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Bond length and radii variations in fluoride and oxide molecules and crystals

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Abstract

Molecular orbital calculations completed on fluoride molecules containing first and second row cations have generated bond lengths, R, that match those observed for coordinated polyhedra in crystals to within ∼0.04 Å, on average. The calculated bond lengths and those observed for fluoride crystals can be ranked with the expression R=Kp −0.22, where p=s/r, s is the Pauling strength of the bond, r is the row number of the cation and K=1.34. The exponent -0.22 (≈ -2/9) is the same as that observed for oxide, nitride and sulfide molecules and crystals. Bonded radii for the fluoride anion, obtained from theoretical electron density maps, increase linearly with bond length. Those calculated for the cations as well as for the fluoride anion match calculated promolecule radii to within ∼0.03 Å, on average, suggesting that the electron density distributions in the vicinity of the minima along the bond paths possess a significant atomic component despite bond type.

Bonded radii for Si and O ions provided by experimental electron density maps measured for the oxides coesite, danburite and stishovite match those calculated for a series of monosilicic acid molecules. The resulting radii increase with bond length and coordination number with the radius of the oxide ion increasing at a faster rate than that of the Si cation. The oxide ion within danburite exhibits several distinct radii, ranging between 0.9 and 1.2 Å, rather than a single radius with each exhibiting a different radius along each of the nonequivalent bonds with B, Si and Ca. Promolecule radii calculated for the coordinated polyhedra in danburite match procrystal radii obtained in a structure analysis to within 0.002 Å. The close agreement between these two sets of radii and experimentally determined bonded radii lends credence to Slater's statement that the difference between the electron density distribution observed for a crystal and that calculated for a procrystal (IAM) model of the crystal “would be small and subtle, and very hard to determine by examination of the total charge density.”

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References

  1. Bader RFW, Beddall PM, Cade PE (1971) Partitioning and characterization of molecular charge distributions. J Amer Chem Soc 93:3095–3107

  2. Bartelmehs KL, Gibbs GV, Boisen Jr. MB (1989) Bond-length and bonded-radii variations in sulfide molecules and crystals containing main-group cations: A comparison with oxides. Am Mineral 74:620–626

  3. Baur WH (1970) Bond length variation and distorted coordination polyhedra in inorganic crystals. Transactions of the Am Crystallogr Assoc 6:129–155

  4. Baur WH (1987) Effective ionic radii in nitrides. Chem Rev 1:59–83

  5. Boisen Jr. MB, Gibbs GV (1988) MATOP: An interactive FORTRAN77 program for solving problems in geometrical crystallography. Comput Geosci 14:37–53

  6. Boisen Jr. MB, Gibbs GV, Downs RT, D'Arco P (1990) The dependence of the SiO bond length on structural parameters in coesite, the silica polymorphs and the clathrasils. Am Mineral 75:748–754

  7. Boisen Jr. MB, Gibbs GV (1993) A modeling of the structure and compressibility of quartz with a molecular potential and its transferability to cristobalite and coesite. Phys Chem Minerals 19:120–135

  8. Bragg WL (1920) The arrangement of atoms in crystals. Philos Mag J Sci 40:169–189

  9. Brown GE, Gibbs GV, Ribbe PH (1969) The nature and variation in length of the Si-O and Al-O bonds in framework silicates. Am Mineral 54:1044–1061

  10. Brown ID, Shannon RD (1973) Empirical bond-strength-bondlength curves for oxides. Acta Crystallogr A 29:266–282

  11. Buterakos LA (1990) Bond length and bonded radii variations in nitride molecules and crystals. MS Dissertation. Virginia Polytechnic Institute and State University, 28 pp. Blacksburg, Virginia

  12. Buterakos LA, Gibbs GV, Boisen Jr MB (1992) Bond length variation in hydronitride molecules and nitride crystals. Phys Chem Minerals 19:127–132

  13. Cahen D (1988) Atomic radii in ternary adamantines. J Phys Chem Sol 49(1):103–111

  14. Chelikowsky JR, King Jr. HE, Troullier N, Martins JL, Glinnemann J (1990) Structural properties of α-quartz near the amorphous transition. Phys Rev Lett 65:3309–3312

