Shapes and Thermodynamic Stabilities of E(CH3)4 Compounds (E

Colin J. Marsden, and Bruce A. Smart. Organometallics , 1995, 14 (11), pp 5399–5409. DOI: 10.1021/om00011a067. Publication Date: November 1995...
0 downloads 0 Views 1MB Size
Download PDF
Organometallics 1996, 14, 5399-5409

5399

Shapes and Thermodynamic Stabilities of E(CH& Compounds (E= S, Se, Te) Colin J. Marsden” Laboratoire de Physique Quantique, URA 505 du CNRS, Universitk Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France

Bruce A. Smart School of Chemistry, The University of Melbourne, Parkville, Victoria 3052, Australia Received October 26, 1994t@ We report a systematic ab initio computational study, using a carefully graded range of basis sets with full geometry optimization a t both SCF and MP2 levels of theory, of the structures, isomerism, binding energies and vibrational frequencies of E(CH3)4 compounds (E = S, Se, Te). Some higher-level calculations were also undertaken at MP2 geometries. The related dimethyl compounds have also been studied to indicate the accuracy which should be achieved in our calculations for the tetramethyl compounds, which are as yet unknown for E = S or Se. The equilibrium molecular structure of each tetramethyl compound is based on a trigonal bipyramid, with an equatorial lone pair (CZ,symmetry). Inter-methyl repulsions have significant structural effects for the S derivative, but these are progressively less important for the Se and Te species. All E(CH& compounds are fluxional, especially the Te system; barriers to Berry pseudorotation are estimated to be about 20,15,and 3 kJ/mol for the S, Se, and Te tetramethyl. The low-frequency vibrational spectra for Te(CH3)4 have been satisfactorily assigned and provide no evidence for the coexistence of CZ,and C4uisomers. All E(CH3)4 compounds are thermodynamically unstable with respect to (E(CH3)z ethane), but the instability decreases with the size of the central atom; estimated binding energies are about -350, -300, or -225 kJ/mol for E = S, Se, or Te. The influence which d-type orbitals on E have on the stability of the tetramethyls is discussed. As the Te compound has recently been prepared, the S and Se derivatives seem possible but difficult synthetic targets .

+

Introduction There has been substantial interest in “hypervalent” compounds (those which violate the octet rule) of group 16 (Group VI) elements for some time, since they pose intriguing questions about b0nding.l Derivatives of S(W)and S(VI) are, in general, stable only if highly electronegative substituents such as 0 or F are bonded to S. Thus SF4, SF6, so3, etc., are known compounds, but SH4, S(CH3)4, or SHs are not. There has been extensive debate about the contribution made by d-type orbitals on S t o the bonding in hypervalent compounds. While compounds of Se and Te in high oxidation states tend to be more stable than their S counterparts (for example, TeC14 is thermally stable to at least 400 “C, whereas sc4 decomposes above -30 “C ), the successful preparation of Te(CH3)4, by reduction of TeC14 with methyllithium, has been achieved only relatively re~ e n t l y .The ~ compound was characterized by NMR and vibrational spectroscopies. Compounds of the type ER4, where E is an element of the chalcogen group such as S, Se, or Te, almost invariably have a structure derived from a slightly Delayed publication due to loss of revised manuscript in the mail. @Abstractpublished in Advance ACS Abstracts, October 1, 1995. 1993, 115, (1) See, for example: Magnusson, E. J . Am. Chem. SOC. 1051 and references therein. (2) See, for example: Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry; Wiley-Interscience: New York, 1988; p513. (3)Gedridge, R. W., Jr.; Harris, D. C.; Higa, K. T.; Nissan, R. A. Organometallics 1989, 8, 2817.

distorted trigonal bipyramid, in which one equatorial position is occupied by a lone pair to give Czusymmetry. This is the structure predicted by the VSEPR rules,4 which have an impressive record of success in maingroup structural chemistry. In the case of Te(CH3)4, however, the 13C NMR spectra at room temperature displayed only a single peak,3which stays single down to -90 “C, presumably because the compound is fluxional, with equatorial and axial CH3 groups interchanging rapidly by the process known as Berry pseudorotat i ~ n However, .~ such a spectrum would also be compatible with a square-pyramidal structure of C4usymmetry. The vibrational spectra of Te(CH3)4 were not assigned in detail, but it was suggested that the large number of peaks in the low-frequency region could indicate that both square-pyramidal and trigonal-bipyramidal isomers coexist. A few years ago, such a suggestion would probably have been regarded as far-fetched, but the work of Seppelt has shown that five-coordinatebismuth systems adopt both square-pyramidal and trigonalbipyramidal geometries? In conjunction with the squarepyramidal structures found for InC15- and Sb(c~Hg)5,~ Seppelt’s results imply that heavy elements favor the

+

(4) Gillespie, R. J.; Hargittai, I. The VSEPR Model of Molecular Geometry;Allyn and Bacon: Boston, MA, 1991. 15) Berry, R. S. J . Chem. Phys. 1960,32, 933. ( 8 ) Schmuck, A.; Seppelt, K. Chem. Ber. 1989, 122, 803. (7) Brown, D. S.; Einstein, F. W. B.; Tuck, D. G. Inorg. Chem. 1960, 8, 14. (8)Wheatley, P. J. J . Chem. SOC. 1964, 3718.

0276-733319512314-5399$09.00/0 0 1995 American Chemical Society

5400

Organometallics, Vol. 14, No. 11, 1995

C4u structures more than do lighter ones. Gedridge's suggestion for Te(CH3)4 must therefore be taken seriously. Since experimental data had not been able to provide unequivocal results concerning the molecular structure of Te(CHd4, we decided that a theoretical study would be worthwhile. The techniques of computational quantum chemistry are now sufficiently refined to be able t o yield reliable data on the structures, vibrational frequencies, and binding energies of small molecule^.^ We decided that a parallel study of the related compounds S(CH3)4 and Se(CH3)4would be valuable, even though these have not yet been prepared. The comparison of their binding energies with that calculated for Te(CH3)4 would be of considerable interest. Moreover, as CdUstructures have been predicted for SH4, SeH4, and TeH4,I0it cannot be assumed with certainty that CaUstructures will be adopted by the tetramethyl derivatives. We are not aware of any theoretical study of these compounds published before the recent paper by Fowler and Schaefer, which appeared just after the submission of the original version of our own work." They also examined the three E(CH3)4 compounds (E = S, Se, and Te) which are the subject of our own work, using computational methods. Their results, which are broadly similar to our own, will be compared with ours at appropriate places in the text. We predict that all three tetramethyl derivatives adopt trigonal-bipyramidal structures of CzVsymmetry, that all are thermodynamically unstable with respect to (E(CH& CzHs), by about 350,280 and 200 kJ/mol for E = S, Se, Te, respectively, but that all are local minima on their potential energy surfaces. All three molecules are fluxional, but there are important differences in behavior between Te and the other group 16 elements. The bariers to pseudorotation are found to be about 20 or 15 kJ/mol for E = S or Se but as little as 3 kJ/mol for Te(CH3)d. Independently of our work, two other groups of structural chemists also decided that the intriguing problems posed by tetramethyltellurium merited further attention. The compound has very recently been studied in the solid phase by X-ray diffraction and in the gas phase by electron diffraction; a preliminary account of these studies has already appeared.12 The essential features of the results obtained by all three groups are closely similar, so there can now be no doubt that a C2" structure is preferred for tetramethyltellurium.

+

Theoretical Methods We have employed a carefully graded range of both allelectron and pseudopotential basis sets in this work. Since the computational cost of performing SCF calculations rises roughly as the fourth power of the number of electrons, while the factor for the more reliable correlated calculations involves the fifth or even sixth power, it was not feasible for us to use (9) See, for example: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; J. Wiley & Sons: New York, 1986. (10) (a)Yoshioka, Y.; Goddard, J. D.; Schaeffer, H. F., 111. J.Chem. Phys. 1981, 74, 1855. (b) Moc, J.; Dorigo, A. E.; Morokuma, K. Chem. Phys. Lett. 1993, 204, 65. (c) Marsden, C. J.; Smart, B. A. Aust. J.

