Molecular structure of tetramethoxygermane, Ge(OCH3)4, determined by gas-phase electron diffraction and ab initio molecular orbital calculations

MOLSTR 11156

Journal of Molecular Structure 522 (2000) 125–134 www.elsevier.nl/locate/molstruc

Molecular structure of tetramethoxygermane, Ge(OCH3)4, determined by gas-phase electron diffraction and ab initio molecular orbital calculations K. Aarset, F.J. Brady, E.M. Page*, D.A. Rice Department of Chemistry, University of Reading, Whiteknights, Reading RG6 6AD, UK Received 23 March 1999; accepted 18 August 1999

Abstract The structure of tetramethoxygermane, Ge(OCH3)4, has been determined by gas-phase electron diffraction (GED) and ab initio molecular orbital calculations. Two distinct conformational geometries are feasible for this molecule, one having S4 symmetry and the other D2d symmetry. The S4 conformer was calculated to be about 3 kcal mol 21 lower in energy than the D2d conformer. Refinements, based upon a dynamic model with S4 symmetry, gave a satisfactory fit to the experimental data. Results for the principal distances (rg) and angles /a from the combined GED/ab initio, with estimated 2s uncertainties are:  r…Ge–O† ˆ 1:743…3†; r…C–O† ˆ 1:413…5†; r…C–H†ave ˆ 1:075…13† A; /O2 GeO7 ˆ 110:1…19†; /GeOC ˆ 122:7…8†; /OCHave ˆ 109:9…24†; F…C3 O2 GeO7 † ˆ 728 (ab initio), F…H6 C3 O2 Ge† ˆ 1768 (ab initio). q 2000 Elsevier Science B.V. All rights reserved. Keywords: Electron diffraction; Gas phase; Molecular structure; Ab initio calculations; Tetramethoxygermane

1. Introduction The title compound is the simplest member of the tetra-alkoxygermanes. First reported in 1953, it finds applications in sol–gel [1] and chemical vapour deposition [2] reactions on account of its volatility and stability. It can be prepared totally free from chlorine which is a great advantage, as the presence of chlorine can have adverse effects on the properties of the products obtained by sol–gel and chemical vapour deposition. For some sol–gel methods higher tetra-alkoxygermanes are required and these are synthesised readily from Ge(OCH3)4. * Corresponding author. Tel.: 1 44-118-931-8454; fax: 1 44118-931-6331. E-mail address: [email protected] (E.M. Page).

Although the structure of Ge(OCH3)4 has not been determined previously an electric dipole moment study of C(OCH3)4, Si(OCH3)4 and Ge(OCH3)4 [3] concluded that rotation around the X–O bond …X ˆ C, Ge or Si) is relatively free. Later the results of electron diffraction studies were interpreted to show that C(OCH3)4 [4] and Si(OCH3)4 [5] exist in the gas phase as monomers with S4 symmetry (see Fig. 1). It is against this background that our study of Ge(OCH3)4 is presented.

2. Experimental 2.1. Preparation Tetramethoxygermane, Ge(OCH3)4, was prepared

0022-2860/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0022-286 0(99)00349-X

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Fig. 1. Diagram of the S4 and the D2d conformers of Ge(OCH3)4.

according to the method of Johnson and Fritz [6]. Dry, degassed MeOH (400 cm 3) was placed under argon in a 1 dm 3 flask that was cooled in an ice bath. Sodium (9.8 g, 0.43 mol) was added and, upon its complete consumption, GeCl4 (20 g, 10.64 cm 3, 0.093 mol) was added dropwise by cannula while the mixture was being stirred vigorously. After completion of the addition, and the subsidence of any visible reaction, the reaction mixture was heated under reflux for 6 h. After this time, the reaction mixture was allowed to cool to room temperature, and the NaCl which precipitated was removed by vacuum filtration. The residual NaCl was washed with dry, degassed Et2O …3 × 20 cm3 † and any further precipitate also removed by vacuum filtration. The ethereal solution was added to the main filtrate and the solvents were removed by distillation (up to 1008C at atmospheric pressure). The residual liquid was distilled in vacuo. A second distillation at atmospheric pressure and 1468C under Ar, yielded the pure product. The product was assessed for purity by 1H NMR (d 3.63, s). No peaks were seen attributable to partly methoxylated germanium, and all impurities in the spectrum amounted to less than 0.05% by integration.

