Rep:Mod:HAS1502
Module 2
Part I
Computational chemistry allows a vast amount of molecular properties to be predicted. It has already been shown that within organic chemistry, minimum energies (and hence thermodynamically preferred conformations) can be calculated through molecular modelling; furthermore molecular orbitals of compounds can be calculated, allowing explanation as to why one functional group within a molecule is more reactive that other equivalents. Within this module, techniques already employed within modelling organic compounds, as well as others, shall be used to perform analysis on several molecules from an inorganic perspective. Initially, a structural analysis of TlBr3 shall be performed, before an investigation into the molecular orbitals of BH3 is carried out. Following this, the effect of trans- and cis-isomerism on the vibrational spectra of an octahedral complex shall be examined, before the module is concluded with a mini-project exploring the effect of ligands upon the preferred geometry of a 4 co-ordinate Nickel complex.
Structural Analysis of TlBr3
Initially, a molecule of TlBr3 was drawn in Gaussview; the point-group of this molecule was restricted to D3h, before the molecule was subjected to geometry optimization (DOI:10042/to-9640) and frequency analysis. Information regarding the former calculation is shown in Table 1. The optimised structure is shown in Figure 1; 3D structure is shown via the link.
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | LANL2DZ |
| Total Energy (a.u.) | -91.2 |
| RMS Gradient Norm (a.u.) | 9 x 10-7 |
| Job Calculation Time | 33 seconds |
Figures 2 and 3 show the total energy graph and the RMS gradient obtained for the optimisation calculation. The energy of the molecule is reported in atomic units (1 a.u. = 262.55 kJ mol-1). It is known that Gaussian energy calculations have an error of around 10 kJ mol-1, which is equivalent to 0.00381 a.u. With regards to the energy stated, the reported energy (to 3 decimal places) was -91.218 a.u. Taking the error into account, this implies that the 'real' energy of the molecule could range from -91.222 a.u. to - 91.214 a.u. Due to these discrepancies, the energy value can only be confidently reported to 1 decimal place.
The value of the gradient is reported as 0.0000009. This is close to zero and less than 0.01 suggesting that a stationary point has been determined with the molecule in this configuration. The molecule was then subjected to frequency analysis to confirm that this was in fact a minimum energy point. The same basis set and method was used for this calculation as was for the optimisation. This is because if a different method and basis set were to be used, an alternate energy minima may be calculated; a differing basis set would result in a differing degree of accuracy within the calculation whilst a different method would also result in alternate minimum energy values. Hence, since the frequency analysis is used to clarify that the determined energy is in fact a minimum point, the same basis set and method must be employed for both calculations.
A frequency analysis is required as this confirms that the energy stationary point located is a minima. The initial optimisation determines points at which the energy gradient is equal to 0, however it does not imply whether this point is a maximum or a minimum. The frequency analysis determines the second derivative of the gradient; if all frequencies determined from this method are positive then the energy point originally determined can be confidently labelled as a minimum.
Table 2. shows the calculation summary of the aforementioned frequency analysis, whilst Table 3 lists the low frequencies that were determined (DOI:10042/to-9716). The predicted IR spectrum for the compound is shown in Figure 4.
| Calculation Type | FREQ |
| Calculation Method | RB3LYP |
| Basis Set | LANL2DZ |
| Total Energy (a.u.) | -91.2 |
| RMS Gradient Norm (a.u.) | 8.8 x 10-7 |
| Job Calculation Time | 39 seconds |
| Number | Vibrational Mode (D3h Point Group) | Frequency (cm-1 | Intensity |
|---|---|---|---|
| 1 | E' | 46 | 4 |
| 2 | E' | 46 | 4 |
| 3 | A2" | 52 | 6 |
| 4 | A1' | 165 | 0 |
| 5 | E' | 211 | 25 |
| 6 | E' | 211 | 25 |
Low frequencies for the molecule are found to be -3.4213, -0.0026, -0.0004, 0.0015, 3.9367, 3.9367. These were deemed as acceptable for the calculation. It can hence be seen from the vibrational analysis that the lowest "real" normal mode of the molecule is the e' vibrations at 46cm-1.