Chem. 1994,47, 1431. (11)Fowler, J. E.; Schaefer, H. F., 111. J. Am. Chem. SOC.1994, 116, 9596.

(12)Blake, A. J.; Pulham, C. R.; Greene, T. M.; Downs, A. J.; Haaland, A.; Verne, H. P.; Volden, H. V.; Marsden, C. J.; Smart, B. A.

J . A m . Chem. SOC.1994,116,6043.

Marsden and Smart all-electron basis sets for the tellurium-containing molecules. We wished to show that our calculated results are not especially sensitive to the size of basis set and to establish that pseudopotential methods are reliable for this class of compound, by comparing all-electron and pseudopotential results for the S and Se derivatives, where both styles of calculation were feasible. The Gaussian series of programs13J4 was used for all the calculations in this work, which were performed in Melbourne, Australia. Geometries were optimized using gradient methods and vibrational frequencies were calculated either from analytical second derivatives or numerically from first derivatives, at both SCF and MP2 levels of theory. A few calculations were undertaken using more elaborate correlation treatments (MP4SDQ, QCISD, and QCISD(T)) a t MP2 geometries. Calculations were performed on all of the molecules considered in this work using the pseudopotential basis sets of Hay and Wadt15 (hereinafter referred to as PS). These bases were supplemented first with a single d-type function on the central atom with exponents of 0.6 for S, 0.38 for Se and 0.3 for Te, to give the PS(P) set, and then with a single d-type function on the carbon atoms (exponent 0.75) to give the PSP basis. The five spherical-harmonic components of d-type functions were adopted. No p-type functions were used on hydrogen with pseudopotential bases. The sulfur compounds were investigated using several standard all-electron basis sets,ranging in size from 3-21G* 16~17 through DZPIs and DZP* t o valence triple-5; (TZP); the latter comprised 6-311G* or 6-311G bases for C or HI9 and a 12s9pl 6s5p set for d-type polarization functions were added to S and C atoms in the DZP and TZP bases, with exponents of 0.532 and 0.75, respectively. In a few cases, a larger TZ(2)P basis was used, which differs from TZP in having two sets of d functions on S, whose exponents are 1.1and 0.35. For the DZP* basis we also added p-type functions to the hydrogen atoms (exponent 1.0). All-electron calculations were performed on the selenium compounds using a DZ(P)-style set. The Se basis was of the form 14sllp6d&6p3d, as proposed by Dunning.21 This contraction is a little more flexible than that used by Fowler and Schaefer, which was 7s5p3d,11and as a result our total energy of Se(CH& is lower than theirs by nearly 20 kJ/mol. An additional d-type function was added to allow for polarization effects, the exponent of 0.38 being adopted from the optimized value found with the pseudopotential basis. Standard double-5; basesI8 were used for the carbon and hydrogen atoms.

Results and Discussion (a) E(CH&. In order to obtain binding energies for the tetramethyl molecules, we needed calculated energies for their dimethyl analogues. Since these species are well characterized, our results for these molecules (13)Gaussian 86. Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Khan, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.;Fleuder, E. M.; Pople, J. A. CarnegieMellon Quantum Chemistry Publishing Unit, Pittsburgh, PA, 1984. (14) Gaussian 90, Revision F. Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. Gaussian Inc., Pittsburgh, PA, 1990. (15) Wadt, W. R.; Hay, P. J. J . Chem. Phys. 1986, 82, 284. (16) Binkley, J. S.; Pople, J. A,; Hehre, W. J. J. Am. Chem. SOC.1980, 102, 939. (17) Pietro, W. J.;Francl, M. M.; Hehre, W. J.; Defrees, D. J.; Pople, J. A.;. Binkley, J. S. J.Am. Chem. SOC. 1982, 104, 5039. (18) Dunning, T. H., Jr.; Hay, P. J. Modern Theoretical Chemistry; Plenum: New York, 1976; pp 1-28. (19) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J . Chem. Phys. 1980, 72, 650. (20) McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980, 72,5639. (21) Dunning, T. H., Jr. J . Chem. Phys. 1977, 66, 1382.

E(CHd4 Compounds

Organometallics, Vol. 14, No. 11, 1995 5401

Table 1. Structural Parameters and Energies Calculated for S(CHs)f 3-21G* DZP

SCF SCF MP2 TZP SCF MP2 PS SCF MP2 PS(P) SCF MP2 PSP SCF MP2 exptP

-474.456 985 -476.739063 -477.222 489 -476.771 822 -477.339 021 -89.078447 5 -89.307 578 -89.112 733 -89.410 713 -89.145731 -89.527 500

1.813 1.812 1.814 1.809 1.803 1.864 1.894 1.809 1.827 1.801 1.808 1.802(2)

1.082 99.5 1.083 99.8 1.097 98.3 1.081 100.0 1.091 98.6 1.079 100.2 1.101 98.4 1.082 100.1 1.103 98.8 1.082 99.9 1.095 98.6 1.091(5) 98.9(2)

a Bond lengths in 8, bond angles in deg, energies in hartree. Reference 22, with uncertainties in parentheses.

serve to calibrate the accuracy which should be achieved for the structures and vibrational frequencies predicted for the tetramethyl systems. Fowler and Schaefer did not present results for these molecules.ll Our results for the principal structural parameters of dimethyl sulfide are presented in Table 1,together with experimental data for comparison. Czv molecular symmetry was assumed. The molecular geometry of dimethyl sulfide was predicted with satisfying accuracy at both the SCF and MP2 levels of theory, with all bases except the simplest (PS, which lacked any polarization functions). The PSP basis predicted geometrical parameters to within 1.5% a t both the SCF and MP2 levels. The S-C bond length was found to be 1.801A (SCF) or 1.808 A (MP2) compared to the experimental value of 1.802(2)A.22 The most pleasing results were obtained using the TZP basis at the MP2 level, where the two bond lengths were predicted to lie within the experimental uncertainties, while the C-S-C angle lay outside that uncertainty by only 0.1". When making these comparisons, it should be appreciated that the experimental structural parameters are vibrational averages, while the computed results are equilibrium values, so exact agreement between the two sets should not be expected; we may anticipate that equilibrium bond lengths will be slightly shorter than thermal-average values, by a few thousandths of an A, but that equilibrium bond angles should be very similar to vibrationally averaged quantities for the E(CH3)z molecules under consideration here. The vibrational frequencies for S(CH3)z were also calculated. Many of the vibrational motions for E(CH3)2 and E(CH3)4 molecules are of course internal to the methyl groups and are thus of limited interest t o the general reader. They may be obtained from either author on request. Our results for the skeletal modes are presented in Table 2, together with the torsional vibrations, since these are a t low frequency and could conceivably be confused with bending motions in some cases. The experimental results obtained by Allkins and Hendraz3 and by Durig et aLz4 are also displayed in Table 2. We have attempted to correlate the experimentally observed W a n and infrared spectra with our calculated values, from reported infrared intensities and frequencies. It is difficult to classify bands in certain (22) Pierce, L.; Hayashi, M. J. Chem. Phys. 1961,35, 479. (23) Allkins, J.; Hendra, P. J. Spectrochim. Acta 1966,22, 2075. (24) Durig, J. R.; Player, C. M., Jr.; Bragin, J.; Li, Y. S. J . Chem. Phys. 1971,55, 2895.

