Mendeleev Communications Electronic Version, Issue 6, 1999 (pp. 213–255) The molecular structure and the puckering potential function of octamethylcyclotetrasilane, Si4Me8, determined by gas electron diffraction and ab initio calculations Vladimir P. Novikov,*a Svetlana A. Tarasenko,a Svein Samdalb and Lev V. Vilkova a Department of Chemistry, M. V. Lomonosov Moscow State University, 119899 Moscow, Russian Federation.Fax: +7 095 932 8846; e-mail: VPNovikov@phys.chem.msu.ru b Department of Chemistry, University of Oslo, N-0315 Oslo, Norway The structural parameters, the barrier of inversion and the equilibrium puckering angle of Si4Me8 were determined using a dynamic model (V0 = 1.0±0.5 kcal mol–1, je = 28.3±1.9°). The reactivity of silacyclobutane derivatives is closely related to the ring strain energy.Since the balance of angular and torsional strains in the ring determines the degree of its planarity,1 it can be expected that the structure of this class of compounds is responsible for their reactivity. However, the data on the molecular structure of cyclotetrasilane derivatives are inconsistent in many respects. Thus, for crystals of Si4Cl8 and Si4Br8, a planar ring structure was found,2 whereas a vibrational spectroscopy study revealed a nonplanar ring structure.3 The molecule of octamethylcyclotetrasilane shows no exception.The results of X-ray analysis give evidence of a planar ring, while it is nonplanar according to vibrational spectroscopy data.5 Earlier, the Si4Me8 molecule was studied by gas electron diffraction within the static model approximation,6 and the average dihedral angle j (Figure 1) was found to be 29.4±4.0°.Note that this angle can differ from zero even if the ring has a planar equilibrium configuration. This follows from the fact that the static model produces the mean value of j averaged over vibrational levels of the puckering motion. As a rule, the puckering of four-membered rings is a large-amplitude motion of high anharmonicity.Therefore, to solve the problem whether the ring is planar or not, we should introduce a potential function to describe this motion and use a dynamic model which takes into account contributions to the scattering from all local conformations arising along the puckering pathway in accordance to their population.To describe the ring puckering, it is convenient to use the puckering coordinate z (Figure 1), which is defined as a half-height between the diagonals Si···Si in the ring and characterises the displacement of atoms from a planar configuration. This description corresponds to the normal mode of ring puckering. The Si4Me8 molecule has D2d symmetry for the nonplanar ring and D4h for the planar one.With these types of symmetry, the relation between the dihedral angle and the coordinate z can be expressed as follows: where a is the Si–Si–Si angle: a = 2arctan[cos(j/2)], which is valid if the Si–Si bond length does not change during the ring puckering. However, an electron diffraction study7 of 1,1-dichlorosilacyclobutane showed that changes in the bond lengths and valence angles of the ring are sufficiently large, and that these changes should be included in the structure analysis. Therefore, in this work, for more accurate determination of the structure of Si4Me8, we applied a dynamic model which takes into account the relaxation of geometric parameters estimated from ab initio calculations.These calculations were also used to obtain the mean-square amplitudes and vibration corrections. We used the total scattering intensity It(s) and the background line Ib(s) data obtained in the Budapest laboratory of electron diffraction6 and deposited at the British Library.8 The range of experimental sM(s) values was 2–36 Å–1. The numbering of atoms of the Si4Me8 molecule is shown in Figure 1.The deviations of the bisectors of the C–Si–C angles from the Si–Si–Si planes are denoted as dC.The relaxation effects were estimated by an optimization of the geometric parameters for a number of fixed j values in the range 0–50° with a step of 10°. The ab initio MO calculations were carried out at the Hartree–Fock level of the theory using the 6-311G** basis set with polarization functions and the GAUSSIAN-94 program.9 It was found that the puckering potential of Si4Me8 is adequately described by the following quadratic-quartic function: V(j) = V0[(j/je)2 – 1]2, where V0 = = 0.65 kcal mol–1 and je = 25.6°.z = 