Ab initio calculated geometries and charge distributions for H4SiO4 and H6Si2O7 compared with experimental values for silicates and siloxanes

Appelo, C.A.J.: Layer deformation and crystal energy of micas and related minerals. I. Structural models for 1M and 2M1 polytypes. Am. Mineral. 63, 782?792 (1978)

Baur, W.H.: The prediction of bond length variations in silicon-oxygen bonds. Am. Mineral. 56, 1573?1599 (1971)

Baur, W.H.: Silicon-oxygen bond lengths, bridging angles, SiOSi and synthetic low tridymite. Acta Crystallogr. Sect. B: 33, 2615?2619 (1977)

Baur, W.H.: Variation of mean Si-O bond lengths in silicon-oxygen tetrahedra. Acta Crystallogr. Sect. B: 34, 1751?1756 (1978)

Binkley, J.S.: The 6-6-31G basis is an elaboration of the 4-4-31G basis (private communication) (1979)

Binkley, J.S., Whiteside, R., Haribaran, P.C., Seeger, R., Hehre, W.J., Lathan, W.A., Newton, M.D., Ditchfield, R., Pople, J.A.: Gaussian 76 ? an ab initio molecular orbital program. Quantum Program Chemistry Exchange, Bloomington, IN (1978)

Bokii, N.G., Struchkov, Y.T.: Structural chemistry of organic compounds of the nontransition elements of group IV (Si, Ge, Sn, Pb). Zh. Strukt. Khim. 4, 722 (1968)

Brown, G.E., Gibbs, G.V., Ribbe, P.H.: The nature and variation in length of the Si-O bond and Al-O bonds in framework silicates. Am. Mineral. 54, 1044?1061 (1969)

Burdett, J.K.: How some simple solids hold together: The use of the fragment formalism in crystal chemistry. J. Am. Chem. Soc. in press (1980)

Clark, J.R., Appleman, D.E., Papike, J.J.: Crystal-chemical characterization of clinopyroxenes based on eight new structure refinements. M.S.A. Spec. Publ. No. 2, 31?50 (1969)

Cohen, J.P., Ross, F.K., Gibbs, G.V.: An X-ray and neutron diffraction study of hydrous low cordierite. Am. Mineral. 62, 67?78 (1977)

Collins, G.A.D., Cruickshank, D.W.J., Breeze, A.: Ab initio calculations on the silicate ion, orthosilicic acid and their L 2,3 X-ray spectra. J. Chem. Soc. Faraday Trans. 2 68, 1189?1195 (1972)

Collins, J.B., Schleyer, P. von R., Binkley, J.S., Pople, J.A.: Self-consistent molecular orbital methods. XVII. Geometries and binding energies of second-row molecules. A comparison of three basis sets. J. Chem. Phys. 64, 5142?5151 (1976)

Coulson, C.A.: Valence. London: Oxford University Press 1961

Craig, D.P., Maccoll, A., Nyholm, R.S., Orgel, L.E., Sutton, L.E.: Chemical bonds involving d-orbitals. J. Chem. Soc. 1954, 332?357 (1954)

Cruickshank, D.W.J.: The role of 3 d-orbitals in ?-bonds between (a) silicon, phosphorus, sulfur, or chlorine and (b) oxygen or nitrogen. J. Chem. Soc. 1077, 5486?5504 (1961)

Dewar, M.J.S., Schmeising, H.N.: Resonance and conjugation-II. Factors determining bond lengths and heats of formation. Tetrahedron 11, 96?120 (1960)

DeJong, B.H.W.S., Brown, G.E.: Molecular orbital study of (Si, Al)2O 4 n? groups in silicates (abstr.). Eos 56, 1076?1077 (1975)

Ditchfield, R., Hehre, W.J., Pople, J.A.: Self-consistent molecular-orbital methods. IX. An extended Gaussian-type basis for molecular-orbital studies of organic molecules. J. Chem. Phys. 54, 724?728 (1971)

Dollase, W.A.: Reinvestigation of the structure of low cristobalite. Z. Kristallogr. 121, 369?377 (1965)

Durig, J.R., Flanagan, M.J., Kalasinsky, V.F.: The determination of the potential function governing the low frequency bending mode of disiloxane. J. Chem. Phys. 66, 2775?2785 (1977)

Gait, R.I., Ferguson, R.B.: Electrostatic charge distributions in the structure of low albite, NaAlSi3O8. Acta Crystallogr. Sect. B: 26, 68?77 (1970)