crowded regions of the spectra, and we do not claim that our assignments are unequivocal. Most basis sets provided at least reasonably good estimates for each of the 21 vibrational mo+s, with the PS(P) basis set at the MP2 level of theory proving most accurate overall, while the DZP and TZP bases at the same level of theory are also very satisfactory. The nonpolarized PS basis was, however, significantly less reliable than the others. In general, frequencies were overestimated by between 3% and 4% using the better basis sets when secondorder Mdler-Plesset perturbation theory was used. SCF values were found t o be overestimated by about 7% to 8%. Systematic errors of this magnitude are quite t y p i ~ a l .It~may appear from Table 2 that the frequencies calculated for the torsional modes are less accurate than for the others, as they are apparently underestimated by as much as 60 cm-l, or 25% of the value reported. However, it should be noted that the experimental measurements were obtained from the solid phase,24and it seems quite possible for intermolecular interactions to provide an additional restriction on torsional motion in the solid, leading to a higher frequency than that which would be observed in the gas phase. It is also possible, as suggested by a reviewer, that the anharmonicity correction is positive, rather than negative as usually found, i.e. that the representation of the real torsional potential as a cosine function which is then approximated as a harmonic function is inadequate. These structural and vibrational results for S(CH3h show the following desirable features: the experimental results are well reproduced, provided that the basis contains polarization functions on the central atom; further improvement of the basis beyond PS(P) or DZ(P)quality has only marginal effects on the geometrical parameters or vibrational frequencies predicted; the performance of the pseudopotential and all-electron bases is almost equivalent; and the influence of electron correlation effects on the structural parameters is only slight. Other E(CH3)2 molecules need not be analyzed in such detail, but the results for the S derivative are in no way exceptional. The molecular geometry and vibrational frequencies for dimethyl selenide were calculated using a smaller number of basis sets than for the corresponding sulfur species, since there was so little variation in the results once the basis contained polarization functions on S. Our structural results are presented in Table 3. Once again the polarized bases give good structural results at both SCF and MP2 levels of theory, with the MP2 values being slightly better. An electron diffraction . ~the ~ experiment performed by Goldish et ~ 1 found selenium-to-carbonbond distance to be 1.977(12)A. The DZ(P) and PS(P) MP2 values of 1.971 and 1.977 A both lie comfortably within the experimental uncertainty, while the PSPIMP2 result of 1.956 is just a little outside it. The study by Goldish et al. also determined the C-Se-C bond angle t o be 98" but with a large uncertainty of 10". Our results suggest that their quoted uncertainty is unnecessarily pessimistic, and we expect that the bond angle lies within the range 95.5-98.5". Our calculated skeletal and torsional vibrational frequencies for Se(CH3)z are reported in Supporting (25)Goldish, E.; Hedberg, K.; Marsh, R. E.; Schomaker, V. J Am. Chem. SOC.1966,77, 2948.

5402 Organometallics, Vol. 14,No. 11, 1995

Marsden and Smart

Table 2. Skeletal and Torsional Vibrational Frequencies for S(CH,&f skeletal motions basis set 3-21G* DZP

theory SCF SCF MP2 SCF MP2 SCF MP2 SCF MP2

TZP PS PS(P)

a1 727 (3.9) 755 (5.4) 736 (3.2) 744 (5.4) 736 (3.3) 692 (4.8) 645 (1.2) 755 (4.2) 710 (3.3) 69 1

exptW4

a1

288 (0.0) 284 (0.1) 274 (0.1) 285 (0.0) 273 (0.1) 269 (0.2) 251 (0.2) 293 (0.1) 275 (0.2) 284

torsional motions bi 1107 (9.0) 1086 (3.5) 1028 (6.9) 1090 (11) 1041 (18) 1105 (10) 1023 (12) 1103 (9.5) 1037 (9.7) 1027

a2 198 (0.0) 191 (0.0) 160 (0.0) 198 (0.0) 181 (0.0) 169 (0.0) 129 (0.0) 188 (0.0) 147 (0.0) 210b

bi 204 (1.3) 197 (1.3) 191 (1.3) 205 (1.1) 196 (1.1) 173 (1.6) 157 (1.1) 200 (1.7) 183 (1.5) 247b

Frequencies in cm-l, infrared intensities in parentheses. Solid-phase experimental data.

Table 3. Structural Parameters and Energies Calculated for Se(CH&" basis theory DZ(PIb SCF MP2 PS SCF MP2 PS(P) SCF MP2 PSP SCF MP2 exptP5

energy -78.938 380 -79.593 061 -88.203638 -88.428 042 -88.226459 -88.516 017 -88.255983 -88.628 270

r(Se-C) 1.950 1.971 1.986 2.013 1.955 1.977 1.952 1.956 1.977 (12)

r(C-H) L(C-Se-C) 1.082 97.9 1.103 96.4 1.080 97.6 1.101 95.9 1.082 97.5 1.103 96.1 1.081 97.5 1.094 95.9 1.094 (ass) 98 (10)

Bond lengths in A, bond angles in degrees, energies in hartree. Energy below -2400 Eh,

Table 4. Structural Parameters and Energies Calculated for Te(CHd2" basis PS

theory SCF MP2 PS(P) SCF MP2 PSP SCF MP2 exptP

energy -87.038229 -87.260 200 -87.051 168 -87.326 746 -87.077749 -87.436 589

r(Te-C) 2.158 2.182 2.143 2.168 2.144 2.148 2.142 (5)

dC-H) L(C-Te-C ) 1.081 95.0 93.8 1.102 95.3 1.083 93.7 1.103 95.2 1.081 93.5 1.095 1.07 (2) 94 (2) Bond lengths in A, bond angles in deg, energies in hartree.

Information Table S1, in the interests of using less journal space, together with the experimental res u l t ~ . Once ~ ~ >again ~ ~ some of the frequencies predicted by the nonpolarized PS basis were underestimated, particularly at the MP2 level of theory. Other bases performed well, with frequencies typically being overestimated by up to 10% at the SCF level, while the errors were reduced t o about 5% with the inclusion of second-order Mgller-Plesset perturbation theory. The calculated frequencies for the torsional modes are again appreciably lower than those measured for the solid.24 Calculations on dimethyl tellurium were performed using pseudopotential basis sets only, and our principal geometrical results are shown in Table 4. An electron diffraction study b Blom et al. reported a Te-C bond length of 2.142(5) which is scarcely distinguishable from our best (PSP)results of 2.144 A (SCF) or 2.148 A (MP2). Addition of a set of d functions to the Te basis produces a shortening of the Te-C distance of only 0.015/0.014A at the SCFIMP2 level, which is noticeably smaller than the comparable changes found for the S-C (0.055/0.067A) and Se-C (0.031/0.036A) bonds. These differences are provocative, since the d functions are

iz6

(26) Blom, R.; Haaland, A,; Seip, R. Acta Chem. Scand. 1983,A37, 595.

expected to act almost wholly as "polarization" rather than "hybridization"functions for these E(CH3)z species, and one might expect the larger, less electronegative Te atom to be more polarizable than the smaller, more electronegative S atom. This comparison of the behaviors of different group 16 elements is considered in more detail below for the tetramethyls. The C-Te-C bond angle was observed to be 94(2)",26which again compares very favorably with our PSP results of 95.2" (SCF) or 93.5" (MP2). Vibrational frequencies were also calculated for Te(CH3)2, and our results for the skeletal and torsional modes may be found in Supporting Information Table S2. They are also available from the authors on request. As was found for the corresponding sulfur and selenium species, the PS basis yielded frequencies which were somewhat unreliable, but again when this basis is supplemented with a single d-function, reasonably accurate predictions of frequencies are obtained. At the SCF level the frequencies were characteristically overestimated by up to 10%compared to the values reported by Allkins and HendraZ3and by Durig et ~ l .but , with ~ ~ the introduction of second-order Mgller-Plesset perturbation theory these errors were reduced to about 5%, a value which seems to be characteristic of this type of compound at this level of theory. However, the frequencies calculated for the torsional modes once again are substantially lower than the single experimental observation made on the solid phase. E(CH&. Two basic structural types can be envisaged for EL4 compounds, where E is an element from group 16. The first has CzUsymmetry and may be described as a distorted trigonal bipyramid in which the lone pair on E occupies an equatorial position. In the second structure, which has CdUsymmetry, the four L groups occupy equivalent positions at the base of a square pyramid while the lone pair on E is in the apical position. However, where L is a methyl group, several different conformations are possible within the constraints of either CzUor Cd,, symmetries. Four possible arrangements of the methyl groups were considered for S(CH& with CzU symmetry imposed. They are illustrated in Figure 1as 1-4. In order of increasing energy, after full geometry optimization at the DZPISCF level of theory, they are as follows. (1) Both equatorial and axial methyl groups are staggered with respect to the lone pair: this conformer was found to be a true minimum with all real vibrational frequencies. (2) The equatorial groups are eclipsed but the axial groups staggered: this structure is 11.1 kJ/mol above (1) and has two imaginary vibrational

