Rep:Mod:asdf0987

Imperial College
London

MODULE 2
Note: This page is optimized for a window of width ~1400px

Part 1

BCl₃ Information

B-Cl bond distance / Å Cl-B-Cl bond angle File Type Calculation type Calculation method Basis set Final Energy / au Dipole Moment / D Point Group Calculation Time / s 1.86639 120.000° .log FOPT RB3LYP LanL2MB -69.43928116 0 D3h 12.0

Individual Small Molecule: Acetone

.

Acetone

All unique bond angles have been illustrated on the image (left) for clarity, whilst the xyz coordinates of the atoms can be found by following this link. Having done this optimisation it is evident that gaussian has incorrectly given the molecule a C1 point group. Thus the point group was then specified as C2v, obtained via inspection and following a point group flow chart . The calculation was then re-run to yield the following results: The H1-C1-H2 bond angle increased by 0.057° to 109.293°. The H2-C1-H3 bond angle decreased by 0.111° to 107.919°. In addition to the full data presented in the table below, the revised xyz coordinates have also been included. Acetone Unique Identifier

Acetone "C1 Symmetry" C-H (for H1 & 6) bond distances / Å 1.09990 C-H (for H2-5) bond distances / Å 1.10197 C-C bond distance / Å 1.56660 C=O bond distance / Å 1.25220 Calculation method RB3LYP Basis Set LanL2MB Final Energy / au -190.67645018 Dipole moment / D 1.7588 Point Group C1 Calculation Time 3m 2s Acetone C2v Symmetry C-H (for H1 & 6) bond distances / Å 1.09989 C-H (for H2-5) bond distances / Å 1.10198 C-C bond distance / Å 1.56660 C=O bond distance / Å 1.25219 Calculation method RB3LYP Basis Set LanL2MB Final Energy / au -190.67644928 Dipole moment / D 1.7601 Point Group C2v Calculation Time 11s

Vibrational Analysis of BH₃

Summary energy for both BH₃ optimised and the frequency calculated version were the same -26.29366788 au.

No vibrations with a negative frequency, thus the structure was fully optimized.

No. Vibrational Form Description Frequency / cm-1 Intensity Symmetry D3hPoint Group 1 All the hydrogen atoms move up and down relative to the σh plane of symmetry whilst the boron atom appears to move slightly in an opposing direction. 1244.56 126.121 A2 2 The two hydrogen atoms move towards (and away) from each other in the σh plane. 1368.2 17.0387 E' 3 All atoms move in the σh plane, with two H's vibrating in the same direction around the B atom, whilst the 3rd H oscillates perpendicular to the C3 axis and the C2 axis that runs through it. 1368.23 17.0399 E' 4 All H atoms vibrate in a concerted fashion, towards and away from the B atom which remains stationary. 2909.05 0 A1' 5 Two of the hydrogens vibrate towards and away from the stationary boron atom, out of sync with each other. 3136.68 10.8829 E' 6 Two of the hydrogens vibrate towards and away from the B atom in sync with each other, whilst the third shows a vibration of greater amplitude, out of sync with the other two. The central B atom shows a slight oscillation opposing the motion of the unique hydrogen. 3136.83 10.8916 E'

Note: The principal axis (C₃ axis) was taken as the Z-axis in obtaining the symmetry labels for the vibrations.

BH₃ IR Absorption Spectra

Only 3 peaks are observed despite there being 6 vibrations since one of the vibrations is of zero intensity, whilst two pairs of the remaining 5 are degenerate, having almost identical vibrational frequencies.

Molecular orbitals of BH₃

In this section, the quantitative MOs of BH₃ are to be calculated and then compared with the qualitative MOs of an MO diagram.

