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Module 2: Bonding (Ab initio and density functional molecular orbital)
Optimising a Molecule of BH3
A molecule of BH3 was created in GaussView and all three B-H bond lengths were set to 1.5 angstrom. Then a calculation to optimise the molecule was run by using the method as DFT B3LYP, the basis set as 3-21G and the type of calculation as OPT. The optimised output was analysed and the optimised B-H bond length for all three B-H bonds was is 1.19 Angstroms and the optimised H-B-H angle was 120 degrees. A summary of the results was found and reported below. From the results it can be seen that the gradient is very small so the molecule is actually optimised. The real output file was also checked to show that the forces and displacement have converged.
GaussView was then opened with the output log file and then two graphs were generated as shown on the right, the top one shoes the energy of the molecule at each step of the optimisation an the bottom shows the gradient of the energy of the molecule at each step of the optimisation. The top graph shows the optimal structure is the one with the lowest energy and the bottom graph is the first derivative of the slope above, this should be zero when the optimised structure has been reached. There are different structures shown for the optimisation steps, two of the structures do not have bonds, this is because of the way gaussview has defined bonds to have a maximum distance value. The definition of a bond is discussed later
The checkpoint file of the optimised molecule of BH3 was then opened with GaussView and the method was changed to energy, a basis set of 3-21G basis set was used and full NBO was selected. The job was run, the completed checkpoint analysis can be found here https://www.ch.ic.ac.uk/wiki/index.php/Image:NAFEEZAH_BH3_POP.LOG The molecular orbitals were generated. MOs numbered 1 to 8 were inspected and are shown below.
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The LCAOs give a very good picture of what the actual MOs look like. The main difference is that the overlap of the actual MOs can not be shown using the LCAO method. However the idea of the overlap can be seen from the phases in the LCAO diagrams. However the actual MOs show the shape of the interacting orbitals. The actual MOS also show that sometimes the orbitals can become distored for exampple in MO6. Overall this diagram shows how useful qualitative MO theory as the predicted pictures give a good understanding of how the orbitals would look with an adjustment for the change in shape for negative and positive interactions.
The charge distribtion of this molecule was then investigated by opening the log file from the population analysis. The NBO charges for the B atom is 0.332 which shows boron is electron deficient and the charge for both H atoms is -0.111. The results file can also be viewed to give more information on bonding in the orbital, the summary of the information is shown in the table. It shows that the B has formed three sp3 orbitals which interact with a s atomic orbital of H, there is also a core orbital which is 100% s orbital. There is also an unoccupied Pz orbital which is perpendicular to the plane of the molecule. The table showing occupancy and energies shows the unoccupied orbitals to be lower in energy than the occupied, this is because the unoccupied orbital will readily accept electrons. A vibration and frequency analysis was carried out on the optimised geometry, the energy was the same as the optimised structure and the vibrations were checked, the motions of the centre of mass are much smaller than the first vibrations listed.
