J . Phys. Chem. 1987, 91, 5347-5354 viously been proposed,I7 is unlikely. The alternative mechanism is rapid charge transfer from the complex of CH2Cl' with Ph21PF, to the aromatic compounds. The results of the present study demonstrate that the effect of Ph2IPF6 (or PhJAsF,) in the radiolysis differs from that in the photolysis. This may be attributed to the radiolytic formation of the reactive radicals from the chlorohydrocarbon solvents. The
5347
difference in the effects between Ph21PF6and Ph3SPF6is another feature of the radiolysis. Acknowledgment. We are grateful to Prof. S. P. Pappas of the North Dakota State University for helpful suggestions. We are also indebted to the members of the Radiation Laboratory of this institute for help with the pulse radiolysis experiments.
Molecular Mimicry of Bond Length and Angle Variations in Germanate and Thiogermanate Crystals: A Comparison with Variations Calculated for C-, Si-, and Sn-Containing Oxide and Sulfide Molecules G. V. Gibbs,* Department of Geological Sciences, Virginia Tech, Blacksburg, Virginia 24061
Philippe D'Arco, Ecole Normale Superieure, Laboratoire de Geologie, 75230 Paris Cedex 05, France
and M. B. Boisen, Jr. Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061 (Received: March 30, 1987)
Molecular orbital calculations have been completed on a variety of germanate and thiogermanate molecules, using a newly published 3-21G* basis set for Ge. Potential energy curves and minimum energy bond lengths and angles obtained in these calculations match bond length and angle variations observed in chemically similar crystals. A comparison of these calculations with those completed for silicate and thiosilicate molecules provides insight into why chemically similar Si- and Ge-containing compounds have similar structures, physical properties, and glass-formingtendencies. A comparison of the calculated geometries for H4TX4and H6T2Xmolecules (T = C, Si, Ge, Sn; X = 0,S) provides insights into the local force fields and charge density distributions of the TX bonds and the TXT groups. The calculations provide an understanding of the relative size of the bridging angle of the H6T2Xmolecules in terms of the electron density distribution of the bridging TXT group with wider angles being associated with a delocalization of charge density on the interior side of the angle between bonding peaks. They also indicate that an H4T04 molecule with S4 point symmetry is stabilized relative to one with D2d symmetry as the TO bond length increases in the series T = C, Si, Ge, and Sn.
Introduction The crystal chemistry of Si- and Ge-containing compounds is strikingly similar.] Not only do Si and Ge both crystallize with the well-known diamond structure, but gas phase molecules like H6Si20and H 6 G e 2 0adopt topologically equivalent structures. In addition, germanate analogues of almost all of the major silicates have been synthesized including oligo-, poly-, phyllo-, and tektogermanates.2 Thus, it may be possible to make a structural copy of almost every silicate but the converse may not be true. There are, for example, a variety of germanates3 such as KNd4(Ge4013)(OH,F)4,Sm4Ge3(0H)6and Na4Sc2Ge4OI3that crystallize with structures that have yet to be reported for a silicate. Germanates also differ in that the digermyl GeOGe group bridging two G e 0 4 tetrahedra is about 15' narrower than the bridging disiloxy SiOSi group in silicates and the GeO bond is about 0.15 A longer than the Si0 bond. Since germanates are similar to silicates, molecular orbital (MO) methods that have been used successfully to study the bonding in silicate molecules and crystals should provide valuable (1) Goldschmidt, V. M. Nachr. Ges. Wiss. Gottingen, Math.-Phys. KI. 1931, 184.
(2) Wittmanm, A. Fortschr. Mineral. 1966, 43, 230. (3) Demianets, L. N.; Lobachev, A. N.; Emelchenks, G. A. In RareEarth Germanatec., Organic Crystals. Germanates and Semiconductors; Freyhardt, H. C . , Ed.; Springer: Verlag, 1980; pp 102-144.