Forming a qualitative BH₃ MO diagram

BH₃ adopts a trigonal planar geometry and has the D_3h point group. The z axis coincides with the highest rotation axis, which in this case is the C₃ axis out of the plane of the molecule, which itself is in the (x,y) plane. All of the symmetry elements of the D_3h molecule are shown on the diagram below:

BH₃ symmetry elements

The chemical fragments can be identified as a B and a H₃ fragment. The energy levels and symmetry labels of the fragment orbitals must now be determined, as shown on the MO diagram below:

BH₃ fragment MO diagram

The symmetry labels for the fragment MOs are derived from the D_3h point group tables. The H₃ totally bonding fragment orbital is totally symmetric so has a₁' symmetry. The H₃ degenerate fragment orbitals have e' symmetry, since the first has the same symmetry as the x-axis, which on inspection of the character tables corresponds to e' symmetry. Regarding the central boron atom fragment, the symmetries are determined by considering the symmetry labels of the x,y and z axes. Thus, as drawn above, the p_x and p_y have e' symmetry and the p_z has a₂^,, symmetry. The s atomic orbital, being totally symmetric, has a₁' symmetry. With the H1 sAO present as a reference, one must predict the relative enrergies of the two fragments. B and H are both electropositive and their sAOs will start at roughly the same level, however the all in-phase bonding fragment of the H₃ fragment will experience some stabilisation (this will only be small because of poor orbital overlap due to their spatial separation). The out of phase H₃ interactions will be slightly higher than the lone sAO because of the antibonding component, but not too high again due to the large spatial separation.

Following this, fragment orbitals of the same symmetry must be combined, their bonding/antibonding character estimated and the extent of energy splitting ascertained. The a₁' fragment orbitals will combine and since they are on atoms directly bonded and involve sAOs, the interactions will be large. The e' orbitals will also combine, and the splitting will again be quite large since the interactions are between directly bonded atoms. Finally the a₂^,, p_z AO of boron will remain non-bonding (no H₃ orbitals of this symmetry. The 3 pairs of electrons are then added to give the final MO diagram below.

H₃ MO diagram

LUMO +3 LUMO +3 LUMO +3 LUMO +2 LUMO +2 LUMO +3 LUMO +1 HOMO LUMO +3 LUMO LUMO LUMO +3 HOMO HOMO LUMO +3 HOMO -1 HOMO -1 LUMO +3 HOMO -2 HOMO -2 LUMO +3

There are no significant differences between the qualitative and quantitative MOs produced, with the possible exception of the LUMO +1, which deviates slightly from the qualitative version. Still, the correlation is superb, demonstrating that qualitative MO theory is very useful, since it maintains a high level of accuracy whilst being considerably cheaper than the full quantum mechanical calculation.

Part 2

Ground State Optimised structures of cis and trans Mo(CO)₄(pip)₂

It was decided to compute the ground state optimised structures of cis and trans Mo(CO)₄(pip)₂ (where 'pip' = piperidine, HNC₅H₁₀, since the ligands provide a direct analogue to those investigated in a previous lab.

cis and trans Mo(CO)4(pip)2

Both the cis and trans-isomers were initially drawn and optimised using molecular dynamics within the ChemBio3D utility. A Gaussian Input File was then saved from this program and imported into Gaussview. Initially, I started with the B3LYP method and the low level LANL2MB to provide an initial optimization (with a specified loose convergence as per instruction).

LANL2MB Optimised structure summary

cis Mo(CO)4(pip)2 Calculation Type FOPT Calculation Method RB3LYP Basis Set LANL2MB Total Energy / a.u. -1011.4289 (4 d.p.) Dipole Moment / D 1.9645 C=O bond lengths (trans to pip) / Å 1.19754, 1.19755 C=O bond lengths (trans to C=O) / Å 1.20047, 1.20053 Mo-N bond lengths / Å 2.03328 and 2.03423 Ring C-N bond lengths / Å 1.51809, 1.51801, 1.51721, 1.51732 trans Mo(CO)4(pip)2 Calculation Type FOPT Calculation Method RB3LYP Basis Set LANL2MB Total Energy / a.u. -1011.4313 (4 d.p.) Dipole Moment / D 0.0302 C=O bond lengths / Å 1.20002, 1.19866, 1.19961, 1.19755 Mo-N bond lengths / Å 2.05934, 2.06195 Ring C-N bond lengths / Å 1.52146, 1.51815, 1.52044, 1.52116

The weakness/ low accuracy of this method is evident in the discrepancies between bonds that one would expect to be of equal length.