0.5r(Si–Si)cos(a/2)sin(j/2), H(13) H(22) H(21) C(5) H(29) H(30) H(17) C(9) H(23) H(24) H(14) C(6) H(19) H(33) H(34) C(11) H(15) H(26) H(25) C(7) H(36) H(20) H(35) C(12) H(32) C(10) H(18) H(28) H(16) H(27) C(8) H(31) Si(1) Si(2) Si(3) Si(4) dC 2z j dC Figure 1 Molecular structure of Si4Me8; definition of the puckering coordinate z.aDistances, Å; angles, degrees; the GED parameters ra and �a; errors are given in parentheses as 3s. bJoint analysis of GED and ab initio data. cFound from ab initio calculations. Table 1 Main geometric parameters of Si4Me8 a (gas electron diffraction, GED, ab initio HF/6-311G** calculations, AI, and X-ray data).Parameter This work GED6 X-ray4 GED + AIb AI Si–C 1.896(3) 1.903 1.893(3) 1.889 Si–Si 2.370(2) 2.398 2.362(4) 2.363 C–H 1.104(3) 1.087 1.096(11) — �CSiC 109.5(6) 108.6 110.8(16) 110.0 �SiSiSi 88.2(2) 88.6 88.1(5) 90.0 �SiCH 111.7(6) 112.0 111.7(15) — dC 4.1c 4.1 0.8(17) — V0/kcal mol–1 1.0(5) 0.65 — — je 28.3(19) 25.6 29.4(40) 0.0 R-factor (%) 4.8 — 10.3 —Mendeleev Communications Electronic Version, Issue 6, 1999 (pp. 213–255) The ab initio calculations showed that the bond lengths can change by 0.01 Å during the puckering motion, and the valence and d angles, by 2.5 and 4.2°, respectively. Thus, the relaxation effects in Si4Me8 are too large to be neglected in the description of the geometry of local conformers.To take into account these relaxation effects, the calculated geometric parameters P(j) were approximated by the third degree polynomials P(j) = a0 +Sanjn. The polynomial factors an were used in the structural analysis to compute the geometric parameters at a given value of j, while the factors a0 were variable parameters. For the angle dC, the factor a0 is equal to zero by symmetry reasons because d = 0° at j = 0°.Therefore, these angles were parametrised by the function d(j) = k0Sanjn, where k0 is a variable parameter having the meaning of a scale factor. For a complete description of the molecular geometry, the following six parameters were used: r(Si–C), r(Si–Si), �CSiC, dC, �SiCH, r(C–H). All of the parameters, with the exception of r(C–H), were parametrised as functions of the angle j.The frequencies and normal modes of Si4Me8 were calculated using the force field on Cartesian coordinates obtained in the full geometry optimization by the GAUSSIAN-94 program using the HF/6-311G** basis set. The transformation of the force field to symmetry coordinates and the optimization of scaling factors were carried out by the SHRINK4 program10 using experimental frequencies.5 The results of normal coordinate calculations agree well with the frequency assignment of Si4Me8 made earlier in the 900–100 cm–1 region.5 Normal coordinate analysis showed that the puckering mode has the lowest frequency, 33 cm–1 (A1 symmetry).The nearest frequency of the same symmetry is the SiC2 deformation, but it lies considerably higher than the ring puckering frequency at 161 cm–1.Other low-frequency vibrations have different types of symmetry: SiC2 twist, 87 cm–1 (A2); SiC2 rock, 74 cm–1 (B1) and 73 cm–1 (E). Therefore, the puckering mode can be reliably separated from the framework vibrations, which were treated in a harmonic approximation. The amplitudes and vibration corrections were calculated for the framework at fixed j values (0, 10, 20, 30, 40, and 50°) using the optimised geometry for the corresponding j values.The root-mean-square amplitudibration corrections (d = ra – ra) were calculated using the technique10 which applies a nonlinear transformation of internal coordinates into Cartesian displacements of atoms.This technique gives more reliable values of d corrections than the standard method11 if the molecule possesses low-frequency vibrations. For each internuclear distance, the functions u(j) and d(j) were interpolated during calculations of the reduced molecular intensity sM(s) in the range j = 0–50° with a step of 2.5° according to the formula where W(j) is the classical probability density of the angle j, W(j) = Q–1exp[–V(j)/RT], where R is the gas constant, T is the absolute temperature, V(j) is the potential function and Q is the normalising factor.The structural analysis was carried out using the modified ELED program12 with the starting values of the parameters taken from the ab initio calculations. The refinement of the geometry was carried out using a conventional procedure.7 At the first stage of the structural analysis, we varied the set of well-defined parameters (the Si–Si and Si–C bond lengths and the �CSiC angles) as well as the parameters V0 and je for the potential function.The model with