E(CH& Compounds

Organometallics, Vol. 14, No. 11, 1995 5403 I

pound (see below). The C,-S-C, angle is consistently found to lie between 172 and 175", scarcely different from the angle of 173" found in SF4. Although the CeqS-Ceq angle lies between 110 and 113", with our highest-level prediction being 111.4' (111.6"in the work of Fowler and Schaefer) compared to 101.5"for SF4, a widening of the bond angle should not be unexpected; it is almost certainly due to the bulky nature of the methyl group as compared to fluorine. The closest H- -H distance between equatorial methyl groups is about 2.39 A with the optimum geometrical parameters but would be only about 2.05 8,if the equatorial angle were the same as in SF4. This latter value would result in substantial steric distress, as the sum of the van der Waals radii for two H atoms is usually taken t o be 2.4

.

I

I

A.28

5

6

Figure 1. Different structural forms of S(CH3)4discussed in the text. The predicted equilibrium structure is 1.Pointgroup symmetries are Czv for isomers 1-4, C4" for 5, and C4 for 8. Principal geometrical parameters are indicated. frequencies. (3)The equatorial groups are staggered but the axial groups eclipsed: this arrangement is 39.7 kJ/ mol above (1) and has four imaginary vibrational frequencies. (4) Both equatorial and axial methyl groups are eclipsed with respect to the lone pair: this conformer is 39.9 kJ/mol above (1) and also has four imaginary vibrational frequencies. There are two possible arrangements for the methyl groups for symmetry S(CH314; either all methyl groups are staggered, or all are eclipsed, with respect to the lone pair. No stationary point could be located for the latter, as it reverted spontaneously to the staggered conformer by undergoing an inversion at S. The staggered conformer is illustrated in Figure 1 as 5. Isomers 1 and 5 of tetramethylsulfur were examined with the set of bases adopted for the dimethyl species. Structural results for the Czv isomer 1 are displayed in Table 5. The same symmetry and conformation were found by Fowler and Schaefer.ll The two carbon-tosulfur bond distances are quite different; the axial bonds are consistently longer than the equatorial bonds by a surprisingly large amount (0.228 8,at the highest level of theory used; Fowler and Schaefer report a difference of 0.241 A using DZ(P)/CISD theory). In the isoelectronic compound SF4, the difference between axial and Comparison equatorial bond lengths is only 0.099 of the results in Tables 1 and 5 shows that the equatorial bonds in tetramethylsulfur are scarcely different in length from those in the analogous dimethyl derivative. It is likely that the very long axial bonds in S(CH3)4 reflect the weakly bound nature of this com(27) Tolles, M.W.;Gwinn, W. D. J . Chem. Phys. 1962, 36, 1119.

The Cb isomer 5 of S(CH& was found to have a single imaginary vibrational frequency of b2 symmetry a t the 3-21G*/SCF level of theory, indicating that this isomer is the transition state along the Berry pseudorotation p a t h ~ a y However, .~ when the DZP basis set was used, a second imaginary frequency was found, of a2 symmetry, corresponding t o a spontaneous rotation of the four methyl groups about their local approximate 3-fold axes, to give a C4 structure in which the methyl groups were twisted by 9" from the all-staggered C4, conformation. This C4 isomer, illustrated in Figure l as 6, was then found to have only a single imaginary vibrational frequency. The C4" structure was also found to have two imaginary frequencies with both PS(P) and PSP bases, at both SCF and MP2 levels of theory. The twist angle of the methyl groups increases from about 10" at the SCF level to about 17" when MP2 theory is used. Fowler and Schaefer also report that the pseudorotation transition state has C4 rather than C4, symmetry, with methyl twist angles of 8.8" (SCF) or 15.6" (CISD theory).ll This rotation is presumably caused by repulsions between hydrogen atoms on neighboring methyl groups; their separation is only 2.055 8, at the DZP/SCF level of theory for the C4, structure, which is substantially less than the sum of the van der Waals radii, but the concerted methyl twisting motion increases this distance slightly. Full details of the structural parameters found for isomer 6 of S(CH& are presented in Supporting Information Table S4. Here we note particularly that the S-C bonds are rather long, at 1.913 A with our most reliable level of theory (1.922 A in the work by Fowler and Schaefer); they are thus close to the average of the axial and equatorial values for the CZ,geometry. In SF4, by way of contrast, the calculated bond length (SCF theory with a DZ(P) basis) in the C4, which is pseudorotation transition state is 1.609 only 0.06 A longer than the equatorial bonds in the ground-state CZ" structure, but again close t o the average of the axial and equatorial bond lengths. The C-S-C bond angle in the C4 structure of S(CH& is 87", which corresponds to an angle of 104"between the lone pair and an S-C bond. In SF4, where the ligands are less bulky, more space is available to the lone pair; we find that the F-S-F angle is 83" in the C4, transition state structure for SF4, which corresponds to an angle of 110"between the lone pair and an S-F bond. These geometrical comparisons clearly indicate the significant (281 Pauling, L. Nature Of The Chemical Bond; Cornel1 University Press: Ithaca, NY,1960; p 260. (29) Marsden, C. J.;Smart, B. A. Unpublished observations.

5404 Organometallics, Vol. 14, No. 11, 1995

Marsden and Smart

Table 5. Structural Parameters and Energies Calculated for S(CH3I4(C2,)a basis

theory

3-21G* DZP

SCF SCF MP2 SCF MP2 SCF MP2 SCF MP2 SCF MP2

TZP

PS PS(P) PSP

S-C,

energy -553.094 -555.808 -556.615 -555.847 -556.773 -168.077 -168.536 -168.157 -168.667 -168.217 -168.896

dC-S,)

r(C-S,)

2.028 2.032 2.060 2.018 2.036 2.176 2.275 2.025 2.083 2.013 2.037

265 432 211 970 858 885 195 290 435 020 907

L(X-S-C,,)b

1.811 1.817 1.818 1.814 1.808 1.870 1.893 1.810 1.830 1.812 1.814

Bond lengths in A, bond angles in deg, energies in hartree. Angle between bond.