LANL2DZ Optimised structure summary

Cis Mo(CO)₄(pip)₂ Unique Identifier & Trans Mo(CO)₄(pip)₂ Unique Identifier

cis Mo(CO)4(pip)2 Calculation Type FOPT Calculation Method RB3LYP Basis Set LANL2DZ Total Energy / a.u. -1023.3739 (4 d.p.) Dipole Moment / D 4.0180 C=O bond lengths (trans to pip) / Å 1.17806, 1.17807 C=O bond lengths (trans to C=O) / Å 1.18227, 1.18223 Mo-N bond lengths / Å 2.05522, 2.05547 Ring C-N bond lengths / Å 1.48917, 1.48827, 1.48831, 1.48913 trans Mo(CO)4(pip)2 Calculation Type FOPT Calculation Method RB3LYP Basis Set LANL2DZ Total Energy / a.u. -1023.3713 Dipole Moment / D 0.0008 C=O bond lengths / Å 2 x 1.17865, 2 x 1.17868 Mo-N bond lengths / Å 2.06804, 2.06800 Ring C-N bond lengths / Å 2 x 1.48689, 2 x 1.48691

At first glance this calculation is indeed more accurate since equivalent bonds have lengths of increasing similarity, and the dipole moment of the trans structure is beginning to converge to 0 as one would have expected for this molecule. In addition, and more importantly, the overall energy of the molecule is considerably lower for this calculation thus has improved geometry.

The calculated Mo-N value compares well with the average literature value of 2.266 Å. As do the C-N bond lengths in the piperidine unit, which become closer to the literature value of 1.455 Å, on performing the higher level calculation. The point being that these bond lengths are of the correct order, suggesting that the results of the calculations are solid.

Below are the cis and trans Mo(CO)₄(pip)₂ spectra along with cropped fully assigned versions for the CO stretches present in each. Evidently there are 4 observed stretching frequencies for the cis isomer and 3 (although one of these is of very low intensity) for the trans isomer. This is because the fully symmetric vibration of the trans isomer occurring at 2001.82 cm^-1 does not involve a change in dipole moment (unlike for the cis isomer), hence it is not observed.

Cis Mo(CO)₄(pip)₂ Frequency Analysis Identifier & Trans Mo(CO)₄(pip)₂ Frequency Analysis Identifier

cis Mo(CO)4(pip)2	cis Mo(CO)4(pip)2 CO ν's	trans Mo(CO)4(pip)2	trans Mo(CO)4(pip)2 CO ν's

The experimental CO vibrational frequencies (all cm ^-1 for the cis isomer are 1839.76, 1889.90, 1908.04, 2011.40., calculated 1847.6, 1907.81, 1928.82, 1992.37. Considering these experimental values are my own, there is remarkable correlation between them and the calculated values, again showing the accuracy of the computational techniques employed.

On employing the LANL2DZ method, the cis isomer has an energy of -1023.37390868 a.u. whilst the trans isomer has an energy of -1023.37138603 a.u.. Evidently the cis isomer is more stable, by 2.52265x10^-3 a.u..

cis Mo(CO)4(pip)2	trans Mo(CO)4(pip)2
notitle	notitle

Part 3

NH₃ Symmetry

To start with, an NH₃ molecule was created in Gaussview and its geometry optimised using a 6-31G basis set and the B3LYP method. A summary of the calculation has been included in the table titled NH₃.

