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Applications of quantum mechanical potential surfaces to mineral physics calculations

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Abstract

Ab-Initio quantum mechanical calculations on molecular clusters are used to obtain potential surfaces for the SiO bond in silicates. These potential surfaces form the basis for extracting the key parameters in various commonly employed potential functions. Applications to the usual ionic model demonstates a close relation between the ab-initio derived ionic potential and those empirically dervied. The ionic model is then used to predict structures and elastic properties of orthosilicates and of the silica polymorphs. The deficiencies in the ionic model lead to the application of the quantum results to covalent models. These latter models are then used in theoretical calculations of the properties of silica polymorphs.

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References

  • Allinger NL, Sprague JT (1973) Calculation of the structures of hydrocarbons containing delocalized electronic systems by the molecular mechanics method. J Am Chem Soc 95:3893–3907

    Google Scholar 

  • Angell CA, Cheeseman PA, Tammaddon S (1982) Pressure enhancement of ion mobilities in liquid silicates from computer simulation studies to 800 Kilobars. Science 218:85–887

    Google Scholar 

  • Baur WH (1976) Rutile-type compounds. V. Refinement of MnO2 and MgF2. Acta Crystallogr B32:2200–2204

    Google Scholar 

  • Bonczar LJ, Graham EK, Wang H (1977) The pressure and temperature dependence of the elastic constants of pyrope garnet. J Geophys Res 82:2529–2534

    Google Scholar 

  • Bukowinski MST (1980) Effect of pressure on MgO. J Geophys Res 85:285–292

    Google Scholar 

  • Bukowinski MST (1982) Pressure effects on bonding in CaO: Comparison with MgO. J Geophys Res 87:303–310

    Google Scholar 

  • Burdett JK (1982) Predictions of structure of complex solids. Advances in Chemical Physics 49:47–112

    Google Scholar 

  • Busing WR (1981) WMIN. A Computer Program to Model Molecules and Crystals in Terms of Potential Energy Functions. Oak Ridge National Laboratory, Oak Ridge

  • Busing WR, Matsui M (1984) The application of external forces to computational models of crystals. Acta Crystallogr A40:532–538

    Google Scholar 

  • Catlow CRA, Norgett MJ (1973) Shell model calculations of the energies of formation of point defects in alkaline earth fluorides. J Phys C 6:325–1339

    Article  Google Scholar 

  • Catlow CRA, Norgett MJ (1976) Lattice structure and stability of ionic materials. UKAEA Report AERE M 2936

  • Catlow CRA, Norgett MJ, Ross TA (1977) Ion transport and interatomic potentials in the alkaline-earth-fluoride crystals. J Phys C10:1627–1640

    Google Scholar 

  • Catlow CRA, Thomas JM, Parker SC, Jefferson DA (1982) Simulating silicate structures and the structural chemistry of pyroxenoids. Nature 295:658–662

    Article  Google Scholar 

  • Catti M (1982) Atomic charges in Mg2SiO4 (forsterite) fitted to thermoelastic and structural properties. J Phys Chem Solids 43:1111–1118

    Google Scholar 

  • Catti M, Ivaldi G (1983) Charge distribution from least-energy structure in Ca-Mg orthosilicates. Phys Chem Minerals 9:160–166

    Article  Google Scholar 

  • Cohen AJ, Gordon RG (1976) Modified electron-gas study of the stability, elastic properties and high-pressure behavior of MgO and CaO crystals. Phys Rev B, 14:4503–4605

    Article  Google Scholar 

  • Dick BG Jr, Overhauser AW (1958) Theory of the dielectric constants of alkalie halide crystals. Phys Rev 112:1

    Article  Google Scholar 

  • Dienes GJ, Welch DO, Fischer CR, Hatcher RD, Lazareth O, Samberg M (1975) Shell-model calculation of some point-defect properties in α-Al2O3. Phys Rev B 11:3060–3070