The optimised geometry resulted in a Tl-Br bond distance of 2.7Å and a Br-Tl-Br angle of 120 degrees. The angle is that expected for the molecule of this form, and the Tl-Br bond length is quoted to be 2.41Å1. The computational predicted can be seen to be a reasonably good match with the literature, although slightly longer than is found experimentally.
For some structures, it was found that the optimised geometry was reported to not bear a bond between atoms which were stated to be bonded; this does not mean that there is no bond present. It is simply that Gaussview has a maximum bond length setting, and so for large diffuse molecules or those which bond with a largely ionic component, the bond may be too long for Gaussian to comprehend. It is better suited for small covalently bound molecules.
Gaussview uses the juvenile concept of distance to define whether or not a bond is present between two atoms within a molecule; clearly this is not a sufficient definition of a bond. From an ionic perspective, a bond can be defined as the region between two atoms where a sufficiently high attractive electrostatic potential presides. If one were to view a bond from the LCAO approach, then a bond could also be considered to be the region where valence orbitals of atoms were similar enough in energy and size as to form a favourable overlap. From a purely covalent perspective, a bond can be viewed as the sharing of electron density between two atoms- a process where internuclear distance is most likely to be smallest, and hence is best modelled by Gaussian.
Molecular Orbital Analysis of BH3
The following molecule of BH3 (Figure 5) was drawn in Gaussview and subjected to geometry optimization to determine to lowest energy configuration of the molecule (DOI:10042/to-9940). Frequency analysis was then performed to confirm that this was an energy minima (DOI:10042/to-9941); Tables 4 and 5 show summaries of these calculations. Figures 6 and 7 show the total energy curve and the RMS gradient of the optimisation calculation.
| Calculation Type: | FOPT |
| Calculation Method: | RB3LYP |
| Basis Set: | 3-21G |
| Energy (a.u.): | -26.5 |
| RMS Gradient Norm (a.u.): | 2.067 x 10-4 |
| Job Calculation Time: | 34 seconds |
| Calculation Type: | FREQ |
| Calculation Method: | RB3LYP |
| Basis Set: | 3-21G |
| Energy (a.u.): | -26.5 |
| RMS Gradient Norm (a.u.): | 2.066 x 10-4 |
| Job Calculation Time: | 16 seconds |
As mentioned previously, energy values can only be quoted to one decimal place due to the error discrepancy involved in Gaussian calculations. Both optimisation and frequency calculations yield identical energy results, indicating that the stationary point located is a minimum. The RMS gradient of both is less than 0.01, which also suggests that the calculation has been successfully performed, and a stationary point is located with the molecule in this configuration. For the same reasons as stated previously, the method and basis set used were the same for both optimisation and frequency analysis. In this case, a basis set of lower accuracy was used, since the atoms involved in the molecule are all relatively light and hence do not require the use of pseudo-potentials (as was the case for TlBr3); for molecules of this type, a substantial result is obtained from the use of a low accuracy basis set, and the extra computational time required in the use of a more accurate one would not be justified.
With regards to the graphs obtained from the optimisation, it can be seen that as expected, both tend to zero as the optimisation step number increases.
The resulting optimised geometry had bond angles and lengths as are reported in Table 6.
| Calculated | Literature | |
| Bond Angle (degrees) | 120 | --- |
| Bond Length (Å) | 1.19 | 1.20 |
The calculated bond length is in good agreement with literature reports2; the bond angle is as would be expected for a molecule of this form.
Low frequencies obtained from the frequency analysis and the corresponding molecular vibrational modes are shown in Table 7. All frequencies and intensities are quoted to the nearest integer, in accordance with convention.
| Number | Form of the Vibration | Frequency (cm-1) | Intensity | Symmetry (D3h Point Group) |
|---|---|---|---|---|
| 1 |  |
1144 | 93 | A" |
| 2 |  |
1204 | 12 | E' |
| 3 |  |
1204 | 12 | E' |
| 4 |  |
2598 | 0 | A' |
| 5 |  |
2737 | 104 | E' |
| 6 |  |
2737 | 104 | E' |
Figure 8. shows the calculated IR spectrum of BH3. It can be seen that only three peaks are present in the spectrum, despite there being 6 vibrations. The first point to note is that only 5 of the vibrations are IR-active; the A' totally symmetric vibrational mode is infact IR-inactive. Since this vibration results in no change of dipole moment within the molecule, and no change in the magnitude of the dipole moment, no peak results from this vibration. This accounts for the loss of one of the peaks. A further two peaks are 'lost' since the vibrational modes are degenerate; numbers 2 & 3 and 5 & 6 in the table above correspond to two degenerate pairs of vibrations. Since these are both equivalent in energy, they will result in absorbance at the same wavelength. Therefore, only three peaks are produced despite there being six vibrational modes.