C2

axis and S-C,,

L(X-S-C,,Y

93.2 92.9 93.4 92.9 93.6 92.8 94.0 92.5 92.9 92.9 93.4

124.3 123.6 124.6 123.6 124.6 124.4 126.6 123.7 124.7 123.4 124.3

bond. Angle between

C2

axis and

Table 6. Skeletal Vibrational Frequencies for S(C&)4 skeletal motions basis 3-21G* DZP TZP PS

PS(P)

theory SCF SCF MP2 SCF SCF MP2 SCF MP2

a1 699 (1.3) 717 (1.7) 689 (0.9) 706 (1.6) 665 (3.8) 623 (2.7) 726 (1.2) 671 (0.7)

a1 433 (0.6) 424 (0.3) 391 (170) 429 (1.6) 368 (14) 313 (12) 374 (3.7) 406 (130)

a1 335 (0.1) 316 (0.1) 293 (0.01) 325 (0.5) 269 (920) 246 (3.2) 331 (0.1) 290 (0.01)

a1 193 (2.7) 180 (3.2) 177 (2.3) 184 (3.8) 135 (5.3) 158 (2.9) 187 (2.9) 177 (2.2)

a2

445 (0.0) 430 (0.0) 408 (0.0) 438 (0.0) 364 (0.0) 310 (0.0) 441 (0.0) 361 (0.0)

bi 764 (18) 783 (4.4) 740 (3.8) 774 (2.7) 708 (7.3) 654 (15) 797 (2.1) 728 (2.80)

bi 374 (3.0) 338 (670) 345 (3.1) 371 (0.1) 289 (0.3) 251 (0.3) 425 (1.5) 363 (0.8)

443 (0.6) 425 (1.5) 409 (240) 431 (0.3) 421 (0.3) 401 (200) 436 (0.08) 443 (2.6)

bz 403 (480) 363 (4.2) 383 (0.9) 377 (3.6) 297 (36) 305 (0.2) 351 (640) 374 (240)

Frequencies in cm-l, infrared intensities in parentheses.

structural influence of H. * .H interactions in S(CH3)4. Their thermodynamic consequences also appear to be significant, as discussed below. The important skeletal vibrational frequencies calculated for isomer l of S(CH3)4 are reported in Table 6. It is hoped that these results may be useful for future experiments designed to synthesize the compound. Frequencies for the modes which are essentially internal to the methyl groups are not reported, as they are unlikely to be particularly useful for the characterization of the compound, but they may be obtained from either author on request. As for the dimethyl derivative, we note that none of the calculated frequencies is particularly sensitive t o the type of basis used, once polarization functions are included on the sulfur atom, and correlation effects do not appear to be especially important. By analogy with the results already obtained for S(CH3)2,we anticipate that the frequencies in Table 6 will be about 8-10% too high if calculated a t the SCF level and perhaps 4-5% too high at the MP2 level. The IR intensities should be semiquantitatively useful, particularly for the MP2 results. The most easily identified IR bands for S(CH3)4appear to be the axial symmetric (all and antisymmetric (b2) stretching modes, both of which are intense and which both lie near 400 cm-'. The frequencies and intensities reported by Fowler and Schaefer were limited to DZ(P)/SCF results,ll which agree very well with our DZP/SCF values; however, they used a different choice of axis system which interchanges the bl and bz symmetry labels compared with our work. Calculated torsional frequencies are presented in Supporting Information Table S5. These will not be easy to observe, as they lie a t low frequencies and have zero or very low IR intensities. We have calculated the thermodynamic stability of tetramethyl sulfur, or more precisely its electronic binding energy compared to (dimethyl sulfide ethane), with a variety of basis sets, at both SCF and MP2 levels of theory, and with more sophisticated methods up to

+

Table 7. Binding Energiesa for E(CHd4 Relative to (E(C&)2 + C 2 W basis 3-21G* DZP DZP*

TZP TZ(2)P

PS PS(P) PSP

theory SCF SCF MP2 SCF MP2 MP3 MP4SDQ SCF MP2 SCF MP2 MP3 MP4SDQ SCF MP2 SCF MP2 SCF MP2

S(CH& -411 -444 -352 -440 -340 -363 -364 -438 -336 -427 -329 -353 -351 -542 -410 -424 -336 -439 -328

Se(CH3)4

Te(CH3)4

-374 -300

-452 -330 -360 -287 -381 -283

-322 -226 -269 -198 -295 -207

Binding energies are in kJ/mol. Geometry taken from TZPi MP2 optimization.

fourth-order perturbation theory (MP4SDQ))as this is such an important indication of whether the compound can ever be prepared. Our results in Table 7 show that S(CH3)4 is consistently unstable in a thermodynamic sense. There is some variation with the size of the basis used, with the compound becoming slightly less unstable as the basis is enlarged, and it is possible that even larger basis sets than those used here would lead to further reductions in the calculated thermodynamic instability. Correlation effects make the compound appreciably less unstable, by about 100 kJ/mol. But as the basis-set effects are relatively minor, and as the use of progressively more exact treatments of correlation (MP2 through MP3 to MP4SDQ) changes the predicted binding energy by only some 20 or 25 kJ/mol, we are confident that the thermodynamic instability of S(CH3h is firmly established; our best estimate of the binding energy is -350 kJ/mol. Fowler and Schaefer did not

E(CH& Compounds

Organometallics, Vol.14,No. 11, 1995 5405

Table 8. Structural Parameters and Energies for Se(CHs)d (CZ,)~ basis

theory

DW)

SCF MP2 SCF MP2 SCF MP2 SCF MP2

energy

r(C-Se,)

r(C -Sew)

L(C,,-Se-C,)

dC,-

Se -CeJ

~

PS PS(P) PSP a

-2558.002 -2558.863 -167.237 -167.687 -167.295 -167.791 -167.347 -167.997

017 386 640 030 224 473 355 949

2.137 2.181 2.201 2.248 2.132 2.172 2.128 2.141

1.944 1.968 1.978 2.007 1.947 1.973 1.947 1.954

169.8 168.4 168.8 166.4 169.5 168.0 168.9 167.4

110.5 109.0 110.5 107.5 110.7 109.3 111.2 109.9

Bond lengths in A, angles in deg, energies in hartree.

discuss the thermodynamic stability of the tetramethyl compounds.ll Although S(CH3)4 is thermodynamically unstable, its future preparation is of course not absolutely excluded by these results. Its possible kinetic stability would be determined by the barrier to dissociation t o (S(CH3)z ethane), but it was beyond the scope of this work to locate the corresponding transition state, which probably has only C1 symmetry.lob As the barrier to dissociation is quite unknown at present, it is not very important t o attempt to give uncertainty limits for the thermodynamic instability. Interesting information concerning the importance of d orbitals for the bonding of the hypervalent tetramethyl compounds may be obtained from Table 7. By comparing the SCF results for the PS and PS(P) basis sets, we learn that d-type functions on S improve the binding energy of S(CH3)4by about 100 kJ/mol. This does not mean that the total energy of S(CH3)4 is lowered only by that amount but rather that it is lowered by 100 kJ/ mol more than the energy of S(CH&, a compound where S follows the octet rule. In fact the total energetic effect a t the SCF level in S(CH& of d-type orbitals on S is just over 200 kJ/mol, as shown by the data in Table 5. Now 100 kJ/mol is not a trivial amount of energy when considering binding, but it is not sufficiently large to be taken as a dominant contribution, in general terms. We note that the correlation contribution t o the binding energy is also of the order of 100 kJ/mol, while the total valence correlation energy obtained in our MP2 calculations is as large as 1785 kJ/mol. Correlation effects arise from the inadequacies of the one-electron or orbital model, the model which is used almost to the exclusion of all others by chemists who are not experts in electronic structure calculations. As the energetic consequences of d-type orbital contributions to the binding energy are similar in magnitude to those due to the failure of the orbital model itself, it does not seem reasonable to ascribe a primary importance to d-type bonding contributions. We believe that a more realistic approach is to consider the d-type orbitals as polarization functions, which are important in a quantitative sense for relatively “soft” (polarizable) atoms such as S. More detailed numerical analyses of many hypervalent compounds may be found in ref 1. The barrier t o Berry pseudorotation in S(CH&, i.e. the difference in energy between the Czuand C4 isomers, is not large. Calculated values at the SCF level of theory are 32.5 (3-21G* basis), 28.7 (DZP), 31.1 (PS(P)),or 26.2 (PSP)kJ/mol. These decrease to 21.3 (DZP), 24.9 (PS(P)),or 20.0 (PSP)kJ/mol when MP2 theory is used. Fowler and Schaefer obtained barriers with their DZ(P)basis of 32.6 (SCF) or 25.1 (CISD)kJ/mol,ll which are quite consistent with our own results. They also located transition states on the methyl rotation surface, finding low barriers of 12.5 or 3.8 kJ/mol for axial or