Gaskell, P.H.: Thermal properties of silica Part 2. Thermal expansion coefficient of vitreous silica. Trans. Faraday Soc. 62, 1505?1510 (1966)

Ghose, S.: Charge density distribution in enstatite, Mg2Si2O6 ? preliminary results (abstr.). Eos 60, 415 (1979)

Gibbs, G.V., Hamil, M.M., Louisnathan, S.J., Bartell, L.S., Yow, H.: Correlations between Si-O bond length, SiOSi angle and bond overlap populations calculated using extended Hückel molecular orbital theory. Am. Mineral. 57, 1578?1613 (1972)

Gibbs, G.V., Hill, R.J., Ross, F.K., Coppens, P.: Net charge distributions and radial dependences of the valence electrons on the Si and O atoms in coesite (abstr.). Abstr. Progr. 3, 407 (1978)

Gibbs, G.V., Louisnathan, S.J., Ribbe, P.H., Phillips, M.W.: Semiempirical molecular orbital calculations for the atoms of the tetrahedral framework in anorthite, low albite, maximum microcline and reedmergnerite. In: The Feldspars, Mackenzie, W.S., Zussman, J. (eds.). Manchester: Manchester Univ. Press 1974, pp. 49?67

Gibbs, G.V., Prewitt, C.T., Baldwin, K.J.: A study of the structural chemistry of coesite. Z. Kristallogr. 145, 108?123 (1977a)

Gibbs, G.V., Meagher, E.P., Smith, J.V., Pluth, J.J.: Molecular orbital calculations for atoms in the tetrahedral frameworks of zeolites. In: Molecular Sieves-II, Katzer, J.R. (ed.) New York: Am. Chem. Soc. 1977b, pp. 19?29

Gilbert, T.L., Stevens, W.J., Schrenk, H., Yoshimine, M., Bagus, P.S.: Chemical bonding effects in the oxygen K? X-ray emission bands of silica. Phys. Rev. B 8, 5977?5998 (1973)

Glasser, L.S Dent, Jamieson, P.B.: Sodium silicate hydrates, V. The crystal structure of Na2O-·SiO2·8H2O. Acta Crystallogr. Sect. B: 32, 705?710 (1976)

Harrison, W.A.: Is silicon dioxide covalent or ionic? In: Physics of SiO2, Pantelides, S.T. (ed.). New York: Pergamon Press 1978, pp. 105?110

Hehre, W.J., Ditchfield, R., Stewart, R.F., Pople, J.A.: Self-consistent molecular orbital methods. IV. Use of Gaussian expansions of Slater-type orbitals. Extension to second row molecules. J. Chem. Phys. 52, 2769?2773 (1970)

Hehre, W.J., Lathan, W.A.: Self-consistent molecular orbital methods. XIV. An extended Gaussian-type basis for molecular orbital studies of organic molecules. Inclusion of second row elements. J. Chem. Phys. 56, 5255?5257 (1972)

Hehre, W.J., Stewart, R.F., Pople, J.A.: Self-consistent molecular-orbital methods. I. Use of Gaussian expansions of Slater-type atomic orbitals. J. Chem. Phys. 51, 2657?2664 (1969)

Hill, R.J., Gibbs, G.V.: Variation in d(T-O), d(T...T) and ?TOT in silica and silicate minerals, phosphates and aluminates. Acta Crystallogr. Sect. B: 35, 25?30 (1979)

Hill, R.J., Gibbs, G.V., Peterson, R.C.: A molecular orbital study of the stereochemistry of pentacoordinated aluminum. Aust. J. Chem. 32, 231?241 (1979)

Iishi, K.: The analysis of the phonon spectrum of ? quartz based on a polarizable ion model. Z. Kristallogr. 144, 289?303 (1976)

Iishi, K.: Lattice dynamics of forsterite. Am. Mineral. 63, 1198?1208 (1978)

Jorgensen, J.D.: Compression mechanisms in ?-quartz structures SiO2 and GeO2. J. Appl. Phys. 49, 5473?5478 (1978)

Konnert, J.H., Appleman, D.E.: The crystal structure of low tridymite. Acta Crystallogr. Sect. B: 34, 391?403 (1978)

Lager, G.A., Hill, R.J., Ross, F.K., Gibbs, G.V.: A difference-Fourier study of electron density in forsterite, Mg2SiO4 (abstr.). Eos 60, 415 (1979)

Lasaga, A.C.: Optimization of CNDO for molecular calculations on silicates (abstr.). Eos 60, 414?415 (1979)