2.2. The electron diffraction experiment Electron diffraction data were obtained with the electron diffraction apparatus at the University of Reading [7] using Kodak Electron Image plates and a nozzle temperature of around 308C. The electron wavelength was calibrated before each experiment ˚ against benzene and was found to be 0.058778 A ˚ (short camera). The (long camera) and 0.058858 A plates were traced using the scanner at the University of Oslo [8]. Five plates from the long camera (ca. 50 cm) and two from the short camera (ca. 25 cm) distances were used in the final refinements. The data covering the ranges 3:00 # s=A 21 # 15:00 and 7:00 # s=A 21 # 25:50 at intervals of Ds ˆ 0:25 A 21 (where s ˆ 4pl21 sin u and 2u is the scattering angle) were processed as previously described [9,10]. A calculated background was subtracted from the data for each plate to yield experimental molecular intensity curves in the form sIm …s† [11]. The experimental intensity curves are shown in Fig. 2 and the data are available as supplementary material. The radial distribution (RD) curve (Fig. 3) was calculated in the usual way by Fourier transformation of the function I 0 m …s† ˆ ZGe ZO …AGe AO †21 sI m …s†exp…2Bs2 †

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Fig. 2. Experimental intensity curves …s4 I t …s††: Each plate is shown magnified 7 × with respect to the final backgrounds on which they are superimposed. The average curves are sI m …s† ˆ s…s4 I t 2 background†:

with B ˆ 0:0025 A 22 and where A ˆ s2 F and F is the absolute value of the complex scattering amplitude. The scattering amplitudes and phases were taken from tables [12].

3. Theoretical model used for refinement of the electron diffraction data It was decided to use a dynamic model in the electron diffraction refinements of Ge(OCH3)4 following consideration of the results of theoretical calculations, carried out as described in the next section. The results predicted the existence, in the gas phase, of two stable conformers with the S4 and D2d symmetry which are depicted in Fig. 1. The rotational barriers between the S4 and D2d conformers are too high (about 4 kcal mol 21) to suggest the presence of free rotation as can be seen from a consideration of the torsional

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potential (see Fig. 4). The calculated frequencies for the torsions around the Ge–O and C–O bonds were predicted to be low (around 40–90 cm 21) and some of the calculated vibrational parameters (root-meansquare amplitudes (l) and perpendicular corrections (K)), obtained using the force-field provided by the ab initio calculations, were large suggesting the presence of significant vibrational motion. Thus it was clear from the theoretical calculations that refinements of the electron diffraction data using nondynamic models were not appropriate. A dynamic model was developed based on the concept that large-amplitude motions of a torsional nature may be represented by a set of pseudo-conformers distributed around the torsional angle such that the sum of the individual contributions represents the torsional motion [13]. Preliminary least-squares refinements of the electron diffraction data were inconclusive in determining if a given conformer (i.e. of either S4 or D2d symmetry) or a mixture was present in the gas phase. A slightly better fit was found for a model consisting of the S4 conformer alone and, since the theoretical calculations predicted this form to be about 3 kcal mol 21 lower in energy than the D2d form (see Fig. 4), a theoretical model with the S4 conformer was used in the analysis. It is not practicable to have a dynamic model that takes into account all eight torsional angles in the molecule. Since four of the torsions are of methyl groups about the C–O bonds it was decided to exclude these from the dynamic model as the hydrogen atoms make little contribution to the scattering intensity. Thus in the dynamic model only the torsions of the methoxy groups were included. These were each assumed to undergo the same degree of rotation and to be ‘in-phase’. This means that when two of the methoxy groups rotate in one direction (represented by F (C3O2GeO7) and F (C8O7GeO2)) the other two rotate by the same amount in the opposite direction. With these provisos eight pseudoconformers were used to describe the torsion around the optimised S4 form at intervals of 58 ranging from F ˆ 57 to 928 with the torsional angle C3O2GeO7 defined as zero when the C3 –O2 bond eclipsed the Ge–O7 bond. The individual pseudo-conformers were weighted by Boltzmann factors determined by a potential …V…F† ˆ V0 1 V1 F 1 V2 F2 1 V3 F3 †; obtained from the ab initio calculations employing

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Fig. 3. Radial distribution curves for Ge(OCH3)4. The experimental curve was calculated from the composite of the two average intensity curves with the use of theoretical data for the region 0 # s=A 21 # 3:00 and B=A 2 ˆ 0:0025: The difference curve is the experimental minus the theoretical curve. The vertical lines indicate important interatomic distances and have lengths proportional to the distance weights.