Molecular orbitals for BH3 were then calculated (DOI:10042/to-9639); Table 7 gives a summary of this job calculation. The LCAO method was employed to create an MO diagram for what would be expected for BH3 using fragment orbitals of B and a trigonal planar H3 unit; Figure 9. shows the results of the LCAO MO diagram, alongside the Gaussian calculated molecular orbitals.
It can be seen that the orbitals calculated computationally are all in good agreement with those predicted using LCAO. From this, it can be stated that qualitative MO theory (i.e. LCAO) is a highly reliable method of calculating molecular orbitals, for small molecules at least. The relative contributions predicted for each of the orbitals in comparison to those calculated are also in agreement. Energy values of each of the orbitals calculated have been included on the diagram, and show that with regards to the spacing of the orbitals, the 3a1' and the 2e' should be a lot closer in energy. This is a key advantage of computationally calculated orbitals over LCAO, since the relative energies of the orbitals can only be estimated as opposed to quantitatively determined.
Isomers of Mo(CO)4L2
For octahedral molybdenum carbonyl complexes of the form Mo(CO)4L2, it can be seen that two isomers can be formed; the L ligands can either be oriented cis- to one another or they can be located in the trans- positions. In the case where L = triphenylphosphine (PPh3), it is well documented that this orientation of the L ligands has a marked effect on the infrared spectra of the complex, namely the absorption bands reported for the carbonyl ligand. The cis-complex results in the presence of four such bands, whereas the trans-isomer only yields one.
The reason for the difference in the spectra that these compounds yield is related to group theory. The point group of the cis-complex is found to be C2v; the irreducible representation of this group can be represented as: Γ(C2v)= 2A1+B1+B2. If each of these symmetry operations are performed upon the cis-molybdenum molecule, it can be seen that each results in a change in dipole moment; hence all four of these vibrational modes are found to be IR active and four carbonyl absorption bands are formed. In contrast, the point group of the trans-isomer is D4h. The irreducible rotation in this case is: Γ(D4h)= 2A1g+B1g+Eu. Performance of these symmetry operations upon the molecule shows that only the E transformation results in a change in dipole; in this case 3 of the vibrational modes are IR-inactive and so only one peak is located within the spectrum.
With regards to modelling these molecules computationally, PCl3 ligands were used in place of the triphenylphosphine groups. This was due to the large computational demand of the phenyl rings, and the additional time that would be required in modelling them; since it has been shown that Cl has a similar electronic bonding contribution and is a sterically large molecule, it can be stated as a suitable substitute for the rings.
Initially each of the molecules were optimised using a low-level basis set and pseudo-potential to obtain a rough geometry for each of the isomers- this resulted in the location of a stationary point which corresponded to a false minima for each of the complexes (DOI:10042/to-9970, 10042/to-9971); the molecules were then manually manipulated to obtain a more appropriate starting geometry for optimisation and then subjected to optimisation using a higher level basis set and pseudo-potential(DOI:10042/to-9641, 10042/to-9642). A frequency analysis was then performed on these final optimised geometries of the complexes (DOI:10042/to-9643, 10042/to-9644). Tables 8 to 10 show summaries of each of these calculations. Figures 10 and 11 show the optimised geometries of the cis- and trans-isomers, respectively.
