for the calculations not to take a very long time. In fact, the calculations very very fast, on average only took about 25 seconds. The Si=Si double bond came back as a partial double bond, the Ge=Ge bond became a single bond and as for the Si=Ge bond it also came back as a single bond.
2nd optimisation
For the second optimisation the same method was used but a different basis set, 3-31G(d) basis set was used for a more precise optimisation since the molecules are not very big and complicated the (d) was added to the calculations.
Unfortunately all the calculations came back with an error and since there was little time left till the submission the calculations will be rerun overnight and further comments added on Wed, 9th of December!
The calculations were run the 2nd time and this time all of them were run staright away and were successful so I assume that the errors in the calculations were due to everyone submitting a lot of jobs at the same time and overloading the SCAN.
After the 2nd optimisation of the molecules, visually there is no change in the appearance of the molecules, but if the bond lengths were compared then after the 2nd optimisation these were slightly shorter. One example is cis-isomer of Si2F2H2, where the Si=Si bond after 1st optimisation was 2.129Å but after the 2nd optimisation it was 2.126Å.
References
- D. J. Darensbourg and R. L. Kemp., J. Inorg. Chem., 1978, 17, 2680. DOI:10.1021/ic50187a062