0022-3654/87/2091-5347$01.50/0
insights into the bonding in germanate molecules and crystals. It is well kn0wn~3~ that the bond lengths and angles of the SiXSi groups (X = 0,s) in small gas phase molecules like H3SiXSiH, are similar to those in crystalline Six,. Thus, it is not surprising that MO calculations on protonated fragments of silicate and thiosilicate crystal structures have advanced our understanding of the bonding in such crystal^.^-'^ In these calculations, the (4) Almenningen, A.; Bastiansen, 0.;Ewing, V.; Hedberg, K.; Traetteberg, M. Acta. Chem. Scand. 1963, 17, 2455. (5) Gibbs, G. V.; Meagher, E. P.; Newton, M. D.; Swanson, D. K. Structure and Bonding in Crystals; O'Keeffe, M., Navrotsky, A,, Eds.; Academic: New York, 1981; Vol 1, pp 195-225. (6) Tossell, J. A,; Gibbs, G. V. Acta Crystallogr., Sect. A 1978, A34, 463. (7) S a w , J.; Zurawski, B. Chem. Phys. Lett. 1979, 65, 587. (8) OKeeffe, M.; Newton, M. D.; Gibbs, G. V. Phys. Chem. Min., 1980, 6 305. (9) Newton, M. D.; Gibbs, G. V. Phys. Chem. Miner. 1980, 6 , 221. (10) Geisinger, K. L.; Gibbs, G. V. Phys. Chem. Miner. 1981, 7 , 204. (1 1) Gibbs, G. V. A m . Mineral 1982, 67, 421. (12) O'Keeffe, M.; Domenges, B.; Gibbs, G. V. J . Phys. Chem. 1985,89, 2304. (13) OKeeffe M.; Gibbs, G. V. J . Phys. Chem. 1985, 89, 4574. (14) Boisen, Jr., M. B.; Gibbs, G. V . Phys. Chem. Miner., in press. (15) Hess, A. C.; McMillan, P. F.; OKeeffe, M. J . Phys. Chem. 1986, 90, 5661. (16) Gibbs, G. V.; Boisen, Jr., M. B. Better Ceramics Through Chemistry II; Brinker, C. J., Clark, D. E., Ulrich, D. R., Eds.; Materials Research Society, 1986; Vol 73, p 515. (17) Gibbs, G. V.; Finger, L. W.; Boisen, Jr., M. B. Phys. Chem. Miner. 1987, 14, 327.
0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Gibbs et al.
TABLE I: Optimized Geometries for HdTXa . . Molecules, Sa Point Symmetry: T = C, Si, Ge, Sn and X = 0, S H4TX4 HnCOa HiSi0; H4Ge04 H4Sn04 H4CS4 H4SiS4 H4GeS4 H4SnS,
R(TX), A 1.367 1.626 1.742 1.925 1.830 2.138 2.229 2.441
R(OH), A 0.945 0.942 0.965 0.985 1.328 1.329 1.353 1.353
L X T X ( ~ X )deg , 113.2 1 1 5.4 114.7 114.8 112.6 114.6 114.1 115.9
geometries of small molecules like H4SiX4and H6Si2Xare varied in a systematic way until the energies of the resulting configurations are minimized, yielding molecules whose geometries are described as "optimized". These optimized molecules have been taken as mathematical models for the corresponding fragments of silicate and thiosilicate crystals of interest. Not only do the bond lengths and angles calculated for these molecules match those observed for the crystals, but also the shapes of the potential energy curves generated for these molecules conform with the observed SiXSi angle variations. In particular, the wide range of SiOSi angles (1 20-1 80') observed for silicates and silica glass conforms with a broad shallow curve calculated for (OH)3SiOSi(OH)3as a function of the angle. Similarly, the narrow range of SiSSi angles (105-1 15') observed for thiosilicates conforms with the substantially deeper potential energy curve calculated for H6Si2S5. The contrasting shapes of these curves also provide insight into the large variety of polyanions of Si04 tetrahedra adopted by silicate minerals and silica glass compared with the more limited variety of polyanions of SiS4tetrahedra adopted by thiosilicates. Such curves have also been used to explain the ease of SiOzglass formation compared with the more difficult formation of SiS2 g1ass.l0~'* In a study of quantum mechanically derived potential energy surfaces, Lasaga and GibbsIg recently obtained a least-squares fit of an energy surface calculated for the disilicic acid molecule H6Si2O7,using an extended valence type force field model. When this force field was used in a modified version of Busing's WMIN program20 in calculating the structures and elastic properties of the silica polymorphs a-quartz and a-cristobalite, they found that they could reproduce the structures and physical properties of these minerals much better than could be done with an ionic model. The success of these calculations bodes well for future studies of the structural and physical properties for a wide class of materials using the methods of molecular mechanics. It also supports the assertion that the forces that govern the structure of a molecule are not all that different from those that govern the structure of a chemically similar crystal. Because the geometries of the bridging GeXGe groups of the gas-phase molecules H3GeOGeH3 and H3GeSGeH3 are also similar to those recorded for such crystals as G e 0 2 and GeS2, respectively, MO studies of these molecules and chemically related ones should advance our understanding of the GeX bond in both molecular and crystalline germanates and thiogermanates. In this paper, we will undertake a number of such MO calculations as they relate to the bond length and angle variations of germanate and thiogermanate crystals and with the bond lengths and angles calculated for H4TX4and H6T2X(T = C, Si, Ge, Sn) molecules. Also, deformation maps of the TXT groups of the H,TzX molecules will be related to the sizes of TXT angles calculated for these molecules.