| Cis-Isomer | Trans-Isomer | |
| Calculation Type | FOPT | FOPT |
| Calculation Method | RB3LYP | RB3LYP |
| Basis Set | LANL2MB | LANL2MB |
| Total Energy (a.u.) | -617.5 | -617.5 |
| RMS Gradient Norm (a.u.) | 6.01 x 10-6 | 6.17 x 10-5 |
| Dipole Moment (Debye) | 8.63 | 0.00 |
| Point Group | C2v | D4h |
| Job Calculation Time | 17 minutes 41 seconds | 7 minutes 19 seconds |
| Cis-Isomer | Trans-Isomer | |
| Calculation Type | FOPT | FOPT |
| Calculation Method | RB3LYP | RB3LYP |
| Basis Set | LANL2DZ | LANL2DZ |
| Total Energy (a.u.) | -623.6 | -623.6 |
| RMS Gradient Norm (a.u.) | 8.01 x 10-6 | 2.07 x 10-5 |
| Dipole Moment (Debye) | 1.31 | 0.30 |
| Point Group | C2v | D4h |
| Job Calculation Time | 45 minutes 12 seconds | 47 minutes 41 seconds |
| Cis-Isomer | Trans-Isomer | |
| Calculation Type | FREQ | FREQ |
| Calculation Method | RB3LYP | RB3LYP |
| Basis Set | LANL2DZ | LANL2DZ |
| Total Energy (a.u.) | -623.6 | -623.6 |
| RMS Gradient Norm (a.u.) | 7.95 x 10-6 | 2.07 x 10-5 |
| Dipole Moment (Debye) | 1.31 | 0.30 |
| Point Group | C2v | D4h |
| Job Calculation Time | 27 minutes 30 seconds | 27 minutes 27 seconds |
Bond lengths and angles within each of the isomers are shown in Table 11. Bond lengths are reported to the nearest 0.01Å and bond angles to the nearest 0.1 degree, in accordance with convention. Note that for the cis-complex, axial C regards those belonging to carbonyl groups opposite a second carbonyl group, whilst equatorial refers to those opposite the phosphine ligands.
| Cis-Isomer | Literature Value3, 4 | Trans-Isomer | Literature Value5 | |
| C-O bond (Å) | 1.17 | 1.14-1.16 | 1.17 | 1.14-1.16 |
| Mo-C bond (Å) | 2.06 (ax), 2.01 (eq) | 2.02/2.06 (ax), 1.97 (av eq) | 2.06 | 1.85-1.89 |
| Mo-P bond (Å) | 2.51 | 2.58 | 2.44 | 2.35-2.38 |
| P-Cl bond (Å) | 2.24 | 1.83-1.86 | 2.24 | 1.83-1.86 |
| Cl-P-Cl angle (deg) | 99.4 | 99.0-103.9 | 99.1 | --- |
| P-Mo-C angle (deg) | 89.4 (eq), 91.9 (ax) | 80.6 (eq), | 90.0 | 88.0-92.0 |
| Cl-P-Mo-C dihedral (deg) | -6.4, -6.6 | --- | 0.0 | --- |
It can be seen that distances within the ligand groups (i.e. P-Cl and C-O) are consistent in both calculated molecules. Both molecules show an Mo-C bond distance of 2.06Å when the opposite ligand is a carbonyl, but this distance decreases slightly within the cis-compound when the carbonyl group is located opposite a phosphine ligand. The Mo-P bond can be seen to be somewhat shorter in the trans-complex than the cis; this is most likely due to the increased steric demand of the phosphine ligands in the latter. Bond angles within both of the complexes are comparable, apart from the dihedral Cl-P-Mo-C angle, which shows more distortion from the octahedral geometry than the trans-complex. Literature values noted for the cis-complex correspond to Mo(CO)4(PPh3)2, but those noted for the trans- are in fact recorded for trans-Cr(CO)4(PPh3)2. The point of comparing them to this alternate molecule was to ensure that none of the values obtained computationally were grossly unrealistic. It can be seen though, from comparison to both sets of literature values, that most calculated parameters are in good agreement, although some are slightly larger than what is noted experimentally.
The precise energy results obtained from the optimised geometries of the cis- and trans-complexes were determined to be -623.57707194 a.u. and -623.57603111 a.u. respectively. Conversion of these figures into kJ mol-1 shows that the cis-complex is calculated to be the more stable isomer by 273 J mol-1. It has been reported, however that the trans-isomer is the more thermodynamically stable of the two, whereas the cis-isomer is favoured kinetically due to the trans-effect of the CO ligand6; CO is a strong pi-acceptor ligand and as such incoming ligands tend to orient themselves trans- to a carbonyl group. The pi-acceptor ability of the CO stabilises the increased electron density that the new ligand imposes upon the metal, and hence during formation, the PPh3 ligands are inserted trans- to the carbonyl ligands and cis- to one another. It has also been reported that the cis-isomer tends to isomerise to the trans-form upon standing. From a modelling perspective, the computational method shows the incorrect energy ordering of the cis- and trans-isomers; this is most likely due to the accuracy of the basis set used. Were a basis set of greater accuracy to be employed, the energy ordering of the molecules would be more likely to be calculated correctly.