Hartree–Fock (HF) level of theory and the 6-311G(d) basis set. The pseudo-conformers were treated as distinct molecules undergoing the usual frame vibrations, except for torsional motions about the Ge–O bonds. The structure of each pseudo-conformer was defined using the parameters in the optimised S4 form, modified by the addition of the differences between the parameters of the optimised S4 form and those of the pseudo-conformer in question. These differences

were obtained by ab initio calculations, as described in Section 4. The constraints were applied to the ra model, with the assumption that Dra is equal to Dre, i.e. the vibrational correction is negligible. Cartesian force constants were calculated for the optimised S4 structure using HF/6-311G(d). Using the set of force constants (scaled by a factor of 0.9), but omitting those of the torsional modes, the rootmean-square amplitudes (l), perpendicular corrections

Fig. 4. Torsional potential for Ge(OCH3)4 obtained by ab initio calculations using HF/6-311G(d). The potential was obtained assuming an ‘inphase’ torsion around the Ge–O bonds (see text for explanation).

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Table 1 Results from the ab initio calculations (HF/6-311G(d)) for Ge(OCH3)4 with the C3O2GeC7 torsional angle fixed at different values Parameters a

F ˆ 928

F ˆ 828

F ˆ 728

F ˆ 628

F ˆ 528

r(Ge–O) r(O–C) r(C–H)ave /GeOC /O2GeO7 /O2GeO17 /OCHave F (C3O2GeO7) b F (H6C3O2Ge) E 1 2533 c

1.7321 1.4039 1.0832 126.19 113.96 107.28 110.08 92.0 189.8 20.38738195

1.7322 1.4042 1.0833 125.50 114.05 107.23 110.08 82.0 190.0 20.38838879

1.7324 1.4042 1.0834 125.09 113.77 107.37 110.09 71.7 175.7 20.38859129

1.7326 1.4037 1.0836 124.93 112.84 107.81 110.16 62.0 178.0 20.38745038

1.7326 1.4026 1.8035 126.08 112.81 107.81 110.25 52.0 171.3 20.38465653

˚ and the angles are in degrees. The distances are in A F…C3 O2 GeO7 † ˆ F…C8 O7 GeO2 † ˆ 2F…C13 O12 GeO17 † ˆ 2F…C18 O17 GeO12 †: c Total energies, E, are in Hartree. a

b

(K) and centrifugal distortions (d r) were calculated using ASYM40 [14] for the molecular frame of each pseudo-conformer. The vibrational amplitudes associated with distances characterising each pseudoconformer were linked to the amplitudes in the S4 form with the differences constrained at values obtained by the force-field calculation. Using this theoretical model the structure and vibrational amplitudes of the entire system were defined in terms of the properties of the optimised S4 form. The structural parameters used to describe the S4 form for the analysis of the electron diffraction data were as follows: r(Ge–O), r(C–O), r(C–H)ave, /O2GeO7, /(OCH)ave, /GeOC, F (C3O2GeC7), F (H6C3O2Ge) and the coefficients for the torsion potential (V0, V1, V2, V3). The methyl groups were assumed to have local C3v symmetry. The torsional angle H6C3O2Ge was defined as zero when H6 –C3 eclipsed the O2 –Ge bond. Positive rotation was defined as anti-clockwise rotation of the front group.