Basis Sets and Previous Calculations for Germanium-ContainingCompounds In a preliminary study of the bonding in germanates, Chakoumakos2' calculated minimum energy geometries for the mol( I 8) Navrotsky, A.; Geisinger, K.; McMillan, P.; Gibbs, G. V. Phys. Chem. Miner. 1985, 11, 284. (19) Lasaga, A. C.; Gibbs, G. V. Phys. Chem. Miner. 1987, 14, 107. (20) Busing, W. R. WMIN, a computer program t o model molecules and crystals in terms of potential energy functions: Oak Ridge National Laboratory: Oak Ridge, TN, 1981.
LXTX(4X), deg 107.6 106.6 106.9 106.9 107.9 106.9 107.2 106.3
LTOH, deg 108.7 118.8 118.8 123.8 97.0 97.3 99.0 99.8
f(TX), N / m 905 675 585 430 420 310 270 225
ET,au -339.677 68 -590.920 55 -2365.809 60 -6296.981 15 -1 630.214 60 -1881.42520 -3650.24001 -758 1.490 07
ecules GeO,, H4Ge04,H6Ge20,and H6Ge2O7,using a minimal STO-3G basis set.22 The GeO bond lengths calculated with this basis are uniformly shorter than those observed by about 0.1 8, while the calculated GeOGe angles are wider by 15' or more than observed. As the bond lengths and angles calculated with an STO-3G basis for molecules containing a third- or fourth-row atom are not satisfactory, Dobbs and Hehre23recently developed a more robust split 3-21G basis for these atoms augmented with d-type polarization functions. With the resulting 3-21G* basis set generated for Ge, they calculated a bond length for the germanium monoxide molecule of 1.619 A, a value slightly shorter than that observed (1.625 A), but a value significantly improved over that calculated (1.602 A) with the STO-3G basis. The bond length calculated for the germanium monosulfide molecule (2.004 A) was also found to be slightly shorter than that observed (2.012 A). In the calculations completed in this study, a 3-21G* basis was used on Ge and a 31G* basis was used on H. A 3-21G basis was used on the oxygen atoms of H4Ge04and H6Ge206and on the sulfur atoms of H4GeS4, a 6-31G* basis was used on the 0 of H6Gez0 and a 3-21G* basis was used on the S of H6GezS.
A Comparison of the Molecular Geometries of H4Ge04and H4GeS4with Those of H4TX4(T = C, Si, Sn) A recent optimization of the geometry of H4Si04within the constraints of C1 point symmetry using a 6-31G** basis with polarization functions on all the atoms yielded a set of molecular coordinate^^^ that are S4-equivalentto within 0.001 A. Each of the four S i 0 bond lengths is 1.626 A, each of the four OH bond lengths is 0.942 A, each of the SiOH angles is 118.0°, two of the OSiO angles are 115.5', and four are 106.6' with a total energy of -590.920 55 au. The point symmetry of the molecule agrees with that determined in an earlier study5 using a minimal STO-3G basis and more recent in which the geometry of the molecule was optimized within the constraints of S4point symmetry with a 6-31G* basis with polarizing functions on Si, 0, and H. A geometry optimization of the molecule using the 6-31G** basis and assuming S4point symmetry yielded essentially the same geometry and energy as obtained assuming CI point symmetry (Table I). However, it is not clear why some earlier calculation^^^ yielded a higher energy (-590.8864 au) and a slightly different geometry. To determine the geometries of H4Ge04and H4GeS4,we found the minimum energy geometry of each of these molecules again assuming C1point symmetry. A study of the resulting geometry shows that they both possess S4point symmetry. The GeO and GeS bond lengths obtained in these calculations, 1.742 and 2.229 A, respectively, agree to within 0.01 8, with the average values observed for G e 0 4 (1.75 AZ6)and GeS4 (2.22 A'') tetrahedra in crystals. Frequency distributions for the experimental data are superimposed in Figures 1 and 2 on the potential energy curves (21) Chakoumakos, B. C., Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1984. (22) Pietro, W. J.; Levi, B. A,; Hehre, W. J.; Stewart, R. F. Inorg. Chem. 1980, 19, 2225. (23) Dobbs, K. D.; Hehre, W. J. J . Comput. Chem. 1986, 7 , 359. (24) Boisen, Jr., M. B.; Gibbs, G. V. Comput. Geosci., accepted for publication. (25) Sauer, J. Chem. Phys. Letr. 1983, 97, 275. (26) Shannon, R. D. Acta Crysrallogr., Sect. A . 1976, A32, 751. (27) Shannon, R. D. In "Structure and Bonding in Crystals"; O'Keeffe, M., Navrotsky, A., Eds.; Academic: New York, 1981; Vol 11; pp 53-70.
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MO Calculations on Germanates and Thiogermanates
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-O/
R(Ge'"0) Figure 1. Energy variation of H;1Ge04 as a function af the GeO bond length, R(Ge0). The histogram was constructed with GeO bond length data recorded for tetrahedral G e 0 4 groups in crystals.
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