Lazarev, A.N., Poiker, K.R., Tenisheva, R.F.: The force constants of Si-O bonds and their dependence on the nature of substituents on silicon and oxygen. Akad. Nauk SSSR Dokl. Nov. Ser. 175, 1322?1324 (1967)

Levien, L., Prewitt, C.T.: High-pressure crystal structure and compressibility of coesite. In press (1980)

Levien, L., Prewitt, C.T., Weidner, D.J.: Single-crystal X-ray study of quartz at pressure. In press (1980)

Louisnathan, S.J., Gibbs, G.V.: Bond length variation in TO 4 n? tetrahedral oxyanions of the third row elements: T=Al, Si, P, S and Cl. Mater. Res. Bull. 7, 1281?1292 (1972a)

Louisnathan, S.J., Gibbs, G.V.: The effect of tetrahedral angles on Si-O bond overlap populations for isolated tetrahedra. Am. Mineral. 57, 1614?1642 (1972b)

Louisnathan, S.J., Gibbs, G.V.: Variation of Si-O distances in olivines, soda melilite and sodium metasilicate as predicted by semiempirical molecular orbital calculations. Am. Mineral. 57, 1643?1663 (1972c)

Marsh, F.J., Gordon, M.S.: Second row molecular orbital calculations III. Semi-empirical calculations of geometries. J. Mol. Struct. 31, 345?357 (1976)

McLarnan, T.J., Hill, R.J., Gibbs, G.V.: A CNDO/2 molecular orbital study of shared tetrahedral edge conformations in olivine-type compounds. Aust. J. Chem. 32, 949?959 (1979)

Meagher, E.P.: A study of the stereochemistry and energies of single two-repeat silicate chains. Am. Mineral. 65, in press (1980)

Meagher, E.P., Tossell, J.A., Gibbs, G.V.: A CNDO/2 molecular orbital study of the silica polymorphs (abstr.). Abstr. Progr. 9, 1092 (1977)

Meagher, E.P., Tossell, J.A., Gibbs, G.V.: A CNDO/2 molecular orbital study of the silica polymorphs quartz, cristobalite, and coesite. Phys. Chem. Minerals 4, 11?21 (1979)

Mulliken, R.S.: Electronic population analysis on LCAO-MO molecular wavefunctions. I. J. Chem. Phys. 23, 1833?1840 (1955)

Newton, M.D., Gibbs, G.V.: A calculation of bond length and angles, force constants, vertical ionization potentials and charge density distributions for the silicate ion in H4SiO4, H6Si2O7 and H6Si2O (abstr.). Eos 60, 415 (1979)

O'Keeffe, M., Hyde, B.G.: Cristobalites and topologically-related structures. Acta Crystallogr. Sect. B: 32, 2923?2936 (1976)

O'Keeffe, M., Hyde, B.G.: On Si-O-Si configurations in silicates. Acta Crystallogr. Sect. B: 34, 27?32 (1978)

O'Keeffe, M., Newton, M.D., Gibbs, G.V.: Ab initio calculation of interatomic force constants in H6Si2O7 and the bulk modulus of ?-quartz and ?-cristobalite. Phys. Chem. Minerals (1980)

Pacansky, J., Hermann, K.: Ab initio SCF calculations on molecular silicon dioxide. J. Chem. Phys. 69, 963?967 (1978)

Pantelides, S.T., Harrison, W.A.: Electronic structure, spectra and properties of 4:2-coordination materials. I. Crystalline and amorphous SiO2 and GeO2. Phys. Rev. Sect. B: 13, 2667?2691 (1976)

Papike, J.J., Ross, M., Clark, J.R.: Crystal-chemical characterization of clinoamphiboles based on five new structure refinements. Mineral. Soc. Am. Spec. Pap. 2, 117?136 (1969)

Pauling, L.: The principles determining the structure of complex ionic crystals. J. Am. Chem. Soc. 51, 1010?1026 (1929)

Pauling, L.: The Nature of the Chemical Bond, 1st edn. Ithaca, N.Y.: Cornell Univ. Press 1939

Pauling, L.: The modern theory of valency J. Chem. Soc. 1948, 1461?1467 (1948)

Pauling, L.: Interatomic distances and bond character in the oxygen acids and related substances. J. Phys. Chem. 56, 361?365 (1952)

Pauling, L.: The Nature of the Chemical Bond, 3rd edn. Ithaca, N.Y.: Cornell Univ. Press 1960