+

equatorial rotation. There is some variation in these values for the pseudorotation barrier, but similar trends have been found in detailed studies of the isoelectronic species SF4, where energies were obtained for CzUand C4”isomers using MP4SDQ and QCISD levels of theory with bases ranging to TZ(2)P(D in size a t SCF geometries; enlargement of the basis reduces the, barrier, as does inclusion of electron correlation effects.29 It is clear that S(CH3)4 is a fluxional molecule and more flexible than SF4, whose barrier is about 45 kJ/mol. Tetramethylselenium was examined using the basis sets adopted for the dimethyl species, and isomers of CzU,C4”, and C4 symmetry were investigated. As for S(CHd4,a stationary point of CzUsymmetry was located for Se(CHd4 in which both equatorial and axial methyl groups are staggered with respect t o the equatorial lone pair; it proved to be a true minimum. The CdUisomer was found to have two imaginary frequencies, again like S(CHd4, one corresponding to the collapse t o the Czu species and the other giving the C4 isomer by a concerted methyl group rotation. However, the methyl twist is only some 0.3’, or barely noticeable for Se(CHd4. It seems clear that this reduced departure from idealized ClVsymmetry is due to the longer bonds, and hence reduced steric hindrance, associated with the selenium species. The shortest He *Hdistance between methyl groups is 2.193 8,in CdUSe(CHd4at the DZ(P)/SCFlevel of theory, compared to 2.055 8, for S(CH3)4. Optimized geometrical parameters for the CzUisomer of Se(CHd4 are reported in Table 8. The main structural features, which are not sensitive to details of the basis set used and are not greatly influenced by correlation effects, are very similar to those already described for S(CH3)4. The equatorial C-Se bonds are of “normal” length, being almost exactly the same as those in Se(CH&, but the axial bonds are substantially longer, by about 0.20 8,. Although this difference is slightly less than that described for S(CH3)4,which is some 0.23 A, it is much greater than that found in SeF4 (0.089 8,).30The C,-Se-C, angle is close to 168’, scarcely different from the value of 169”in SeF4, while the Ceq-Se-Cq angle is about 110’, compared to 100.6’ for SeF4. An analogous widening of the equatorial bond angle was noted above for tetramethylsulfur. It is slightly less pronounced for the selenium compound, presumably due t o the reduced H. * *H interactions between equatorial methyl groups, which result from the longer C-Se bonds compared to those between carbon and sulfur. Once again, the results obtained by Fowler and Schaefer are almost identical to our own where they overlap,ll despite the different contraction schemes used in the two studies. (30) Bowater, I. C.; Brown, R. D.; Burden, F. R. J. Mol. Spectrosc. 1968, 28, 454.

5406 Organometallics, Vol. 14, No. 11, 1995

Marsden and Smart

Table 9. Skeletal Vibrational Frequencies for Se(CHd4 (Cda skeletal motions ~~

basis DZ(P) PS PS(P) a

theorv SCF SCF MP2 SCF MP2

a1 631 (0.1) 588 (0.2) 547 (0.2) 612 (1.8) 569 (0.3)

a1 425 (0.9) 307 (6.3) 347 (1.0) 443 (1.5) 382 (0.9)

a1 257 (1.0) 175 (1.8) 217 (0.8) 221 (3.5) 218 (0.2)

a1 159 (2.7) 128 (1.6) 141 (3.0) 110 (0.2) 160 (1.9)

a2 369 (0.0) 351 (0.0) 313 (0.0) 372 (0.0) 327 (0.0)

bi 664 (0.1) 628 (0.03) 580 (0.9) 594 (5.0) 596 (1.0)

bi 289 (3.9) 267 (10) 236 (4.79) 286 (10) 268 (3.6)

~~

b2 395 (220) 345 (25) 361 (190) 385 (250) 378 (210)

bz 327 (170) 148 (230) 298 (15) 333 (110) 327 (15)

Frequencies in cm-l, infrared intensities in parentheses.

Table 10. Structural Parameters and Energies Calculated for Te(CHd4 ( C Z ~ " basis PS PS(P)

PSP

c

theory SCF MP2 SCF MP2 SCF MP2

energy -166.121 718 -166.559 054 -166.154 790 -166.636 088 -166.204 991 -166.852 117

r(C,-Te) 2.268 2.294 2.251 2.277 2.252 2.256

r(C,-Te) 2.142 2.175 2.128 2.161 2.131 2.142

L(C,-Te-C,) 160.0 157.3 161.5 158.9 161.0 158.7

L(C,-Te-C,,) 113.1 112.0 111.8 112.2 112.3 111.6

X-ray Db 2.275( 17) 2.127(6) 162.2(4) 109.1(3) electron DC 2.265(9) 2.140(8) 152(3) 123(5) a Bond lengths in A, bond angles in deg, energies in hartree. X-ray diffraction results for solid, from ref 12; uncertainties in parentheses. Electron diffraction results for gas, from ref 12; uncertainties in parentheses.

Predicted skeletal vibrational frequencies for the CaU isomer of Se(CH3)4are displayed in Table 9. The most reliable values are those calculated with the PS(P)basis. It is likely that the SCF results are too high by about lo%, while the error for the MP2 values is probably of the order of 5%. It is somewhat surprising that correlation effects have a pronounced influence on the IR intensities; MP2 theory predicts that there is only one intense band for Se(CH3)4, located a little below 400 cm-l, whereas there are two intense IR bands in that region for the sulfur compound, and two are predicted for Se(CH& at the SCF level of theory. This observation shows just how difficult it can be to make reliable estimates of vibrational spectra for even moderately complex molecules without assistance from quantitative calculations. Calculated structural parameters for the C4 isomer of Se(CH314 are reported in Supporting Information Table S6. The C-Se bonds are long, at about 2.05 8,or very close to the average of the equatorial and axial bond lengths for the Czu isomer, while the C-Se-C angle of 85' is somewhat smaller than the comparable value of 87' in the C4 isomer of S(CHd4; as argued above, the angle in the sulfur compound is larger than would be expected, so the smaller value here is another indication of the reduced role of Ha .H repulsions in the Se-containing molecule. The barrier to Berry pseudorotation for tetramethylselenium is rather less than for tetramethylsulfur. Calculated values range from 24.7 (DZ(P)/SCF)to 14.2 (PSPMP2) kJ/mol. Fowler and Schaefer also obtained 24.7 kJ/mol at the DZ(P)/SCF level of theoryell As for the sulfur system, the barrier decreases as the basis is enlarged and as correlation effects are considered. We believe that the true value will be close t o 15 kJ/mol. Tetramethylselenium is less thermodynamically unstable than its sulfur analogue. Calculated values of the binding energy, compared t o (ethane and the dimethyl species), are presented in Table 7. Rather similar trends with basis size and theoretical method are found for both tetramethyls, though the selenium compound was studied in less detail than the sulfur species, as the variations with level of theory for the

sulfur compound were not large. Our final estimate for the binding energy of Se(CH3)4,obtained by applying a "correction" to the MP2 result based on the experience obtained from S(CHd4, is about -300 kJ/mol, compared to about -350 kJ/mol for S(CH3)d. Czu and CdUisomers of tetramethyltellurium were examined. The CaU isomer was found to be a true minimum, following the pattern established by the S and Se analogues. The all-staggered conformer similar to 1 in Figure 1was again found to be the most stable, with the equatorial-eclipsedal-staggered, equatorialstaggereaaxial eclipsed and all-eclipsed arrangements higher in energy by 10.0, 22.8 and 31.0 kJ/mol, respectively, a t the PS(P)/SCF level of theory with full geometry optimization. However, only a single imaginary vibrational frequency was found for the ClUisomer, which is therefore a true transition state, in contrast to the selenium and sulfur systems described above for which the transition state has C4 symmetry. Twisting of the methyl groups is not favored for the C4 isomer of Te(CHd4, as due to the long Te-C bonds, the separation between H atoms in different groups has increased to 2.39 8, at thePS(P)/SCF level of theory, indicating insignificant steric repulsion since the sum of the van der Waals radii is 2.4 A.2a Optimized structural parameters for the CzUisomer of Te(CH3)4 are reported in Table 10. The calculated difference between the equatorial and axial bond lengths to carbon is rather small, a t only 0.114 A with the most sophisticated theory we used. This difference is much less than the values of 0.23 or 0.20 A for the S or Se analogues. It is noticeable that the variation in axial bond length for Te(CH3)4 with the size of basis is much less pronounced than found for the S or Se derivatives. When the basis is improved from PS to PSP, the TeC,, bond shortens by only 0.038 8, at the MP2 level, compared to reductions of 0.238 8,for S-C, and 0.107 8, for Se-C,. There is a steady reduction in the CaxE-C, angles as the central atom increases in size; PSPI MP2 values are 173.2' for E = S, 167.4' for the Se compound, and 158.7" for Te(CHd4. This trend appears to be yet another reflection of the decreasing importance of intermethyl Ha .H repulsions as the E-C bonds