| no. | form of the vibration | frequency | intensity | symmetry D3h point group |
|---|---|---|---|---|
| 1 |  |
1146 | 93 | A2" |
| 2 |  |
1205 | 12 | E' |
| 3 |  |
1205 | 12 | E' |
| 4 |  |
2592 | 0 | A1' |
| 5 |  |
2730 | 104 | E' |
| 6 |  |
2730 | 104 | E' |
The IR spectrum of BH3 only has 3 peaks even though there are 6 vibrations, this is because there are two doubly degenerate vibrations which have the same frequency and intensity so only show up as one peak. Vibration number 4 has no intensity so does not show up on the spectrum, this is because the vibration does not cause a change in dipole moment of the moecule so it is not IR active
Optimising a Molecule of BCl3
A molecule of BCl3 was created in GaussView and the symmetry was restricted to D3h. The geometry was optimised using the method DFT B3LYP. A medium level basis set LanL2MB was chosen. The same method and basis set has to be used for optimisation and frequency analysis. This is because for optimisation the potential energy surface of the molecule was used to locate the minimum point and the molecular orbitals were all generated, all this information is needed for a frequency analysis. If the same basis set is not used then the frequencies will not be correct for the optimised molecule. A frequency analysis was carried out,which can be found here https://www.ch.ic.ac.uk/wiki/index.php/Image:NAFEEZAH_BCL3_FREQ.LOG This has to be done to ensure that the structure is the minimal energy structure. The low frequencies have to be much lower than the vibrations listed. For this compound the largest low is -8.77 and the smallest vibration is 214, so they are two orders of magnitude different. The low frequencies are closer to zero than in the BH3 molecule because a medium level method was used for BCL3 so this is more accurate because a low level method was used for BH3
| optimised B-Cl bond length | literature value [1] | optimised B-Cl-B angle | Literature value[1] |
|---|---|---|---|
| 187pm | 175pm | 120 | 120 |
The literature describes the molecule as having a trigonal planar shape which corresponds to a bond angle of 120 degrees and the literature bond length is shorter than the optimised structure is gaussview. This could be because of some extent of pi-bonding as discussed in literature [2] in the molecule which gaussian does not take into account.
As with BH3 there are also structures in the optimisation which do not have bonds, this is not because there are not bonds present. It due to the definition that Gaussview gives to bonds. It has set a maximum distance up to which bonds are drawn which is exceeded in some of the optimisation strucutres. A bond can be defined in many ways, pauli's defintion of a bond is "There is a chemical bond between two atoms or groups of atoms in case that the forces acting between them are such as to lead to the formation of an aggregate with sufficient stability to make it convenient for the chemist to consider it as an independent "molecular species"." However this mainly just considers covalent bonds. For simple molecule availabilty of electrons and VSEPR have to be considered and for more complicated molecules a more detailed molecular orbital approach has to be taken to see whether MOS are at appropriate energies, symmetries and orientations to overlap. The symmetry expected for the ground state molecule is D3h and this is the point group which GaussView uses which can be found in the output file. The optimisation calculation summary on the left shows that the calculation took 7 seconds and the frequency calculation took 18 seconds. The speed of the calculations shows the inaccuracy in the calculations.
Isomers of Mo(CO)4L2
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To investigate the isomers when L=PPh3 is very expensive and time consuming compuatational work so instead L=PCl3 which are similar in electronic contribution and are also large. They require less computing power. Fisrt the cis and trans form were drawn in GaussView then the DFT b3LYP method was used with a basis set of LANL2MB and a loose convergence criteria which is a low level basis set for a rough optimisation. These calcualations were sent off to SCAN because they require a greater computer power. The completed geometry optimisation for the trans isomer can be found here DOI:10042/to-3043 and the cis isomer DOI:10042/to-3044 10042/to-3044 The P-Cl bonds are not shown in the optimisation however the bond is still present, these are for the same reasons as discussed previously. This optimisation gives good bond lenghts and angles but not dihedral angles.
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The torsional angles of PCl3 were then altered as described in the instructions. This is because there can be more than one minimum in the potential energy surface of a compound and if the starting geometry is not exactly in the right orientation then the minimum found might not be the lowest one. Then this geometry was re optimised using LANL2MB which is a different basis set, this is more accurate basis set so a tigher convergence was used "int=ultrafine scf=conver=9" the second geometry optimisation for the trans can be found here DOI:10042/to-3045 and the cis here DOI:10042/to-3046 A frequency analysis was then carried out on both isomers by sending the calculation to SCAN but keeping the same basis set but changing the calculation to a frequency calculation. The frequencies of both files were checked and they were all positive, this means that the geometries are at the correct minimum on the potential energy surface. Any negative value would mean that the optimisation was not carried out properly. The completred frequency analysis for the trans isomer can be found here DOI:10042/to-3047 and the cis isomer can be found here DOI:10042/to-3048
Structures of the optimised geometries
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Both the cis [3] and the trans [4] isomer were compared to literature by analysing the bond lengths and angles. From the data for the trans isomer it can be seen that the calculated and experimental values are very close, the main differences being between the P-C bonds which were actually P-Cl in the model used. P-Cl bonds are longer which explains this difference. The bond angles are also very similar, this is because the big groups are trans to eachother so there is not much steric clash. For this isomer the use of PCl3 is a good model. For the cis isomer the difference is greater for the bond lengths and angles for the calculated and literature values. This can be explained because the PPh3 are larger than the ligands used in the calculation so they would have a greater steric clash, the deviations in the octahedral angles are greater for the literature values than for the calculated values.