    Article  Google Scholar 

  • Downs JW, Gibbs GV (1981) The role of the BeOSi bond in the structures of beryllosilicate minerals. Am Mineral 66:819–826

    Google Scholar 

  • Geisinger, K.L., Gibbs, G.V. (1981) SiSSi and SiOSi bonds in molecules and solids: A comparison. Phys Chem Minerals, 1–7

  • Geisinger KL, Gibbs GV (1983) An x-ray diffraction study of the electron distribution in coesite. Geol Soc Am Annual Meeting, Abstracts 15:580

    Google Scholar 

  • Geisinger KL, Gibbs GV, Navrotsky A (1985) A molecular orbital study of bond length and angle variations in framework structures. Phys Chem Minerals 11:266–283

    Article  Google Scholar 

  • Gibbs GV, Meagher EP, Newton MD, Swanson DK (1981) A comparison of experimental and theoretical bond lengths and angle variations for minerals, inorganic solids, and molecules. In: Structure and Bonding in Crystals, Academic Press Inc, pp 195–225

  • Gibbs GV (1982) Molecules as models for bonding in silicates. Am Mineral 67:421–450

    Google Scholar 

  • Gordon RG, Kim YS (1972) Theory for the forces between closedshell atoms and molecules. J Chem Phys 56:3122–3133

    Article  Google Scholar 

  • Hazen RM, Finger LW (1978) Crystal structures and compressiblities of pyrope and grossular to 60 kbar. Am Mineral 63:297–303

    Google Scholar 

  • Hill RJ, Newton MD, Gibbs GV (1983) A crystal chemical study of stishovite. J Solid State Chem 47:185–200

    Article  Google Scholar 

  • Lasaga AC (1982) Optimization of CNDO for molecular orbital calculations on silicates. Phys Chem Minerals 8:36–46

    Article  Google Scholar 

  • Lasaga AC (1981) The atomistic basis of kinetics: Defects in minerals. In: Lasaga and Kirkpatrick (eds) Rev Mineral Vol. 8: Kinetics of Geochemical Processess, pp 261–317

  • Lasaga AC (1980a) Defect calculations in silicates: Olivine. Am Mineral 65:1237–1248

    Google Scholar 

  • Lasaga AC, Aerni R, Karplus M (1980b) Photodynamics of polyenes I: The effect of electron correlation on potential surfaces. J Chem Phys 73:5230–5243

    Article  Google Scholar 

  • Lasaga AC (1979) Multicomponent exchange and diffusion in silicates. Geochim Cosmochim Acta 43: 455–469

    Google Scholar 

  • Levien L, Prewitt CT, Weidner DJ (1980) Structure and elastic properties of quartz at pressure. Am Mineral 65:920–933

    Google Scholar 

  • Lewis GV, Catlow CRA (1985) Potential models for ionic oxides. J Phys C: Solid State Phys 18:1149–1161

    Google Scholar 

  • Lifson S, Warshel A (1968) Consistent force field for calculations of conformations, vibrational spectra, and enthalpies of cycloalkane and n-alkane molecules. J Chem Phys 49:5116–5127

    Article  Google Scholar 

  • Liu L, Bassett WA, Takahashi T (1974) Effect of pressure on the lattice parameters of stishovite. J Geophys Res 79:1160–1169

    Google Scholar 

  • Matsui M, Busing WR (1983) Calculations of the elastic constants for the olivine and spinel forms of Mg2SiO4. Am Crys Assoc Abs 11:12

    Google Scholar 

  • Matsui M, Matsumoto T (1982) An interatomic potential-function model for Mg, Ca and CaMg olivine. Acta Cryst A 38:513–515

    Article  Google Scholar 

  • Mitra SK, Amini M, Fincham D, Hockney RW (1981) Molecular dynamics simulation of silicon dioxide glass. Philosophical Magazine B 43:365–372