4. Theoretical calculations To obtain the structure parameters required to define the different pseudo-conformers in the model used in the electron diffraction analysis, ab initio calculations using the program gaussian 94 [15] were carried out for five pseudo-conformers. The calculations included structure optimisation over the

range 528 # F # 928 at intervals of 108 for the torsion around the Ge–O bonds, assuming an ‘inphase’ rotation (see Section 3) and employing HF/6311G(d) (see Table 1). In the model adopted in the electron diffraction refinements, pseudo-conformers at intervals of 58 were used (while a 108 interval was used in the theoretical calculations described here). The extra values needed for the various parameters for refinement of the GED data were obtained by fitting polynomials to the differences calculated ab initio at every 108. In addition the torsional potential for the torsion around the Ge–O bonds, assuming ‘in-phase’ rotation, from 0 to 3608, was calculated using HF/6-311G(d) and the results are depicted in Fig. 4. To investigate the dependence of the structural parameters on the number of polarisation and diffuse functions (in the 6-311G basis set) and the level of theory used, several calculations were performed. For the S4 form calculations with both HF and second order Møller–Plesset (MP2) levels of theory were carried out, while for the D2d form only HF was used. The results from these calculations are given in Table 2. From the experimental measurements structural trends were observed in the series Ge(OCH3)4, Si(OCH3)4 [5] and C(OCH3)4 [4]. So to discover if the theoretical models exhibited similar trends, ab initio calculations were also performed for the S4 conformers of Si(OCH3)4 and C(OCH3)4. The results from these calculations are given in Table 3.

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Table 2 Results from the ab initio calculations for Ge(OCH3)4

S4 conformer r(Ge–O) r(O–C) r(C–H)ave /GeOC /O2GeO7 /O2GeO17 /OCHave F (C3O2GeO7) e F (H6C3O2Ge) E 1 const f D2d conformer r(Ge–O) r(O–C) r(C–H)ave /GeOC /OCHave /O2GeO7 /O2GeO17 E 1 const f

HF/6311G(d)

6-3111G(d)

6-31111G(d)

6-311G(d,p)

6-3111G(d,p)

6-31111G(d,p)

MP2 b/6311G(d)

6-311G(d,p)

MP2 c/6311G(d)

MP2 d/6311G(d)

1.7324 1.4042 1.0834 125.09 113.77 107.37 110.09 71.7 175.7 20.38859129

1.7329 1.4043 1.0836 125.77 114.02 107.25 110.08 74.3 176.7 20.39856983

1.7329 1.4044 1.0836 125.71 113.98 107.27 110.08 73.9 176.5 20.39908250

1.7325 1.4060 1.0847 125.08 113.86 107.32 110.09 72.0 174.7 20.40648600

1.7330 1.4061 1.0848 125.71 114.13 107.19 110.05 74.8 175.8 20.41488154

1.7330 1.4061 1.0848 125.64 114.09 107.21 110.05 74.3 175.6 20.41531099

1.7659 1.4317 1.0923 118.59 114.43 107.05 109.79 68.6 176.3 20.80627316

1.7663 1.4303 1.0937 118.48 114.65 107.94 109.91 68.7 174.8 20.89688354

1.7579 1.4318 1.0923 118.05 114.18 107.17 109.77 68.2 177.2 20.9562504

1.7585 1.4305 1.0918 118.00 114.21 107.15 109.78 68.2 177.2 20.34592642

1.7342 1.4030 1.0839 124.34 110.30 104.34 112.09 20.38365753

1.7346 1.4028 1.0840 124.76 110.30 104.43 112.05 20.39371366

1.7346 1.4029 1.0840 124.72 110.30 104.44 112.04 20.39424356

1.7343 1.4046 1.0852 124.28 110.31 104.38 112.08 20.40152278

1.7347 1.4046 1.0853 124.65 110.28 104.46 112.03 20.40999919

1.7347 1.4046 1.0853 124.61 110.28 104.47 112.03 20.41044566

˚ and the angles are in degrees. The distances are in A The core electrons excluded from the correlation calculations (i.e. only 4s and 4p electrons included for Ge). c The 3d electrons in Ge were included in the correlation calculations. d All the electrons included in the correlation calculations. e F…C3 O2 GeO7 † ˆ F…C8 O7 GeO2 † ˆ 2F…C13 O12 GeO17 † ˆ 2F…C18 O17 GeO12 †: f Total energies, E, are in Hartree; constant ˆ 2533 for HF and 2534 for MP2. a

b

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Parameters a

Parameters a

Ge(OCH3)4 GED

r(X–O) r(O–C) r(C–H)ave /O2XO7 /OCHave /XOC F (C3O2XO7)