  15. Coppens P, Hall MB (1982) Electron distributions and the chemical bond. Plenum Press, NY 1–479

  16. Cruickshank DWJ (1961) The role of 3d-orbitals in π-bonds between (a) silicon, phosphorous, sulfur, or chlorine and (b) oxygen or nitrogen. J Chem Soc 1077:5486–5504

  17. Downs JW (1991) Electrostatic properties of minerals from x-ray diffraction data: A Guide for accurate atomistic models. In: Ganguly J (Ed) Diffusion, Atomic Ordering and Mass Transport. Springer-Verlag, NY, 91–119

  18. Downs JW, Swope RJ (1992) The laplacian of the electron density and the electrostatic potential of danburite, CaB2Si2O8. J Phys Chem 96:4834–4840

  19. Feth S, Gibbs GV, Boisen Jr. MB, Myers RH (1993) Promolecule and crystal radii for nitrides, oxides, and sulfides ⊕ comparison with effective and ionic radii. J Phys Chem 11445–11450

  20. Frisch MJ, Binkley JS, Schlegel HB, Rahavachari K, Melius CF Martin RL, Stewart JJP, Bobrowicz FW, Rohlfing CM, Kahn LR, Defrees DJ, Seeger R, Whiteside RA, Fox DJ, Fleuder EM, Pople JA (1984) Gaussian 86. Carnegie-Mellon Quantum Chemistry Publishing Unit, Pittsburgh, PA

  21. Fumi FG, Tosi MP (1964) Ionic sizes and Born repulsion parameters in the NaCl-type alkali halides (I) Huggins-Mayer and Pauling forms. J Phys Chem Sol 25:31–43

  22. Geisinger KL, Gibbs GV (1981) SiSSi and SiOSi bonds in molecules and solids: A comparison. Phys Chem Minerals 7:204–210

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

  24. Gibbs GV, Hamil MM, Louisnathan SJ, Bartell LS, Yow H (1972) Correlations between Si-O bond length, Si-O-Si angle and bond overlap populations calculated using extended Huckel molecular orbital theory. Am Mineral 57:1578–1613

  25. Gibbs GV, Meagher EP, Newton MD, Swanson DK (1981) A comparison of experimental and theoretical bond length and angle variations for minerals, inorganic solids, and molecules. In O'Keeffe M, Navrotsky A, Eds., Structure and Bonding in Crystals. Acad Press, NY 1:195–225

  26. Gibbs GV, Boisen Jr. MB (1986) Molecular mimicry of structure and electron density distributions in minerals. Mat Res Soc Syyp Proc 73:515–527

  27. Gibbs GV, D'Arco P, Boisen Jr. MB (1987) Molecular mimicry of the bond length and angle variations in germinate and thiogerminate crystals: a comparison with variations calculated for carbon-, silicon-, and Sn-containing oxide and sulfide molecules. J Phys Chem 91:5347–5354

  28. Gibbs GV, Finger LW, Boisen Jr. MB (1987) Molecular mimicry of the bond length — bond strength variations in oxide crystals. Phys Chem Minerals 14:327–331

  29. Gibbs GV, Boisen Jr. MB, Downs RT, Lasaga AC (1988) Mathematical modeling of the structures and bulk moduli of TX2 quartz and cristobalite structure-types, T=C,Si,Ge and X=O,S. Mat Res Soc Symp Proc 121:155–165

  30. Gibbs GV, Spackman MA, Boisen Jr. MB (1992) Bonded and promolecule radii for molecules and crystals. Am Mineral 77:741–750

  31. Gourary BS, Adrian FJ (1960) Wave functions for electron-excess color centers in alkali halide crystals. Sol State Phys 10:127–247

  32. Johnson O (1973) Ionic radii for spherical potential ions. I. Inorg Chem 12:780–785

  33. Johnson O (1975) Ionic radii for spherical potential ions. II. Chemic Scr 5–10

  34. Julian MM, Gibbs GV (1985) Bonding in silicon nitrides. J Phys Chem 89(25):5476–5480

  35. Julian MM, Gibbs GV (1988) Modelling the configuration about the nitrogen atom in methyland silyl-substituted amines. J Phys Chem 92(6):1444–1451