NH3 NH3 C3v File Type .log Calculation Type FOPT Calculation Method RB3LYP Basis Set 6-31G Energy / a.u. -56.53188590 Dipole Moment / D 1.3238 Point Group C3v Job Time 33.0 s NH3 Long Bond NH3 C1 File Type .log Calculation Type FOPT Calculation Method RB3LYP Basis Set 6-31G Energy / a.u. -56.53188656 Dipole Moment / D 1.3258 Point Group C1 Job Time 17.0 s NH3 D3h Symmetry NH3 D3h File Type .log Calculation Type FOPT Calculation Method RB3LYP Basis Set 6-31G Energy / a.u. -56.53154189 Dipole Moment / D 0.0000 Point Group D3h Job Time 1m 28.0 s

The symmetry has influenced the final structure obtained in that the first two conformations adopt a trigonal pyramidal geometry whilst the third has a trigonal planar geometry, as shown by the images above. In addition, it is clear that the more symmetrical a molecule (i.e. the greater the number of symmetry operations) the longer it takes to optimize the geometry, with the C_3v geometry taking twice as long as the C₁ to complete and the D_3h taking over twice as long again compared with the C_3v. This is not what I would have expected, as I would have assumed that the more symmetric a molecule the fewer combinations need be calculated / the more quickly a minimum in the PES would be reached. Evidently this is not the case and the greater the level of symmetry the more complex the MO calculations. Thinking of it from this perspective makes more sense in that there are a greater number of symmetry operations that may need to be computed.

The lowest energy geometry is in fact the NH₃ C₁ structure, which has an energy of -56.53188656 a.u.. The next lowest energy structure is that of the typical C_3v NH₃ which has an energy 1.73282990x10^-3 kJ mol^-1 higher than the C_3v structure. The highest energy D_3h structure has an energy 0.90493103 kJ mol^-1 higher than the lowest energy structure. The significance of the difference of these two (subsequent) energies is that it corresponds to the barrier height to inversion. It should be noted that about 1 kJ mol^-1 seems a pretty low energy for this inversion process, with thermal energy at room temperature being over double this (RT≈2.5kJ mol^-1).

NH₃ using different methods

6-311+G(d,p) basis set, MP2 method

NH3 NH3 C3v File Type .log Calculation Type FOPT Calculation Method RMP2-FU Basis Set 6-311+G(d,p) Energy / a.u. -56.43444511 Dipole Moment / D 1.7874 Point Group C3v Job Time 33.0 s NH3 Long Bond NH3 C1 File Type .log Calculation Type FOPT Calculation Method RMP2-FU Basis Set 6-311+G(d,p) Energy / a.u. -56.43444477 Dipole Moment / D 1.7878 Point Group C1 Job Time 33.0 s NH3 D3h Symmetry NH3 D3h File Type .log Calculation Type FOPT Calculation Method RMP2-FU Basis Set 6-311+G(d,p) Energy / a.u. -56.42664911 Dipole Moment / D 0.0000 Point Group D3h Job Time 1 m 41 s

It should be noted that these calculations did not take very much longer than those at a lower level (most likely due to the simplicity of the molecule), with the C₁ geometry taking about twice as long and the D_3h structure only taking ≈15% longer to complete.

In this case, the barrier height to inversion is 20.46839681 kJ mol^-1. Evidently, this energy is substantially larger than that calculated by the previous lower level calculations, which was over an order of magnitude less. Crucially, the energy barrier of the MP2/6-311+G(d,p) method compares much more favourably with the experimental value of 24.3 kJ mol^-1, demonstrating that the higher level calculation is indeed more accurate.

NH₃ the inversion mechanism

NH3 Inversion

Having optimised the ground state for NH3 under both C3v and D3h symmetry, it remains for them to be connected on a reaction pathway. This is done by allowing the coordinates of the hydrogen atoms to vary in an umbrella motion. The details of the calculations to do this are not included here, but the resulting animation showing half of the inversion process is shown to the left. It should be noted that frame 12 (of 21) on transitioning from D3h to C3v geometry, corresponds to the lowest energy point on the potential energy surface.

NH₃ vibrational analysis

A frequency analysis was undertaken for the optimised B3YLP/6-31G C_3v and D_3h structures. From this, the vibrational frequencies along with their infrared spectroscopy intensities and IR spectra have been given below.

NH3 C3v Vibrations Frequency / cm-1 IR intensity 452.302 599.472 1680.47 41.7256 1680.47 41.7245 3575.43 0.0688 3775.76 7.0892 3775.76 7.0884 NH3 D3h Vibrations Frequency / cm-1 IR intensity -318.051 849.113 1640.59 55.9828 1640.59 55.9805 3635.71 0 3854.27 19.5951 3854.27 19.5963

There are six positive frequencies for the C_3v geometry and five for the D_3h geometry.