Relative energies
The energies of both isomers can be compared because the same method was used to optimise both structures and they both have exactly the same atoms. As can be seen from the table on the left it seems that the cis isomer is slighlty lower in energy. However because the energy calculations have an error of about 10kJ/mol[5] and because the PPh3 groups were replaced by PCl3 the determing which one is more stable can not be based on this. The dipole for the cis isomer is much greater as is the steric hinderance because the large groups are cis to eachother. This would cause the trans isomer to be more stable. This is confirmed in literature [4] which says how the trans form is the thermodynamically stable form which means it is lower in energy and the cis form is kinetically stable which means it has a lower energy pathway and is formed quicker. The cis form isomerises to the trans form, this is because the unfavourable steric interactions between the large groups are removed in the trans form. To get a better ordering of isomers the actual ligand of PPh3 could be used, or an even bulkier ligand such as SitBu3 as there will be a greater steric clash so the energy difference between the two isomers would be much larger so this could be determined by the optimisation calculation.
IR Spectra
There are low frequency vibrations for each isomer as shown below. They energy provided at rooom temperature is sufficient to make the vibrations occur at room temperature.
| Vibration | frequency/cm-1 | intensity |
|---|---|---|
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11 | 0.02 |
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18 | 0.007 |
| vibration | frequency cm-1 | intensity |
|---|---|---|
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5 | 0.09 |
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6 | 0 |
The carbonyl stretching frequencies for both isomers were investigated, from symmetry there should be 4 frequencies for the cis isomer which corresponds to the values below from my calculation. However there should only be two for the trans isomer. The reason for this is that two of the frequencies are very close in wavenumber and intensity, they were animated on Gaussview and one is the up and down motion of two opposite carbonly groups, the other frequency is the same motion for the two other carbonyl groups. These vibrations should be the same because of symmetry however Gaussview has assigned a C1 point group so the compound does not have symmetry. One other wavelenght has a very small intensity. A vibration only shows up in IR if it causes a change in dipole of the compound and because of the distored symmetry on Gaussview this stretch shows up when it should not.
| cis frequency/cm-1 | intensity | trans frequency cm-1 | intensity |
|---|---|---|---|
| 1945 | 763 | 1950 | 1475 |
| 1948 | 1498 | 1951 | 1466 |
| 1958 | 632 | 1977 | 0.6 |
| 2020 | 597 | 2031 | 3 |
Comparing the frequencies to literature [6] we can see that the calculated values differ from the literature values. This is because of the same reasons above, due to the different symmetry assigned to the compound the stretching frequencies would differ. The larger PPh3 would also cause a change in the vibrations due to the large steric interations and the shape of the compound.
| cis frequency/cm-1 | literature | trans frequency cm-1 | literature |
|---|---|---|---|
| 1945 | 1893 | 1951 | 1902 |
| 1948 | 1911 | 2031 | 1955 |
| 1958 | 1929 | ||
| 2020 | 2023 |
Mini Project - Structural Variations of Butadiene
Metal complexes with butadiene as a ligand can have structural variation. Three examples will be investiaged. These examples were found in the 3rd year lecture course Advanced Organometallic Chemistry [7] . The butadiene ligand responds to a metal in terms of bonding. The bond lengths of the Carbon carbon bonds in butadiene will vary depening on how it interacts with the metal. The stretching frequencies of the carbon carbon bonds can be investigated, the MO diagrams will give a good indication of the interaction as will NBO analysis. The MO diagram of the π electrons of the butadiene is shown, the ψ1 can form a σ bond with the metal ψ2 can form a π bond with the metal. The empty ψ3 molecular orbital is available for the metal to backbond into.