    Google Scholar 

  • Miyamoto M, Takeda H (1984) An attempt to simulate high pressure structures of Mg-silicates by an energy minimization method. Am Mineral 69:711–718

    Google Scholar 

  • Newton MD, Gibbs GV (1980) Ab-initio calculated geometries and charge distributions for H4SiO4 and H6Si2O7 compared with experimental values for silicates and siloxanes. Phys Chem Minerals 6:221–246

    Google Scholar 

  • Novak GA, Gibbs GV (1971) The crystal chemistry of the silicate garnets. Am Mineral 56:791–825

    Google Scholar 

  • O'Keeffe M, Hyde BG (1976) Cristobalites and topologically related structures. Acta Cryst B 32:2923–2936

    Article  Google Scholar 

  • O'Keeffe M, Gibbs GV (1984) Defects in amorphous silica; Ab initio MO calculations. J Chem Phys 81:876–879

    Google Scholar 

  • O'Keeffe M, Newton MD, Gibbs GV (1980) Ab-initio calculation of interatomic force constants in H6Si2O7 and the bulk modulus of α quartz and α cristobalite. Phys Chem Minerals 6:305–312

    Google Scholar 

  • Parker SC (1982) Computer modelling of minerals. UKAEA Report AERE TP968

  • Parker SC (1983) Prediction of mineral crystal structures. Solid State Ionics 8:179–186

    Article  Google Scholar 

  • Pauling L (1980) The nature of silicon-oxygen bonds. Am Mineral 65:321–323

    Google Scholar 

  • Peacor DR (1973) High-temperature single-crystal study of the cristobalite inversion. Z Kristallogr 138:274–298

    Google Scholar 

  • Price GD, Parker SC (1984) Computer simulations of the structural and physical properties of the olivine and spinel polymorphs of Mg2SiO4. Phys Chem Minerals 10:209–216

    Article  Google Scholar 

  • Sanders MJ, Leslie M, Catlow CRA (1984) Interatomic Potentials for SiO2. J Chem Soc Chem Commun 1271–1274

  • Sangster MJL, Dixon M (1976) Interionic potentials in alkali halides and their use in simulations of the molten salts. Adv Physics 25:247–342

    Google Scholar 

  • Soules TF (1979) A molecular dynamic calculation of the structure of sodium silicate glasses. J Chem Phys 71:4570–4578

    Article  Google Scholar 

  • Stewart RF, Whitehead MA, Donnay G (1980) The ionicity of the Si-O bond in low-quartz. Am Mineral 65:324–326

    Google Scholar 

  • Tossell JA, Gibbs GV (1977) Molecular orbital studies of geometries and spectra of minerals and inorganic compounds. Phys Chem Minerals 2:21–57

    Article  Google Scholar 

  • Vail JM, Harker AH, Harding JH, Saul P (1984) Calculations for electronic point defects with self-consistent lattice polarisation: the F + centre in MgO. J Phys C: Solid State Phys 17:3401–3414

    Article  Google Scholar 

  • Warshel A, Karplus M (1972) Calculation of ground and excited states potential surfaces of conjugated molecules. I. formulation and parameterization. J Am Chem Soc 94:5612–5625

    Article  Google Scholar 

  • Yamashita J, Asano S (1970) Electronic state of doubly charged oxygen negative ion in MgO. J Phys Soc Japan 9:944–953

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Geology and Geophysics, Yale University, P.O. Box 6666, 06511, New Haven, Connecticut, USA

    Antonio C. Lasaga

  2. Department of Geological Sciences, Virginia Polytechnic Institute and State University, 24061, Blacksburg, Virginia, USA

    G. V. Gibbs

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  1. Antonio C. Lasaga
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  2. G. V. Gibbs
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Lasaga, A.C., Gibbs, G.V. Applications of quantum mechanical potential surfaces to mineral physics calculations. Phys Chem Minerals 14, 107–117 (1987). https://doi.org/10.1007/BF00308214

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