Computational chemistry can be used to suggest methods of improving the catalytic behaviour of compounds; for example, altering the ligands of a complex to stabilise the more efficient isomer. If, for the case in question, the energies of the cis-and trans-isomers of the molybdenum complex were taken to be those found experimentally, i.e. the cis-isomer is more unstable, then this task may involve stabilising the cis-form so that it became more energetically favourable than the trans. One possible method that could be employed would be using ligands that resulted in favourable intramolecular bonding interactions when located in the cis-orientation. An example of this has been reported7 with a tungsten complex containing pyridinyl rings; protonation of one of the rings results in the possibility of N-H....N-hydrogen bonding between them which is stated to favour the cis-form of the complex. Applying this to the phosphine ligand, one (or more) of the phenyl groups could be replaced by pyridine.
The computed IR spectra for both isomers are shown in figures 12 and 13. It can be seen quite clearly that the IR spectrum of the cis-compound has four absorption peaks in the carbonyl region, whereas the trans-isomer only has one, as expected. Table 12 shows assignment of the carbonyl peaks, alongside comparison to literature data.
| Isomer | Carbonyl Stretching Frequency (cm-1 | Intensity | Literature Values |
|---|---|---|---|
| Cis | 1945, 1949, 1958, 2023 | 763, 1498, 632, 598 | 1882, 1903, 1917, 20223 |
| Trans | 1950 | 1475 | 18856 |
Literature values agree well with the IR data predicted for the cis-isomer, but the trans-isomer appears significantly higher than that reported; this could be for one of two reasons. The first is the systematic error involved in Gaussian IR calculations (but if that were the case, it would be expected that the cis-results would also suffer from the same error); the second is the solvent used within the data. The IR reported in the literature was measured in heptane solution; Gaussian calculates IR spectra in the gas phase, which could easily account for this difference.
For both the cis- and trans-isomers, there were several vibrations located at low energies. Table 13 shows these vibrations, aswell as the region of the spectra they were located.
| Isomer | Vibrational Mode | Frequency | Intensity |
|---|---|---|---|
| Cis |  |
11 | 0 |
| Cis |  |
18 | 0 |
| Trans |  |
5 | 0 |
| Trans |  |
6 | 0 |
That these vibrations occur at such low frequencies suggests that they are occurring at room temperature. The result of this is that the molecule can never be conceived as being in a 'fixed' state, and so all of it's physical properties are subject to alteration, unless cooled down to far lower temperatures where the energy required for these vibrations is not available. The point group of the molecule is also affected by this occurrence, and so spectroscopic data may be in disagreement with that expected due to the loss of symmetry experienced by this constant molecular motion.
Part II: Mini-Project
Introduction
In the following mini-project, the effect of ligand type upon the preferred geometry of four co-ordinate Nickel complexes of the form NiL4 is to be investigated. Each of the complexes shall be modelled using Gaussview to determine energy minima for both the square-planar and tetrahedral geometries; these calculations shall then be subjected to frequency analysis to confirm that the determined stationary points are in fact energy minima (for the more stable isomer). Energy values for each of the geometric pairs shall then be compared to deduce which is determined to be favoured computationally, and whether this is in accordance with experimental results.
The ligands being investigated are Cl-, CO and OH-;these were chosen due to their location within the spectrochemical series- Cl- has a small crystal field splitting parameter whilst in contrast, CO has a much higher splitting parameter. OH- was simply chosen as an intermediate value ligands, so as to allow the possibility of a correlation between the magnitude of the splitting parameter and the preffered geometry of the complex to be illustrated. Charged ligands aswell as neutral ones were selected, so that the effects of this upon optimised geometries could also be analysed.