NH₃ C_3v and D_3h vibrational modes

The following vibrational modes for the NH₃ C_3v and D_3h geometries have been arranged such that the vibrational modes with the same character of motion are aligned:

NH3 C3v Vibrations Frequency / cm-1 Mode 452.302 1680.47 1680.47 3575.43 3775.76 3775.76 NH3 D3h Vibrations Frequency / cm-1 Mode -318.051 1640.59 1640.59 3635.71 3854.27 3854.27

The worst correlation with experimental values for the C_3v system is for the calculated peak at 452.302 cm^-1 for which the experimental value is 949.83 cm^-1. This discrepancy may be due to the fact that NH₃ can invert via electron tunneling which may not be taken into account in the calculation of the vibrational frequency corresponding to this inversion (at 452.302 cm^-1 and -318.051 cm^-1 for the D_3h system. The remaining frequencies and the experimental equivalents are given below for comparison.

Calculated Frequency / cm-1 Experimental Frequency / cm-1 1680.47 (degenerate) 1627.5 3575.43 3336.7 3775.76 (degenerate) 3414.00

Mini Project

Prologue

1,2-Disilabenzenes

Initially, the plan was to investigate two isomers from Dr David Scheschkewitz's notes on Advanced Main Group Chemistry, which are the 1,2-Disilabenzene structures, given above. These two structures were constructed using ChemBio3D, and optimised using molecular dynamics with a number of manipulations of the geometry. They were then imported into Gaussview and optimised using the B3LYP method and a 3-21G basis set to get the rough geometry right, which took about 6 hours for each. Only to realise on downloading the .chk files, that I had incorrectly constructed the two isomers (missing off 4 trimethylsilyl groups) :-(. Cis 1,2-Disilabenzene (wrong) Unique Identifier & Trans 1,2-Disilabenzene (wrong) Unique Identifier

Where it went wrong

trans 1,2- disilabenzene LUMO-2

Thus, the calculations were re-run, only now it would appear that I underestimated the amount of time these calculations would take. I received the trans isomer back after over 33 hours and am still waiting for the cis isomer (note: this was killed after 3 days). My intention was to optimise these two structures to a fairly high level (B3LYP and 6-31G(d) or MP2 and 6-311G(d,p)), evaluate the relative energies to see which was the more stable isomer, and analyse the molecular orbitals to gain an understanding of the cycloadditional formation. Trans 1,2-Disilabenzene Unique Identifier.

(Note: I calculated the MOs for the low level calculation of the trans isomer. Rendering each molecular orbital takes about 4 minutes to perform on the hp laptops provided..)

This was then to be compared with the literature yields of the two isomers. Followed by an analysis of the mechanism of the reaction to establish whether the formation was under kinetic or thermodynamic control and evaluate the spectra (specifically ¹³C NMR) of these compounds to see if the compounds reported in the paper are indeed correct (since the authors seem somewhat unsure of the latter stages of the addition).

Consequently, due to the excessive computing power/time needed to accomplish this, an alternative project was sought (whilst the aforementioned effort seems somewhat pertinent to mention):

Hexamethyl tungsten, W(CH₃)₆

Introduction

W(CH3)6

This project (hopefully) brings together three inorganic courses: Mimi Hii's 1st Year "Coordination Chemistry", George Britovsek's 2nd Year "Transition Metal Coordination and Organometallic Chemistry", and this Inorganic Computational lab.

Hexamethyl tungsten, W(CH₃)₆ is a red crystalline solid which was first reported to be synthesised by Wilkinson (of Imperial College) in 1973. At this time, Wilkinson concluded that the IR spectrum and photoelectron spectrum were consistent with the structure being of octahedral geometry. In 1998 the crystal structure was determined by Seppelt et al, and it was in fact confirmed that the structure adopts a C_3v / C₃ geometry (i.e. a distorted D_3h) due to the Jahn-Teller Effect. This is achieved by the opening of one of the groups of 3 methyls, with wider C-W-C angles and shorter C-W lengths, and vice versa for the other group of 3 methyls.