  36. Lasaga AC, Gibbs GV (1987) Application of quantum mechanical potential surfaces to mineral physics calculations. Phys Chem Minerals 14:107–117

  37. Lasaga AC, Gibbs GV (1988) Quantum mechanical potential surfaces and calculations on minerals and molecular clusters I: STO-3G and 6–31G* results. Phys Chem Minerals 16:29–41

  38. Lasaga AC, Gibbs GV (1991) Quantum mechanical Hartree-Fock surfaces and calculations on minerals II:6–31G* results. Phys Chem Minerals 17:485–491

  39. Lazarev AN, Mirgorodsky AP (1991) Molecular force constants in dynamical model of α-quartz. Phys Chem Minerals 18:231–243

  40. McMillan PF, Hess AC (1990) Ab initio valence force field calculations for quartz. Phys Chem Minerals 17:97–107

  41. 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

  42. Nicoll JS (1993) Systematics of bond length and radii variations in fluoride and silicate molecules and crystals. MS Dissertation. Virginia Polytechnic Institute and State University, 58 pp. Blacksburg, Virginia

  43. O'Keeffe M (1981) Some aspects of the ionic model for crystals. O'Keeffe M, Navrotsky A (Eds) Struc bonding cryst Vol II, pp 299–322. Acad Press Inc. NY

  44. O'Keeffe M, Hyde BG (1985) An alternative approach to nonmolecular crystal structures with emphasis on arrangements of cations. Struc Bonding Springer-Verlag Berlin, Heidelberg, Vol. 61:77–144

  45. Pauling L (1960) The Nature of the Chemical Bond, 3rd edition. Cornell Univ Press, Ithaca, NY

  46. Purton J, Jones R, Catlow CRA, Leslie M (1993) Ab initio potentials for the calculation of the dynamical and elastic properties of α-quartz. Phys Chem Minerals 19:392–400

  47. Shannon RD (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr 32:751–767

  48. Shannon RD (1981) Bond distances in sulfides and a preliminary table of sulfide crystal radii. In: O'Keeffe O, Navrotsky A (Eds) Struc bonding in cryst. Acad Press Inc. NY, Vol II, pp 53–70

  49. Shannon RD, Prewitt CT (1969) Effective ionic radii in oxides and fluorides. Acta Crystallogr B25:925–946

  50. Slater JC (1965) Quantum theory of molecules and solids.Vol 2: Symmetry and energy bands in crystals. McGraw-Hill Inc. NY

  51. Smith JV (1953) Reexamination of the crystal structure of melilite. Am Mineral 38:643–661

  52. Spackman MA, Hill RJ, Gibbs GV (1987) Exploration of structure and bonding in stishovite with Fourier and pseudoatom refinement methods using single crystal and powder X-ray diffraction data. Phys Chem Minerals 14:139–150

  53. Stixrude L, Bukowinski MST (1988) Simple covalent potential models of tetrahedral SiO2: Applications to α-quartz and coesite at pressure. Phys Chem Minerals 16:199–206

  54. Tossel JA, Gibbs GV (1978) The use of molecular-orbital calculations on model systems for the prediction of bridging-bondangle variations in siloxanes, silicates, silicon nitrides and silicon sulfides. Acta Crystallogr A34:463–472

  55. Tsuneyuki S, Tsukada M, Aoki H, Matsui Y (1988) First-principles interatomic potential of silica applied to molecular dynamics. Phys Rev Lett 61:869–872

  56. van Beest BWH, Kramer GJ, van Santen RA (1990) Force fields for silica and aluminophosphate based ab initio calculations. Phys Rev Lett 64:1955–1958

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Nicoll, J.S., Gibbs, G.V., Boisen, M.B. et al. Bond length and radii variations in fluoride and oxide molecules and crystals. Phys Chem Minerals 20, 617–624 (1994). https://doi.org/10.1007/BF00211857

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Keywords

  • Bond Length
  • Electron Density Distribution
  • Molecular Orbital Calculation
  • Bond Path
  • Fluoride Anion