[Ni(Cl)4]2-
As already mentioned, an optimisation calculation was performed on each of the molecules (DOI:10042/to-9874, 10042/to-9875), before both were subjected to frequency analysis (DOI:10042/to-9878, 10042/to-9879) to confirm the stationary points determined were energy minima. To ensure that the square planar and tetrahedral geometries were retained during the calculation, the point groups were initially restricted to D4h and Td respectively. Table 14 reports the summaries of the optimisation calculations; in Table 15, the summaries of the frequency analysis can be found. Optimised geometries of the complexes are shown in Figures 14 and 15.
| Tetrahedral | Square Planar | |
| Calculation Type | FOPT | FOPT |
| Calculation Method | RB3LYP | RB3LYP |
| Basis Set | LANL2DZ | LANL2DZ |
| Total Energy (a.u.) | -229.1 | -229.1 |
| RMS Gradient Norm (a.u.) | 2.01 x 10-5 | 7.28 x 10-6 |
| Dipole Moment (Debye) | 0.55 | 0.00 |
| Point Group | Cs | D4h |
| Tetrahedral | Square Planar | |
| Calculation Type | FREQ | FREQ |
| Calculation Method | RB3LYP | RB3LYP |
| Basis Set | LANL2DZ | LANL2DZ |
| Total Energy (a.u.) | -229.1 | -229.1 |
| RMS Gradient Norm (a.u.) | 2.01 x 10-5 | 7.30 x 10-6 |
| Dipole Moment (Debye) | 0.55 | 0.00 |
| Point Group | Cs | D4h |
It can be seen that the frequency analysis confirms that the stationary point located for both molecules is infact an energy minima. The low value of the RMS gradient confirms that a stationary point has been found. Note that even though the point groups for the molecules were restricted to those mentioned previously, the tetrahdral isomer has been optimised to the Cs point group. Whilst the energies have only been reported to one decimal place in a.u., there is infact a slight variation between them; on conversion to kJ mol-1, it is found that the tetrahedral geometry is lower in energy by 1.7 kJ mol-1 making this the more favourable geometry.
Table 16 lists bond lengths and angles of the optimised geometries.
| Tetrahedral | Square Planar | |
| Cl-Ni (Å) | 2.18 | 2.20 |
| Cl-Ni-Cl (degrees) | 131.5 | 90 |
It can be seen that within the tetrahedral complex, the Cl-Ni bond is shorter, resulting in a stronger bond and hence greater energy stabilisation; furthermore the angle between each of the Cl atoms is greater than in the square planar complex and so there is less steric hinderance and electrostatic repulsion (both of which would result in a less stable complex). Analysis of these properties clearly shows why the tetrahedral geometry is favoured in this case. The literature value8 for the tetrahedral Ni-Cl complex is stated as 2.26Å; it can be seen that this is in good agreement with the computed figure. Literature data is not available for the square planar complex, since the molecule does not favour this form.
[Ni(CO)4]
Tables 17 and 18 report the summaries of the optimisation (DOI:10042/to-9876, 10042/to-9877) and frequency analyses (DOI:10042/to-9880, 10042/to-9881) for the alternate geometries of the complex. Optimum square-planar and tetrahedral geometries are shown in Figures 16 and 17.
| Tetrahedral | Square Planar | |
| Calculation Type | FOPT | FOPT |
| Calculation Method | RB3LYP | RB3LYP |
| Basis Set | LANL2DZ | LANL2DZ |
| Total Energy (a.u.) | -622.6 | -622.5 |
| RMS Gradient Norm (a.u.) | 7.67 x 10-5 | 8.71 x 10-6 |
| Dipole Moment (Debye) | 0.00 | 0.00 |
| Point Group | Td | D4h |
| Tetrahedral | Square Planar | |
| Calculation Type | FREQ | FREQ |
| Calculation Method | RB3LYP | RB3LYP |
| Basis Set | LANL2DZ | LANL2DZ |
| Total Energy (a.u.) | -622.6 | -622.5 |
| RMS Gradient Norm (a.u.) | 7.56 x 10-5 | 8.81 x 10-6 |
| Dipole Moment (Debye) | 0.00 | 0.00 |
| Point Group | Td | D4h |
Again, the freguency analysis and RMS gradient value confirm the presence of an energy minimum at these geometries. Conversion of the explicit energies to kJ mol-1 gives the result that the tetrahedral geometry is 27.3kJ mol-1 lower in energy than the square planar conformation.