the planar ring configuration and the puckering potential function V(j) = Aj4 + Bj2 was also tested. All starting approximations were shown to converge to the nonplanar ring conformation with the dihedral angle je = 28°.After the background correction, the rest of geometric parameters and the amplitudes were sequentially added to the set of parameters under determination according to their contributions to the scattering. A variation in the scale factor k0 for the angle dC leads to an extremely unstable solution.Therefore, we put k0 = 1 for dC, i.e., it was fixed at its ab initio value. The final results of the structural analysis are presented in Table 1 and compared with the data obtained from ab initio calculations and previous investigations. As can be seen in Table 1, the dynamic model gives better agreement with the experimental data as compared to the static model:6 the R-factor was halved, and this led to a decrease of the error limits.The parameters for both of the models are quite similar. However, this fact cannot be predicted beforehand. This situation can occur when the barrier height V0 is high so that the most populated puckering vibrational levels lie under the barrier. In this case, the potential function can be approximated by a parabola near its minimum, and a simple harmonic approximation can be used for the puckering vibration. Thus, static and dynamic models will give essentially the same results. The dihedral angle and the barrier height clearly indicate that the ring is puckered in the gas phase.This agrees with the vibrational spectra analysis. The planar ring in the solid phase found in an X-ray study4 of Si4Me8 can apparently be explained by the crystal packing effect.Note that cyclotetrasilane has also a puckered conformation according to ab initio calculations: je = 31.2° and V0 = = 0.3–0.4 kcal mol–1.13 The replacement of hydrogen atoms with methyl groups increases the puckering barrier in Si4Me8 up to 1.0±0.5 kcal mol–1, which is seemingly caused by an increase of the torsional strain energy.This is confirmed by the fact that the distances between the nearest nonbonded atoms C(8)···C(9) increase from 3.89 to 3.98 Å when the conformation of the ring changes from planar to puckered with the angle je. This means that in the equilibrium configuration the distance between adjacent methyl groups is equal to the sum of the van der Waals radii of the methyl groups, 4.0 Å.14 The predominance of the torsional strain over the angular strain determines the puckered conformation of the ring in Si4Me8, as it is the case in cyclobutane, though the absolute values of angular and torsional strain energies decrease when carbon atoms of cyclobutane are replaced with silicon atoms.15 This work was supported by the Russian Foundation for Basic Research (grant nos. 99-03-32511a and 96-15-97469) and by the Research Council of Norway (Programme for Supercomputing). References 1 A. C. Legon, Chem. Rev., 1980, 80, 231. 2 J. R. Koe, D. R. Powell, J. J. Buffy and R. West, Polyhedron, 1998, 17, 1791. 3 (a) E . Hengge and D. Kovar, Z. Anorg. Allg. Chem., 1979, 458, 163; (b) K. Hassler, E. Hengge and D. Kovar, J. Mol. Struct., 1980, 66, 25. 4 C. Kratky, H. G. Schuster and E. Hengge, J. Organomet. Chem., 1983, 247, 253. 5 K. Hassler, Spectrochim. Acta, 1981, A37, 541. 6 V. S. Mastryukov, S. A. Strelkov, L. V. Vilkov, M. Kolonits, B. Rozsondai, H. G. Schuster and E. Hengge, J. Mol. Struct., 1990, 238, 433. 7 V. P. Novikov, S. A. Tarasenko, S. Samdal and L. V. Vilkov, J. Mol. Struct., 1998, 445, 207. 8 British Library Lending Division, Boston Spa, Wetherby, Yorkshire LS23 7BQ, Gr.Britain, Supplementary Publication No. SUP 26396. 9 M. J. Frisch, G.W. Trucks, H. B. Schlegel, P. M.W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A. Pople, Gaussian 94 Program, Revision B.3, Gaussian, Inc., Pittsburgh PA, 1995. 10 (a) V. A. Sipachev, J. Mol. Struct., 1985, 121, 143; (b) V. P. Novikov, V. A. Sipachev, E. I. Kulikova and L. V. Vilkov, J. Mol. Struct., 1993, 301, 29. 11 R. Stolevik, H. M. Seip and S. J. Cyvin, J. Chem. Phys. Lett., 1972, 15, 263. 12 V. P. Novikov, S. Samdal and L. V. Vilkov, J. Mol. Struct., 1997, 413/414, 279. 13 R. S. Grev and H. F. Schaefer, J. Am. Chem. Soc., 1987, 109, 6569. 14 Yu. V. Zefirov and P. M. Zorky, Zh. Strukt. Khim., 1976, 17, 745 [J. Struct. Chem. (Engl. Transl.), 1976, 644]. 15 R. L. Rosas, C. Cooper and J. Laane, J. Phys. Chem., 1990, 94, 1830. sM(s) = W(j)sM(s,j)dj, ò0 jmax Received: 7th June 1999; Com. 99/14