All the compounds were initially optimised using a low level basis set and method of B3LYP AND LAN2MB with the additional words of opt=loose. The initial bond length for the butadiene ligand was set to those in literature. The bond lenghts of the other ligands were also looked up. For compound 1 the correct structure was obtained from the first optimisation, a frequency analysis was obtained DOI:10042/to-3248 and one of the vibrations had a negative value. This shows the structure is not at the correct minimum so another optimisation was carried out DOI:10042/to-3285 , this has a tighter convergence criteria. The basis set was changed to LAN2DZ and additional key words as int=ultrafine scf=conver=9. The frequency analysis was carried out, all the frequencies were positive so the optimisation is complete. The same process was carried out for compound 2. However the for the first optimisation the bond lengths calculated were not the same as the literature because the middle bond was shorter but the values were very close. A freqeuncy analysis was carried outDOI:10042/to-3416 and the vibrations were all positive but when the output file was checked the optimisation had not fully converged. The bond lengths were changed to correspond to the literature and optimised again using the second tighter convergence criteria. A frequency analysis was carried out again, DOI:10042/to-3417 again all the vibrations were positive. This time all the bond lengths were equal.
Optimising compound 3 took a lot longer due to human error. When drawing the Cp ligand I did not include the hydrogens, I assumed wrongly they were present but not shown. This lead to all my optimisations not converging. When I opened the optimisation files the end showed the message Convergence failure -- run terminated. The input file was checked and I could not find any errors however the multiplicity of the output file was 2. This would mean the complex had an unpaired electron but this was not the case, from this it was realised that the hydrogens were not included in the structure. The structure was drawn again and optimised as explained above, the structure seemed correct however after the first frequency anlysis DOI:10042/to-3414 one vibration was negative but then after the frequency anlysis for the second optimisation DOI:10042/to-3415 one frequency was still negative. Due to lack of time I did not further optimise this. However a MP2 method with a basis set of 6-311G(d,p) could have been used. This is for more accurate calculations but because my molecule is quite large this would take a long time. This compound probably did not converge because of the large Cp ring. The rest of the calculations were carried out on the structure from the second optimisation
Carbon bond lengths
The optimised structure for compound 1 is shown with the literature bond lengths and the calculated bond lengths. The bond lengths are not exactly the same,however they are similar and follow the same trend, the middle bond is longer and the two side bonds are shorter and show double bond character. This shows typical behaviour of the butadiene ligand, a σ and π bond are formed with the metal so four electrons are involved in the bonding and the ligand is classified as an L2 ligand. Backbonding does not occur, if this was the case the ψ3 would become occupied and and middle bond would be shorter than the two side bonds. This calculation therefore corresponds with the literature for this compound.
In compound 2 butadiene does not show typical bonding, from literature all the expected bond lengths are the same this means that sigma bonding dominates so only ψ1 is involved in bonding. The calculations shows all bond lengths to be the same, just slightly shorter than from literature. This confirms the explaination of the bonding of the ligand. There is not much pi or backbonding.
In compound 3 butadiene also does not show typical bonding. The literature middle bondlength is shorter than the other two, this means that backbonding occurs so ψ3 dominated in bonding, the butadiene acts as an X2 ligand, it has two bonds to the metal each contributes one electron to the metal. The calculated bond lengths correspond to this type of bond length, the values are not exactly the same but they are very similar and the same trend is followed
Carbon Stetching frequencies
Electronic effects with alkenes can be monitored using infrared (IR) spectroscopy. For the compounds individiually the carbond carbon stretching frequencies can be investigated. A carbon carbon double bond would have a higher frequency than a single bond because it a stronger bond. The back bonding can be compared over the compounds, the more pi-backbonding, the weaker the side C=C double bonds and the lower the C=C stretching frequency in the IR. The sigma bonding also reduces the stretching frequency which is why the wavenumbers are lower than in alkenes that are not bonded to a metal.