The purpose of this investigation is firstly to establish whether or not the computational methods employed in this lab can be used to correctly predict the deviation away from the previously expected O_h geometry of W(CO)₆. If successful, the predicted geometric parameters will be compared with those from the recent crystal structure determination, to ascertain if the contraction / opening of the methyl groups along with the longer / shorter C-W bond lengths is seen. A comparison with an alternative reported computational method which predicts a C₃ geometry, with rotation of the methyl groups removing the C_3v symmetry, will also be considered. Following this, the molecular orbitals and their corresponding energies will be calculated.

Method/Results

Initially, the molecule was constructed in Gaussview, then it was optimized using the B3LYP method, a LANL2MB basis set with loose convergence criteria ("opt=loose" was included in the first line of the Gaussian input file). A summary of the results from this calculation are included below (left). W(CH₃)₆ Opt. 1 Unique Identifier

LANL2MB pseudo-potential File Type .fch Calculation Type FOPT Calculation Method RB3LYP Basis Set LANL2MB Total Energy / a.u. -304.24851536 Dipole Moment / D 1.0274 LANL2DZ pseudo-potential File Type .fch Calculation Type FOPT Calculation Method RB3LYP Basis Set LANL2DZ Total Energy / a.u. -307.17882323 Dipole Moment / D 1.1559 Point Group C3 LANL2MB pseudo-potential W - C1 / Å 2.23596 W - C2 / Å 2.23615 W - C3 / Å 2.23588 W - C4 / Å 2.15155 W - C5 / Å 2.15190 W - C6 / Å 2.15152 C1-W-C2 / ° 74.305 C2-W-C3 / ° 74.072 C3-W-C1 / ° 74.000 C4-W-C5 / ° 97.709 C5-W-C6 / ° 97.941 C6-W-C4 / ° 98.353 LANL2DZ pseudo-potential W - C1 / Å 2.19538 W - C2 / Å 2.19578 W - C3 / Å 2.19526 W - C4 / Å 2.13892 W - C5 / Å 2.13869 W - C6 / Å 2.13890 C1-W-C2 / ° 76.808 C2-W-C3 / ° 76.832 C3-W-C1 / ° 76.867 C4-W-C5 / ° 93.784 C5-W-C6 / ° 93.742 C6-W-C4 / ° 93.617

This is very cool. Straight away, what took almost two decades to realize has been demonstrated in the couple of hours taken to run these calculations. For the LANL2MB pseudo-potential there are clearly three methyl groups with shorter bond lengths (2.15166Å avg.) and wider C-W-C angles (98.001° avg.), whilst the other three have longer bond lengths (2.23600Å avg.) and reduced C-W-C angles (74.126° avg.). This shows that the deviation away from an octahedral geometry is pretty substantial, where the C-W-C angles would be ≈90°. This is shown graphically by the image below left.

Contraction of some, expansion of others

W(CH3)6 notitle

To improve the accuracy of the calculation and to prove that these results are not an anomalous consequence of the basis set used, the better LANL2DZ pseudo-potential and basis sets were applied, with increased electronic convergence by specifying "int=ultrafine scf=conver=9" in the first line of the Gaussian Input File, along with "pop=full" which switches on the MO analysis (for later on) W(CH₃)₆ Opt. 2 Unique Identifier. There are two key points to note from this second optimization. Firstly, a more stable structure has been obtained since it has a lower energy by 2.9303 a.u. (4 d.p.), showing the improved accuracy of this calculation. The second, and most important, is that the geometrical prediction of the LANL2MB pseudo-potential is confirmed, although the distortion away from D_3h geometry becomes slightly less pronounced. All of the C-W bond length are shortened (relative to the LANL2MB pseudo-potential), whilst the variation for C-W bonds of similar length is diminished (short C-W bond avg.=2.13884Å, long C-W bond avg.=2.19547Å).