E(CH& Compounds

Organometallics, Vol. 14, No. 11, 1995 5407 Table 11. Skeletal Vibrational Frequenies for Te(CHd4 (CZ,)~ skeletal motions

SCF

PS

MP2

PS(P)

SCF MP2

PSP a

SCF

543 (1.0) 507 (1.1) 566 (1.4) 515 (1.0) 550 (1.2)

429 (0.5) 419 (0.4) 442 (0.3) 406 (0.3) 439 (0.3)

211 (5.4) 193 (3.9) 216 (3.8) 193 (2.3) 209 (3.9)

100 (2.0) 82 (1.2) 112 (1.5) 87 (0.9) 108 (1.7)

313 (0.0) 291 (0.0) 314 (0.0) 296 (0.0) 310 (0.0)

569 (7.3) 523 (10) 586 (9.0) 535 (8.6) 581 (8.1)

exptlb 507 383 520 Frequencies in cm-l, infrared intensities in parentheses. Experimental results from ref 3.

lengthen; following the VSEPR principle^,^ the lone pair is more sterically demanding than the bond pairs, but its desire to seek a large share of the coordination sphere about E is frustrated if E is relatively small by the consequent H. .H nonbonded repulsions. Fowler and Schaeferll used an all-electron basis on Te rather than a pseudopotential of the type used in our work. They obtained nonnegligeable differences for some of the structural parameters. In particular, the C,,-Te-C,, angle is 118.6" in their work, but our SCF values are close to 112";for that parameter, the Te compound has an appreciably larger angle than the S or Se species in their work, whereas we found differences of no more than 1-2" from compound to compound. It is not clear t o us why these differences should arise, but we note that the potential surface for Te(CHd4 is very flat for angular deformations (see below), so the values obtained for equilibrium structural parameters are likely to be unusually sensitive to details of the basis employed. The comparison of our calculated structural results for Te(CH3)4with those available from the recent X-ray diffraction and electron diffraction (ED) experiments l2 is also presented in Table 10. It will be noted that the agreement with our PSPMP2 values is very satisfactory for both axial and equatorial bond lengths, as our results are either within or just outside the experimental uncertainties. The situation regarding the bond angles is more complicated, but particularly interesting. As the ED experiments were performed in the gas phase, one might anticipate that the ED results would be in better agreement with our calculated values, which also refer to isolated molecules, than would the X-ray results which were obtained in the solid phase and which might perhaps be distorted by "packing effects" or by "secondary bonding" in the crystal. The latter are common for atoms as heavy as Te,31 and one would probably anticipate non-negligible interactions with neighboring molecules for a system in which the formal Te coordination number is as low as 5 . However, while the calculated equatorial bond angle agrees tolerably well with the X-ray value, with a difference of only some 2", the ED result is about 12" larger. For the axial bond angle our calculated value is between the X-ray and ED results, though closer t o the X-ray value. We believe that these angular discrepancies are a reflection of the extraordinary fluxional nature of tetramethyltellurium, which is discussed in detail below. Skeletal vibrational frequencies calculated for the CzU isomer of Te(CH3)4are reported in Table 11. We have attempted to assign the experimental observations3 where possible, but unfortunately many of the (3N 6) fundamental vibrational frequencies for tetramethyltellurium have not yet been observed. Although we (31)Alcock, N. R.Adu. Inorg. Chem. Radiochem. 1972,15, 2.

239 (8.8) 221 (7.7) 240 (5.9) 226 (5.8) 240 (5.8)

430 (180) 437 (110) 447 (190) 425 (120) 445 (192)

281 (25) 260 (9.1) 286 (22) 268 (11) 281 (21)

219

383 (?I

263

do not have calculated frequencies at the PSPMP2 level of theory, as those calculations would have been too time-consuming, we can obtain extrapolations by combining the PS(P)/SCFand M P 2 results with the PSP/ SCF data. The resulting estimates are 504, 403, 186, and 83 cm-l for the a1 block, 292 cm-l for the single a2 mode, 530 and 226 cm-l for bl symmetry, and 423 and 263 cm-l for the b2 block. The particularly low a1 bending frequency of only some 83 cm-l implies immediately that the molecule is unusually flexible, as the skeletal bending frequency in dimethyl tellurium is 198 cm-1.23 We expect the a1 modes t o be the most intense in the Raman spectrum and so assign the 507 and 383 cm-l peaks t o the modes predicted near 504 and 403 cm-l. As no spectral features were detected below 200 cm-l, we cannot make assignments for the two remaining a1 skeletal modes. An IR band at 520 cm-l is readily assigned to the skeletal stretching bl mode, while the Raman feature a t 219 cm-' matches quite satisfactorily the bl bend expected near 226 cm-l. It is not clear whether the antisymmetric stretching motion of the Te-C axial bonds (b2 symmetry) expected near 423 cm-l has been detected; unfortunately the IR spectrum could not be studied below 450 cm-l, and while there is a Raman peak at 383 cm-l, it is more natural to assign it to the a1 axial stretching motion, in view of its high intensity and better match with our calculated frequencies. The remaining Raman band a t 263 cm-l fits splendidly with the b2 bending mode expected near 263 cm-'; such good agreement is pleasant but no doubt somewhat fortuitous. This discussion shows that all observed low-frequency bands in both infrared and Raman spectra can be assigned quite satisfactorily to the fundamental skeletal vibrations of CzUTe(CH3)4.In particular, we note that there is no need to invoke a possible co-existence of CzUand ClVisomers, in order to understand the substantial number of low-frequency bands.3 The conclusions reached by Fowler and Schaefer about the vibrational frequencies are broadly similar t o our own,ll though they did not attempt such a detailed assignment of the observed data. In addition to the nine skeletal vibrations, there are four torsional vibrations for Te(CH&. All are at low frequency and all have low IR intensities, so their detection will be difficult. Our detailed calculated values appear in Supporting Information Table S7. Briefly, the expected frequencies are 169 (twice), 143, and 142 cm-l. Calculated structural parameters for the C ~ s y m metry transition-state isomer of Te(CHd4 are presented in Supporting Information Table S8. The predicted Te-C bond length is 2.20 A; as already seen for the other C4 or C4utetramethyls described in this work, this value is very close t o the average of the axial and equatorial bond distances in the CzU ground state.

5408 Organometallics, Vol. 14, No. 11, 1995

Marsden and Smart

Table 12. Pseudorotation Barriers for Te(CH9)p PS(P)

SCF MP2 PSP SCF MP2 PSP(Qb MP2 MP3 MP4DQ MP4SDQ QCISD QCISD(T) QCISD(T) + ZPV"

-166.154 -166.636 -166.204 -166.852 -166.886 -166.947 -166.953 -166.958 -166.960 -166.982

79 09 99 12 25 09 27 06 70 89

-166.145 -166.626 -166.201 -166.850 -166.885 -166.946 -166.952 -166.956 -166.959 -166.981

15 25.3 64 24.8 88 8.4 53 4.2 25 2.6 00 2.9 07 3.1 79 3.3 37 3.5 83 2.8 3.4

Absolute energies E in hartree, energy differences AE in kJ/ mol. Results obtained at PSPIMP2 geometries. Zero-point energies of vibration, unsealed, obtained a t PSP/SCF level of theory.