For compound 1 the carbon carbon stretching frequencies were animated on Gaussview, these show the double bond character in the middle bond because it has a higher frequency. This corresponds to the bond length and bonding already discussed for this compound.
| C2-C3 | C1-C2 and C3-C4 |
|---|---|
| 1463 cm-1 and 1479cm-1 | 1541cm-1 and 1549cm-1 |
In compound 2 all the carbon carbon bonds vibrate under the same frequency as they are the same length. This corresponds to the bonding structure suggested from the bond lengths. The frequency values for compound 2 are inbetween the values for the single and double bond for compound 1, this shows the delocalised nature of the electrons.
| C1-C2 and C2 and C3 and C3-C4 |
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| 1483cm-1 |
| 1522 cm-1 |
In compound 3 the stretching frequencies show the strong double bond character of the middle bond due to back bonding but the weak bond character of the two side bonds. These bonds have been weakend due to the backbonding of the metal to the ligand.
| C2-C3 | C1-C2 and C3-C4 |
|---|---|
| 1583 cm-1 | 1484cm-1 and 1549cm-1 |
MO and NBO analysis
The section in the NBO analysis file called "Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis" is important as it shows any mixing of orbitals, if any values under E(2) are higher than 20kcal per mol they should be looked at. This section shows which molecular oribitals are donating and which are recieving the donation so any backbonding can be identified. For the first compound the NBO will be analysed -we do not expect to see any backbonding. Below are the the values which have a high E(2) value -
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
within unit 1 1. BD ( 1)Rh 1 - C 6 / 43. LP*( 1) C 7 104.63 0.16 0.133 19. BD ( 2) C 8 - C 9 / 43. LP*( 1) C 7 68.15 0.15 0.105 43. LP*( 1) C 7 /105. BD*( 1)Rh 1 - C 6 85.16 0.08 0.087
The main orbital mixings are shown above, The middle one is just carbons interacting, The bottom one is from an orbital on a carbon to an orbital invlving Rh and C. However the first one is an interaction between a bonding orbital between Rh and a C to a lone pair on C.
For compound 2 -
E(2) E(j)-E(i) F(i,j)
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
1. BD ( 1)Fe 1 - C 2 / 42. LP*( 1) C 6 118.53 0.10 0.113 4. BD ( 1)Fe 1 - C 5 / 43. LP ( 1) C 7 118.34 0.10 0.112 41. LP*( 4)Fe 1 / 88. RY*( 1) C 10 92.93 0.05 0.195 103. BD*( 1)Fe 1 - C 3 / 41. LP*( 4)Fe 1 56.93 0.17 0.223 103. BD*( 1)Fe 1 - C 3 /106. BD*( 1)Fe 1 - C 10 75.54 0.08 0.196 104. BD*( 1)Fe 1 - C 4 /106. BD*( 1)Fe 1 - C 10 75.45 0.08 0.196 106. BD*( 1)Fe 1 - C 10 / 41. LP*( 4)Fe 1 142.37 0.08 0.241
All the four bottom ones are just mixing between Fe and the top are from the metal to the carbon. Since compound 3 shows backbonding to a much greater extend it would be expected that the E(2) values for mixing from the Fe to the C would be much larger than the two above. However after inspecting the log file for compound 3 this was not found.