Table 19 gives bond angles and distances determined from the optimisation calculation.
| Tetrahedral | Square Planar | |
| Ni-C (Å) | 1.8 | 2.1 |
| Ni-O (Å) | 1.2 | 1.2 |
| C-Ni-C (degrees) | 110 | 90 |
As for the previous case with the chloride ligands, it can be seen that within the preferred geometry, the bond lengths are shorter and the angles greater than within the disfavoured square planar configuration. This again accounts for the tendence to form tetrahedral complexes with ligands of this form. Literature upon the subject9 agrees that the tetrahedral form is favoured and states Ni-C bond lengths of the complex to be 1.8Å with C-O bond lengths as 1.1Å. This is also in good agreement with the calculated values obtained from the energy minimisation
[Ni(OH)4]2-
For the optimisation of the two geometries of [Ni(OH)4]2-, an issue was discovered with regards to the square planar complex. When the point group was restricted, the geometry could only be calculated using a very low basis set and pseudo potential (as described in Table 20) which was inaccurate in determining the overall energy minimum of either molecular confirmation. When the point group was not restricted, the square-planar molecule immeadiately took on the tetrahedral conformation when subjected to energy optimisation. From this it was reasoned that the tetrahedral geometry must be significantly lower in energy that the square-planar molecule. Information regarding the less accurate basis set calculation has been included (DOI:10042/to-9976, 10042/to-9977), but is not relevant to the overall analysis of the determined lower energy conformation. Figures 18 and 19 show the molecular results obtained from the lower accuracy method whilst Figure 20 is the overall optimised tetrahedral conformation (DOI:10042/to-9885) (which was subjected to frequency analysis following energy minimisation (DOI:10042/to-9978), a summary of which is shown in Table 21).
| Tetrahedral | Square Planar | |
| Calculation Type | FOPT | FOPT |
| Calculation Method | RB3LYP | RB3LYP |
| Basis Set | LANL2MB | LANL2MB |
| Total Energy (a.u.) | -468.2 | -468.2 |
| RMS Gradient Norm (a.u.) | 9.47 x 10-5 | 6.19 x 10-5 |
| Dipole Moment (Debye) | 2.13 | 0.01 |
| Point Group | C1 | C1 |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | LANL2DZ |
| Total Energy (a.u.) | -472.5 |
| RMS Gradient Norm (a.u.) | 1.37 x 10-5 |
| Dipole Moment (Debye) | 2.22 |
| Point Group | C1 |
| Calculation Type | FREQ |
| Calculation Method | RB3LYP |
| Basis Set | LANL2DZ |
| Total Energy (a.u.) | -472.5 |
| RMS Gradient Norm (a.u.) | 1.38 x 10-5 |
| Dipole Moment (Debye) | 2.22 |
| Point Group | C1 |
It can be seen that there is a sufficient energy difference between the optimised structures determined using the lower basis set and the final tetrahedral conformation; the latter is 1129 kJ mol-1 lower in energy. Bond angles and distances are shown in Table 21.
| Ni-O (Å) | 1.79 |
| O-H (Å) | 0.98 |
| H-O-Ni (deg) | 117 |
| O-Ni-O (deg) | 100 |
In comparison to the complexes already modelled and how accurate this process has been, the obtained data for this calculation appears to be reasonable.
Discussion
With regards to the project as a whole, it can be seen that Nickel(II) complexes of the form NiL4 tend to favour the tetrahedral geometry with all ligands studied. Since a range of ligands from the spectrochemical series were involved (both those with high and low crystal field splitting parameters were studied) it can be quite confidently stated that the majority of the time Nickel(II) complexes are tetrahedral in structure.
Comparison of the bond angles and lengths of the three optimised tetrahedral complexes reveals how the effect of changing the ligand alters the preferred geometry of the complex. Whilst all molecules are still 'tetrahedral' each experiences a certain degree of distortion from the pure tetrahedral geometry. The carbonyl complex is the closest (with regards to bond angles) to being tetrahedral, whilst the angles in the chloride and hydroxide complexes are respectively much larger and smaller. This is clearly due to the size of the ligands bound to the Nickel centre; chloride ions are far larger than carbonyl molecules which in turn are larger than hydroxide ions. As the size of the ligand decreases, the tendency to warp towards a square-planar geometry is increased.
References
1. Blixt, J. et al, J. Am Chem Soc, 1995, 117 5089-5104
2. Konecny, R. & Doren, D. J., J. Phys Chem B, 1991 101(51) 10983-10985
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