Continuing another well-establishedtrend in this series, the C-Te-C bond angle of 83" is smaller than those for Se(CH3)4(85") or S(CH314 (87");we argue that the long Te-C bonds allow the lone pair t o acquire its "natural" share of the coordination sphere about tellurium, without having to compromise to reduce H- * .H repulsions. In this case the C-Te-C angle reported by Fowler and Schaefer agrees very well with our value, and the bond length differs by less than l%.ll To our minds, the most interesting aspect of the potential energy surface for Te(CH3)4 is its flatness; in other words, the molecule is extraordinarily fluxional and the barrier to pseudorotation remarkably low. Calculated values are reported in Table 12. It will be seen that the addition of d functions to the C atom basis produces a large reduction in the barrier, and in this respect Te(CH& behaves quite differently from the other tetramethyl compounds already discussed; for the Se derivative, for example, increasing the size of the basis from PS(P) to PSP changes the barrier by only 0.1 kJ/mol with MP2 theory. We have not discovered why the basis requirements for Te(CH3)4 are more stringent than those for the other tetramethyl compounds, but the variational principle is quite clear; the addition of extra functions to a basis necessarily lowers the energy, even if only slightly, and if the extra functions make an appreciable change in the calculated value of some property, then the original basis without those functions was inadequate. We note that the allelectron basis used by Fowler and Schaefer gave a very small pseudorotation barrier of only 2.1 kJ/mol at the SCF leve1,ll whereas our most directly comparable SCF result is 25.3 kJ/mol, obtained with the PS(P) basis. The origin of this discrepancy is not clear to us. To test the adequacy of the PSP basis, we undertook further calculations using a still larger PSP(f) basis, which contained a set of f-type functions on Te only (exponent 0.35). These calculations were performed for both the CzUand C4, isomers of tetramethyltellurium at the geometries obtained at the PSP/MP2 level of theory. This further basis extension reduced the calculated barrier to pseudorotation from 4.2 to 2.6 kJ/mol using MP2 energies; in percentage terms, this is an appreciable change, though in practice its significance is probably limited, as we cannot claim accuracy t o within 1 kJ/mol. The precise value of the barrier fluctuated somewhat as progressively more sophisticated correlation treatments were employed, rising t o 3.5 kJ/mol with QCISD theory but then decreasing to 2.8 kJ/mol at the QCISD(T)level. When the zero-point

vibrational energies of the two isomers are considered, as computed at the PSP/SCF level of theory, the effective barrier increases by 0.6 kJ/mol to 3.4 kJ/mol. Fowler and Schaefer also noted that the zero-point energy calculated for the C4, transition state is, rather unusually, slightly larger than for the CZ, true minimum.ll These results allow us t o understand why the bond angles obtained by gas-phase electron diffraction at room temperature appear to be somewhat different from those calculated for the equilibrium geometry or obtained by X-ray diffraction for the solid phase a t low temperatures (183 K) in the solid phase.12 The average thermal energy available to molecules at 298 K is 2.5 kJ/mol, or about 75% of our most sophisticated calculated barrier t o pseudorotation. Even if this calculated value is not exactly correct, it is clear that a nonnegligeable number of gas-phase molecules will be in excited vibrational states which effectivelylie above the barrier, and thus have 4-fold symmetry, while a substantial number of others will have energies close to the top of the barrier. Now the electron diffraction experiment samples all the molecules distributed over their various vibrational states and thus obtains average bond angles. While for normal, relatively rigid molecules there is little difference between average and equilibrium bond angles, appreciable differences can arise for highly fluxional molecules such as Te(CH314. The apparent bond angles observed by electron diffraction are thus the Boltzmann-weighted superposition of all geometries between the equilibrium CZ,and transition-state C4, geometries. Thus the axial and equatorial angles obtained by electron diffraction are closer to each other (153 and 118") than are the corresponding X-ray (109 and 162")or calculated (113 and 161")values, since all four adjacent C-Te-C angles in the C4" transition state are equal and intermediate between the axial and equatorial angles for the CZ,ground state. The vibrational amplitudes found in the electron diffraction experiment are exceptionally large for the C- *C distances due to the flexible nature of the molecule. We note the particularly low vibrational frequency of only some 83 cm-' estimated for the equatorial bending motion. This large-amplitude vibrational motion causes a smearing-out of the C- *Cdistances, and thus leads to relatively large uncertainties in the bond angles measured by electron diffraction. The X-ray diffraction experiment does not suffer from these difficulties, since it was performed a t lower temperatures and since the molecules are somewhat constrained in the crystal by contacts with their neighbors. Although tetramethyltellurium is thermodynamically unstable, its formation from ethane and the dimethyl derivative is less unfavorable than for either its S or Se analogues. Calculated results are presented in Table 7. Our best estimate of the binding energy is -225 kJ/ mol. Te(CH3)4 is not stable in a practical sense above 100 "C and is light-~ensitive.~ There is a progressive increase in stability as the size of the central atom increases, presumably due at least in part to the reduction in Ha -H steric repulsions, and the change from Se(CH3)4to Te(CH3)4 is substantially greater than that between the S and Se compounds. It is interesting to note from Table 7 that d-type orbitals on Te have a smaller influence on the stability of Te(CH314 (about 50

-

E(CHd4 Compounds

Organometallics, Vol. 14,No. 11, 1995 5409

kJ/mol) than is the case for the corresponding S compound (about 100 kJ/mol). This observation implies that polarization effects are less important for Te than for S; although this may appear surprising, as Te is "softer" than S, the inhomogeneous electric fields about Te in molecular compounds may be expected to be less intense than about S, simply because Te is a larger atom. The orbital model appears to be comparably accurate for Te(CH3)4 and S(CH&; the differences in binding energies calculated at SCF and MP2 levels of theory are about 110 'and 90 kJ/mol, respectively, with the PSP basis.

Conclusions We have undertaken a systematic theoretical study of the tetramethyl derivatives of the chalcogens S, Se, and Te. All three compounds adopt a CZ"geometry at equilibrium, based on a trigonal bipyramid with an equatorial lone pair. Steric repulsions due to CH3. * *CH3 interactions are pronounced for S(CH& but progressively less important as the size of the central atom increases. Calculated vibrational frequencies are reported. Barriers to Berry pseudorotation decrease from 20 kJ/mol for S(CH& through 15 for SeCH3)4 to only 3 kJ/mol for Te(CH3)4. The Te compound is thus exceptionally fluxional, and the concept of an equilibrium structure is perhaps misleading; the flexible nature of this species explains why previous room-temperature

electron difiaction and low-temperature X-ray diffraction experiments obtained rather Merent bond angles.12 All three tetramethyls are thermodynamically unstable with respect to the dimethyl plus ethane, though the instability decreases from about 350 kJ/mol for S(CHJ4 to some 225 kJ/mol for Te(CH314. The contribution of d orbitals to the binding of the tetramethyl compounds is significant but not crucial; in keeping with a recent extensive analysis,l the d-type orbitals on S/Se/ Te are best considered as polarization functions, whose importance decreases as the central atom becomes larger. Since Te(CH3)d has recently been prepared, the other tetramethyl chalcogen derivatives seem feasible but challenging synthetic targets.

Acknowledgment. We thank the Australian Research Council for financial support and both Melbourne University and Cray Reasearch (Australia) for generous access t o supercomputing facilities. B.A.S. thanks Melbourne University for a Melbourne University Postgraduate Award. Supporting Information Available: Tables S1-S8, listing vibrational frequencies, energies, structural parameters, and geometries (5 pages). Ordering information is given on any current masthead page. OM940821A