1.743 (3) 1.413 (5) 1.075 (13) 110.1 (19) 109.9 (24) 122.7 (8) [72] This work

Si(OCH3)4 Ab Initio

GED

HF/6-311G(d)

MP2 b/6-311G(d)

1.732 1.404 1.083 113.8 110.1 125.1 72 This work

1.759 1.431 1.092 114.2 109.8 118.0 68 This work

1.614 (1) 1.416 (2) [1.12] 115.5 (10) 111 (1) 122.3 (3) 64 (1) Ref. [4]

C(OCH3)4 Ab Initio

GED

HF/6-11G(d)

MP2 b/6-311G(d)

1.617 1.401 1.083 113.7 110.0 128.1 73 This work

1.638 1.424 1.091 114.7 109.8 122.0 71 This work

1.395 (5) 1.422 (5) 1.114 (3) 114.6 (5) 112 (1) 113.9 (4) 63 (1) Ref. [3]

Ab Initio HF/6-311G(d)

MP2 b/6-311G(d)

1.367 1.406 1.081 112.4 109.4 117.3 66 This work

1.385 1.427 1.090 113.1 109.1 113.9 66 This work

˚ and angles (/a/e for GED and ab initio, respectively) are in degrees. Values in square brackets were kept constant at Distances (rg/e for GED and ab initio, respectively) are in A the calculated values. b All the electrons included in the correlation calculations. a

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Table 3 Comparison of structure parameters for the molecules X(OCH3)4 from gas-phase electron diffraction (GED) and ab initio calculations …X ˆ Ge; Si, C)

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Table 4 Structural parameters for Ge(OCH3)4 Parameters a

r(Ge–O) r(O–C) r(C–H)ave /O2GeO7 /OCHave /GeOC F (C3O2GeO7) F (H6C3O2Ge) V0 V1 V2 V3 r(Ge–O) r(O–C) r(C–H)ave r(O2…O7) r(O2…O12) r(Ge…C) r(C2…O8) r(C2…O13) r(C2…O18) r(C3…C8) r(C3…C13)

Electron diffraction

Ab initio b

ra //a c

re//e

1.739 (3) 1.405 (5) 1.062 (13) 110.1 (19) 109.9 (24) 122.7 (8) [72] [176] [214.8403] [0.7969] [20.0109] 4.437 × 10 25 rg c 1.743 (3) 1.413 (5) 1.075 (13) 2.855 (32) 2.839 (18) 2.767 (9) 3.536 (43) 4.159 (15) 3.307 (30) 4.313 (53) 4.612 (27)

1.732 1.404 1.083 113.8 110.1 125.1 72 176 214.8403 0.7969 20.0109 4.437210 25 re 1.732 1.404 1.083 2.902 2.792 2.787 3.630 4.139 3.287 4.434 4.610

lrefined 0.052 (6) 0.047 [0.077] 0.106 (8) 0.105 (8) 0.100 (8) [0.126] 0.111 (29) [0.136] [0.086] [0.136]

lcalculated 0.042 0.047 0.077 0.085 0.084 0.079 0.126 0.081 0.136 0.086 0.136

˚ and angles (/) are in degrees. Parenthesized values are 2s and include estimates of uncertainties in Distances (r) and amplitudes (l) are in A voltage/nozzle height and of correlation in experimental data. V0 is in kcal mol 21, V1 is in kcal deg 21 mol 21, V2 is in kcal deg 22 mol 21, V3 is in kcal deg 23 mol 21. Values in square brackets were kept constant at the calculated values. b HF level of theory and 6-311G(d) basis set used. c Average distances over all the pseudo-conformers. a

Table 5 Correlation matrix ( × 100) for parameters refined in the final least-squares refinement for Ge(OCH3)4 Parameter

s LS a

r1

r2

r3

/4

/5

/6

l7

l8

l9

r(Ge–O) r(O–C) r(C–H) /OGeO /OCH /GeOC l(Ge–O2) l(O2 –O7) l(O2 –C13)