The smaller C-W-C bond angles become slightly larger (76.836°), whilst the larger C-W-C bond angles are notably smaller (93.714° avg.). Ok, so the second set of results are almost certainly more accurate due to the lower total energy of the molecule and the reduced range of bond lengths and angles which one would expect to be similar.

It is therefore apparent that a deviation away from D_3h geometry occurs, with a contraction of three methyl groups and an expansion of the other three in the aforementioned manner. In addition, these calculations predict a C₃ rather than a C_3v geometry which does not agree with the results of crystallography, but does agree with other computational calculations.

Taking it further

The literature calculations predict a small rotation of "a few degrees" of the methyl groups, retaining C₃ symmetry. This is indeed what I observed in my calculations as given by the image below. The exact value of the rotation of the methyl group has also been included here:

Rotation of the methyl groups Rotation of C1 methyl group 5.638° Rotation of C2 methyl group 5.666° Rotation of C3 methyl group 5.750° Rotation of C4 methyl group 6.687° Rotation of C5 methyl group 6.904° Rotation of C6 methyl group 6.960°

In the table on the left, the labels for the carbon atoms correspond to those used in giving the bond angles and lengths. Here I thought I should mention how I calculated the CH3 group rotations that were not included in the literature. Referring to the figure (right), for each methyl group, the difference in the absolute values of the a→b→c→d, a→b→c→e dihedral angles was calculated, then multiplied by a factor of 0.5. Interestingly, the methyl groups with shorter C-W lengths and wider C-W-C angles show a larger rotation angle of the methyl groups, breaking C3v geometry, than the other group of 3 methyls.

Methyl Rotations

Comparison with the literature

Note, there are two sets of values for the experimental values since there are two polymorphs of the structure.

Geometric Parameter Experimental Data (1) Experimental Data (2) Literature Calculated LANL2DZ Calculated C-W short / Å 2.107 2.096 2.147 2.139 C-W long / Å 2.194 2.180 2.209 2.195 Large C-W-C angle / ° 96.97 94.70 95.6 93.71 Small C-W-C angle / ° 76.00 75.73 75.6 76.84

The values calculated here compare extremely well with the literature. The bond lengths calculated agree with experimental data more strongly than those calculated by the alternative method, although the bond angles do not. Regardless, it's safe to say that the calculations performed here are along the right lines, and greater understanding/ use of better methods/basis sets may yet improve the results obtained here. It pertains that experimentally, the rotation of the methyls, removing C_3v symmetry, is not as observable as in the geometry obtained via calculation. The rotation of the methyls has been tentatively attributed to weak agostic bonding. If this is indeed the case then the stronger the agostic interaction, the lower the bond order of the C-H bond and thus the longer the bond will become. So one would expect that the methyls that are rotated by a greater angle are subject to stronger agostic bonding and would therefore have longer C-H bonds.

The average C-H bond length for the methyls that suffer less rotation is 1.09837Å. The average C-H bond length for those methyls subject to greater rotation is 1.10009Å. :-) This is pretty good evidence that at least from the calculated geometry, agostic bonding is indeed the cause of the methyl group rotation. Ok so the bonds are only 0.2% longer, but this agostic bonding has been prescribed as weak, and the methyl groups undergoing greater rotation only do so by ≈1°.

Molecular orbitals

Molecular Orbital LANL2DZ Energy / eV LUMO + 2 -1.570 LUMO + 1 -1.570 LUMO -2.358 HOMO -6.599 HOMO - 1 -7.256

If time had permitted I would have furthered this aspect of my project by constructing a qualitative MO diagram with the corresponding cartoon MOs and compared them with the calculated results displayed above, to further evaluate the usefulness of such qualitative methods. Evidently from the complexity of the orbitals, this qualitative diagram is not particularly trivial and unfortunately the time cannot be spared to carry out this analysis.

Acknowledgements / Comments

All images have been produced by myself using a combination of ChemBio3D, Gaussview, Microsoft Paint, ChemDraw Ultra, MarvinView, Adobe Fireworks CS4 and QuteMol. Although effectively in the public domain, it is humbly requested that their use/reproduction be done so via contact (email:rob@gynx.org).