The NBO analysis for these compounds are very complicated. The charge of the metal can also be found and this can be compared to see the extent of backbonding. For the complexes where the metal backbonds to the ligands the charge would either be positive or less negative on the metal. From the charge distribution below it can be seen that the metal on compound 3 has a positve charge which shows the backbonding to the butadiene ligand.
| Metal | Carbon |
|---|---|
| -0.149 | C1+C4 - 0.504 |
| C2+C3 - 0.126 |
| Metal | Carbon |
|---|---|
| -0.495 | C1+C4 - 0.465 |
| C2+C3 - 0.134 |
| Metal | Carbon |
|---|---|
| +0.108 | C1+C4 - 0.659 |
| C2+C3 -0.118 |
Below is the interaction of the relevant orbitals involved in the pi cloud of butadiene with the orbitals of the metal.
From the NBO output file the occupancy of the orbitals were investigated for compound 1
1. (1.58567) BD ( 1)Rh 1 - C 6
( 58.90%) 0.7675*Rh 1 s( 1.19%)p 2.64( 3.15%)d80.29( 95.66%)
0.0056 0.1090 0.0034 -0.0026 -0.0901
0.0014 -0.0039 -0.0468 0.0052 -0.0015
-0.1453 -0.0032 0.0780 -0.0004 0.9698
0.0459 0.0298 -0.0075 0.0590 0.0051
0.0585 -0.0050
( 41.10%) 0.6411* C 6 s( 9.03%)p10.08( 90.97%)
0.0008 0.3004 -0.0070 0.8571 0.0272
-0.1907 0.0112 0.3699 0.0318
105. (0.52892) BD*( 1)Rh 1 - C 6
( 41.10%) 0.6411*Rh 1 s( 1.19%)p 2.64( 3.15%)d80.29( 95.66%)
-0.0056 -0.1090 -0.0034 0.0026 0.0901
-0.0014 0.0039 0.0468 -0.0052 0.0015
0.1453 0.0032 -0.0780 0.0004 -0.9698
-0.0459 -0.0298 0.0075 -0.0590 -0.0051
-0.0585 0.0050
( 58.90%) -0.7675* C 6 s( 9.03%)p10.08( 90.97%)
-0.0008 -0.3004 0.0070 -0.8571 -0.0272
0.1907 -0.0112 -0.3699 -0.0318
Only these orbital contained a mix of Rh s,p and d and C p and s, however these could relate to any of the orbitals shown in the diagram so this does not help with determing which MOs are dominating in the bonding. The HOMO and LUMO are shown below of the compounds
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Conclusion
From these three examples we have seen how butadiene can have structural variations when binding to a metal centre. This makes it a useful ligand as it responds to the need of the metal. The bond lengths and IR confirmed the structure of the ligand and the NBO and MO analysis helped explain the different structures. However a deeper understanding of NBO would be needed for a better explaination because it is very complicated for these molecules. Further optimising compound three should also have been carried out if there was time. My bond lengths were not exactly the same as those calculated in the literature, however considering that those structures could have been carried out with a more accurate method and basis set the values are quite close.
References
- ↑ 1.0 1.1 Pradyot Patnaik. Handbook of Inorganic Chemicals. McGraw-Hill, 2002
- ↑ Greenwood, Norman N.; Earnshaw, A. (1997), Chemistry of the Elements (2nd ed.), Oxford: Butterworth-Heinemann
- ↑ Cotton et al Inorg. Chem., 1982, 21 (1), pp 294–299DOI:10.1021/ic00131a055 10.1021/ic00131a055
- ↑ 4.0 4.1 Graeme Hogarth and Tim Norman,Inorganica Chimica Acta Volume 3, Issue 10, October 2000, Pages 508-510 DOI:10.1016/S0020-1693(96)05133-X 10.1016/S0020-1693(96)05133-X
- ↑ http://www.ch.ic.ac.uk/hunt/teaching/teaching_comp_lab_year3/8a_accuracy.html
- ↑ Cotton Inorg. Chem., 1964, 3 (5), pp 702–711 DOI:10.1021/ic50015a024 10.1021/ic50015a024
- ↑ Ed Marshall -Advanced Organometallic Chemistry Lecture 1