0.0008 0.0017 0.0044 0.6739 0.8361 0.2952 0.0020 0.0022 0.1006

100

14 100

16 14 100

218 1 26 100

39 213 218 231 100

242 248 216 6 2 100

17 5 24 217 49 23 100

28 11 15 15 7 16 50 100

27 4 1 10 26 1 5 22 100

a

˚ and angles (/) are in degrees. Standard deviations from least-squares refinements. Distances (r) and amplitudes (l) are in A

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5. Refinements and results Refinements of the electron diffraction data to obtain structural information were carried out by the least-squares method [16] by adjusting a theoretical sI m …s† curve simultaneously to the intensity curves, using a unit weight matrix. The geometries were calculated on the basis of ra parameters. These were converted to the ra type required by the scattering intensity formula by using values of the centrifugal distortions (d r), perpendicular amplitude corrections (K) and root-mean-square of vibrations (l). All the bond distances and bond angles were refined, but it was not possible to refine the torsional angles. These were therefore constrained at the values obtained by the ab initio calculations (HF/6-311G(d)). Results from the refinements are given in Table 4. Values for the experimental distances and bond angles were averaged over all pseudo-conformers. Intensity curves calculated for the final model are shown in Fig. 2, together with experimental and difference curves. In Fig. 3 is shown the radial distribution (RD) curve and the correlation matrix for the refined parameters is given in Table 5.

6. Discussion Analysis of the electron diffraction data for Ge(OCH3)4 using a dynamic model with S4 symmetry resulted in good agreement between the experimental and theoretical intensity curves. However the existence of the D2d conformer could not be excluded by the results from electron diffraction data alone. Theoretical calculations carried out for Ge(OCH3)4 predicted the S4 conformer to be lower in energy than the D2d conformer by about 3 kcal mol 21. In addition both C(OCH3)4 [4] and Si(OCH3)4 [5] were previously shown to exist as S4 conformers. This evidence, and the fact that the S4 model gave a slightly better fit to the electron diffraction data than did the D2d model, led us to conclude that Ge(OCH3)4 exists as the S4 conformer in the gas phase. This finding contradicts the results of an electric dipole investigation [3] which found virtually free rotation about the Ge–O bond. Results from our theoretical calculations indicated that the rotations are not free, but that the molecule does have large vibrational motions.

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In the refinement of the electron diffraction data, the torsional potential for the dynamic model was not refined nor were the torsional angles as calculations had shown that reasonable changes in the values of these parameters did not change the main structural parameters in the molecule. The results from the different theoretical calculations are given in Table 2. It can be seen that only small differences in the values of variables were obtained for the calculations with different numbers of polarisation and diffuse functions on the 6-311G basis set, but the same level of theory. Larger differences were observed when the level of theory was changed from HF to MP2. Going from HF to MP2 (with all the core electrons excluded from the correlation calculations i.e. only 4s and 4p orbitals included for Ge), the Ge–O bond increased from 1.732 to ˚ and the O–C bond increased from 1.404 to 1.766 A ˚ . The length of the Ge–O bond obtained in the 1.432 A MP2 calculations was also dependent on which orbitals were included in the correlation calculations. Including the Ge 3d orbitals in the correlation calcu˚ but lations reduced the Ge–O bond length to 1.758 A this value was still longer than that obtained for the HF calculation (using the 6-311G(d) basis set). The GeOC angle changed dramatically when going from the HF to MP2 level of theory. In the HF calculations the angle was about 1258 while in MP2 an angle of 1188 was obtained. Similar changes in the X–O …X ˆ C or Si) and O–C bonds and the XOC angles were observed for Si(OCH3)4 and C(OCH3)4, as for Ge(OCH3)4 when changing the level of theory from HF to MP2 (see Table 3). Even though the absolute values of the structural parameters, especially the Ge– O and O–C bonds, changed with the level of theory used the differences between corresponding parameters in the different pseudo-conformers did not. The results from the HF calculations were therefore chosen for use for in setting up the dynamic model. From Table 4 it can be seen that the calculated bond lengths for Ge(OCH3)4, obtained using HF level of theory, were in very good agreement with the experimentally determined ones, with the exception of the C–H bond length, which was calculated to be somewhat longer. Of special interest are the O–Ge–O angles. The O2 –Ge–O7 angle was calculated to be 113.88 (HF/6311G(d)) while refinements found it to be 110.1(19)8,