Peterson, R.C., Hill, R.J., Gibbs, G.V.: A molecular orbital study of distortions in the layer structures brucite, gibbsite and serpentine. Can. Mineral. 17, 703?711 (1979)

Revesz, A.G.: ?-bonding and delocalization effects in SiO2 polymorphs. Phys. Rev. Lett. 27, 1578?1581 (1971)

Rosenberg, M., Martino, F., Reed, W.A., Eisenberger, P.: Compton-profile studies of amorphous and single-crystal SiO2. Phys. Rev. Sect. B: 18, 844?850 (1978)

Sauer, J., Zurawski, B.: Molecular and electronic structure of disiloxane. An ab initio MO study. Chem. Phys. Lett. 65, 587?591 (1979)

Schaefer, N.F. (editor): Modern Theoretical Chemistry, Vol. 4, Applications of Electronic Structure Theory. New York: Plenum Press 1977

Schmiedekamp, A., Cruickshank, D.W.J., Skaarup, S., Pulay, P., Hargittai, I., Boggs, J.E.: Investigation of the basis of the valence shell electron pair repulsion model by ab initio calculation of geometry variations in a series of tetrahedral and related molecules. J. Am. Chem. Soc. 101, 2002?2010 (1979)

Smolin, Yu.I., Shepelev, Yu.F., Butikova, K.: Crystal structure of sodium hydrosilicate Na3HSiO4·5H2O. Sov. Phys. Crystallogr. 18, 173?176 (1973)

Stewart, R.F.: Electron population analysis with rigid pseudoatoms. Acta Crystallogr. Sect. A: 32, 565?574 (1976)

Stone, F.G.A., Seyferth, D.: The chemistry of silicon involving probable use of d-type orbitals. J. Inorg. Nucl. Chem. 1, 112?118 (1955)

Takéuchi, Y., Kudoh, Y.: Hydrogen bonding and cation ordering in Magnet Cove pectolite. Z. Kristallogr. 146, 281?292 (1977)

Takéuchi, Y., Kudoh, Y., Yamanaka, T.: Crystal chemistry of the serandite-pectolite series and related minerals. Am. Mineral. 61, 229?237 (1976)

Tossell, J.A., Gibbs, G.V.: A molecular orbital study of shared-edge distortions in linked polyhedra. Am. Mineral. 61, 287?294 (1976)

Tossell, J.A., Gibbs, G.V.: Molecular orbital studies of geometries and spectra of minerals and inorganic compounds. Phys. Chem. Minerals 2, 21?57 (1977)

Tossell, J.A., Gibbs, G.V.: The use of molecular-orbital calculations on model systems for the prediction of bridging-bond-angle variations in siloxanes, silicates, silicon nitrides and silicon sulfides. Acta Crystallogr. Sect. A: 34, 463?472 (1978)

Tossell, J.A., Vaughan, D.J., Johnson, K.H.: X-ray photoelectron, X-ray emission and UV spectra of SiO2 calculated by the SCF X? scattered wave method. Chem. Phys. Lett. 20, 329?334 (1973)

Urusov, V.S.: Chemical bonding in silica and silicates. Geokhimiya 4, 399?412 (1967)

Varma, R., MacDiarmid, A.G., Miller, J.G.: The dipole moments and structures of disiloxane and methoxysilane. Inorg. Chem. 3, 1756?1757 (1964)

Verhoogen, J.: Physical properties and bond type in Mg-Al oxides and silicates. Am. Mineral. 43, 552?579 (1958)

Wallmeier, H., Kutzelnigg, W.: Nature of the semipolar XO bond. Comparative Ab initio study of H3NO, H2NOH, H3PO, H2POH, H2P(O)E, H2SO, HSOH, HClO, ArO, and related molecules. J. Am. Chem. Soc. 101, 2804?2814 (1979)

Wan, C., Ghose, S., Gibbs, G.V.: Rosenhahnite, Ca3Si3O8(OH)2: crystal structure and the stereochemical configuration of the hydroxylated trisilicate group, [Si3O8(OH)2]. Am. Mineral. 62, 503?512 (1977)

Wenk, H.-R., Raymond, K.N.: Four new structure refinements of olivine. Z. Kristallogr. 137, 86?105 (1973)

Yip, K.L., Fowler, W.B.: Electronic structure of SiO2. II. Calculations and results. Phys. Rev. Sect. B: 10, 1400?1408 (1974)

Zupan, J., Buh, M.: Ab initio calculation on the (Si2O7)6? bitetrahedra. J. Non-Cryst. Solids 27, 127?133 (1978)