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which is close to the tetrahedral value. Thus from the electron diffraction investigation no statistically significant evidence is found for a flattening of the GeO4 tetrahedron. In contrast a flattening of the oxygen tetrahedron was found both in Si(OCH3)4 [5] and C(OCH3)4 [4] …O2 –Si–O7 ˆ 115:5…10† and O2 –C–O7 ˆ 114:6…5†8†: The experimentally determined value for the GeOC angle (122.7(8)8) lies between the values obtained in the HF (1258) and MP2 (1188) calculations. A comparison of the structural parameters, obtained by electron diffraction analysis, of C(OCH3)4, [4] Si(OCH3)4 [5] and Ge(OCH3)4 is given in Table 3. As expected the X–O bond …X ˆ C; Si, Ge) increases on descending Group 14. The length of the O–C bond appears to be largely independent of the central atom (Ge: 1.413(5), Si: ˚ ). This is also in agreement 1.416(2), C: 1.422(5) A with the results from the theoretical calculations (HF/6-311G(d)) for these three molecules where the O–C bonds were calculated to be 1.404, 1.401 and ˚ for Ge(OCH3)4, Si(OCH3)4 and C(OCH3)4, 1.406 A respectively. If the XOC bond angles obtained by electron diffraction are compared it can be seen that the angles in Ge(OCH3)4 and Si(OCH3)4 are similar while the angle in C(OCH3)4 is about 108 smaller. This finding is borne out by theoretical calculations (HF/6311G(d)). Supplementary Data relating to this article are deposited with the B.L.L.D. as Supplementary Publication No. SUP26628. Acknowledgements Financial support from The Norwegian Research Council (NFR) (for KA) is gratefully acknowledged. In addition we thank Snefrid Gundersen of the University of Oslo for measurement of the electron

diffraction intensity data from photographic plates. This work has received support from the Norwegian National Supercomputer Committee (TRU) for a grant of computing time on the Cray J90 and Cray T3E.

References [1] P.J. Melling, J. Am. Chem. Soc. 63 (1984) 1427. [2] J. Pola, R. Fajgar, Z. Bastl, L. Diaz, J. Mater. Chem. 2 (1992) 961. [3] C.W.N. Cumper, A. Melnikoff, A.I. Vogel, J. Chem. Soc. A (1966) 323. [4] F.C. Mijlhoff, H.J. Geise, E.J.M. Van Schaick, J. Mol. Struct. 20 (1973) 393. [5] L.H. Boontstra, F.C. Mijlhoff, G. Renes, A. Spelbos, I. Hargittai, J. Mol. Struct. 28 (1975) 129. [6] O.H. Johnson, H.E. Fritz, J. Am. Chem. Soc. 75 (1953) 718. [7] C.J. Holwill, PhD Thesis, University of Reading, Reading, UK, 1987. [8] S. Gundersen, T. Strand, J. Appl. Cryst. 29 (1996) 638. [9] G. Gundersen, K. Hedberg, J. Chem. Phys. 51 (1969) 2500. [10] K. Hagen, K. Hedberg, J. Am. Chem. Soc. 95 (1973) 1003. [11] L. Hedberg, Abstract of papers, Fifth Austin Symposium on Gas Phase Molecular Structure, Austin TX, March 1974, p. 37. [12] A.W. Ross, M. Fink, R. Hilderbrandt, International Tables of X-ray Crystallography, 4, Kluwer, Dordrecht, Netherlands, 1992. [13] D. Friesen, K. Hedberg, J. Am. Chem. Soc. 102 (1980) 3987. [14] L. Hedberg, I.M. Mills, J. Mol. Spectrosc. 160 (1993) 117. [15] 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. AlLaham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, 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. HeadGordon, C. Gonzalez, J.A. Pople, gaussian 94, Revision D.4, Gaussian, Inc., Pittsburgh, PA, 1995. [16] K. Hedberg, M. Iwasaki, Acta Cryst. 17 (1964) 529.