Skip to main content
Log in

A molecular orbital study of bonding in sulfate molecules: Implications for sulfate crystal structures

  • Published:
Physics and Chemistry of Minerals Aims and scope Submit manuscript

Abstract

Molecular orbital calculations have been completed on sulfate monomers and a dimer in a determination of minimum-energy geometries and electron density distributions. SO bond lengths calculated for the monomer and dimer correlate linearly with the fractional s-characters of the bonds, as observed for sulfate groups in crystals. With increasing coordination number of S, the bonded radii of S and O, as determined from electron density maps, increase at the same rate. This is at variance with the assumption that the radius of the oxide ion is nearly constant and that bond length variations arise primarily from changes in cation radii. The dimer shows a relatively large change in energy as its SOS angle is deformed from its minimum-energy value (125.6°) to 180°, in conformity with the small variation among observed angles. This is in contrast to the wide variation of bridging angles observed for silicate and phosphate dimers in crystals and molecules, and may imply that significant differences should be expected in the behavior of sulfates with respect to polymorphism and glass formation. The reaction energy of SO3 + H2O → H2SO4, calculated with second-order Møller-Plesset perturbation theory, agrees with the experimental value. Other properties of H2SO4 are also calculated and compared with experimental observations and previous calculations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Almenningen A, Bastiansen O, Ewing V, Hedberg K, Traetteberg M (1963) The molecular structure of disiloxane, (SiH3)2O. Acta Chim Scand 17:2455–2460

    Google Scholar 

  • Barrow MJ, Ebsworth EAV, Harding MM (1979) The crystal and molecular structures of disiloxane (at 108K) and hexamethyl-disiloxane (at 148K). Acta Crystallogr B35:2093–2099

    Google Scholar 

  • Baur WH (1970) Bond-length variation and distorted coordination polyhedra in inorganic crystals. Trans Am Crystallogr Assoc 6:125–155

    Google Scholar 

  • Bingel WA, Luttke W (1981) Hybrid orbitals and their applications in structural chemistry. Angew Chemie 20:899–911

    Google Scholar 

  • Binkley JS, Frisch MJ, DeFrees DJ, Raghavachari K, Whiteside RA, Schlegel HB, Fluder EM, Pople JA (1982) GAUSSIAN 82. Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA

    Google Scholar 

  • Boisen Jr MB, Gibbs GV (1987) A method for calculating fractional s-character for bonds of tetrahedral oxyanions in crystals. Phys Chem Minerals 14:373–376

    Google Scholar 

  • Böttger H (1974) Vibrational properties of non-crystalline solids. Phys Status Solidi B64:9–43

    Google Scholar 

  • Chase MW, Curnutt JL, Downey JR, McDonald RA, Syverud AN, Valenzuela EA (1982) JANAF thermochemical tables, 1982 supplement. J Phys Chem Ref Data 11:695–940

    Google Scholar 

  • Chen TS, Plummer PLM (1985) Ab initio MO investigation of the gas-phase reaction SO3 + H2O → H2SO4. J Phys Chem 89:3689–3963

    Google Scholar 

  • Coulson CA (1961) Valence. Oxford University Press, London

    Google Scholar 

  • Dean P (1972) The vibrational properties of disordered systems: numerical studies. Rev Mod Phys 44:127–168

    Google Scholar 

  • Douglade J, Mercier R (1979) Structure crystalline du disulfate d'antimoine (III) Sb2(S2O7)3. Acta Crystallogr B35:1062–1067

    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 

  • Dytrych WJ (1983) A comparison of theoretical and observed bridging bond lengths and angles in condensed phosphates and sulfates. M.S. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA

    Google Scholar 

  • Einstein FW, Willis AC (1981) Structure of tellurium (IV) pyrosulfate. Acta Crystallogr B37:218–220

    Google Scholar 

  • Finger LW, Gibbs GV (1985) A derivation of bonded radii from theoretical molecular charge distributions (abstr). EOS 66(18):356

    Google Scholar 

  • Frisch MJ, Schaefer III HF, Binkley JS (1985) Theoretical study of the structure and spectroscopic characteristics of protonated carbon dioxide. J Phys Chem 89:2192–2194

    Google Scholar 

  • Frisch MJ, Yamaguchi Y, Gaw JF, Schaefer III HF, Binkley JS (1986) Analytic Raman intensities from molecular electronic wave functions. J Chem Phys 84:531–532

    Google Scholar 

  • Geisinger KL (1983) A theoretical and experimental study of bonding in silicates and related materials. Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA

    Google Scholar 

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

    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

    Google Scholar 

  • Geisinger KL, Spackman MA, Gibbs GV (1987) Exploration of structure, electron density distribution and bonding in coesite with Fourier and pseudoatom refinement methods using single crystal x-ray diffraction data. Chem Phys 91:3237–3244

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Gibbs GV, D'Arco P, Boisen Jr MB (1988) 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. Phys Chem Minerals (in press)

  • 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

    Google Scholar 

  • Gibbs GV, Hamil MM, Lousinathan SJ, Bartell LS, Yow H (1972) Correlations between SiO bond length, SiOSi angle, and bond overlap populations calculated using extended Hückel molecular orbital theory. Am Mineral 57:1578–1613

    Google Scholar 

  • 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, Vol 1, pp 195–225. Academic Press, New York

    Google Scholar 

  • Giguere PA, Savoie R (1963) The normal vibrational frequencies and the thermodynamic functions of H2SO4 and D2SO4. J Am Chem Soc 85:287–289

    Google Scholar 

  • Gillespie RJ (1972) Molecular Geometry. Van Nostrand Reinhold, London

    Google Scholar 

  • Goldschmidt VM (1954) Geochemistry (Alex Muir, ed). Oxford University Press, London

    Google Scholar 

  • Hehre WJ, Radom L, Schleyer R, Pople JA (1986) Ab initio Molecular Orbital Theory. Wiley, New York

    Google Scholar 

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

    Google Scholar 

  • Holmquist S (1978) Reaction models for sulphate in glass. Phys Chem Glasses 18:76–77

    Google Scholar 

  • Jackson MD, Gibbs GV (1988) A modeling of the coesite and feldspar framework structure types of silica as a function of pressure using MEG methods. J Phys Chem (in press)

  • Jackson MD, Gordon RG (1987) Electron-gas theory of Mg2SiO4 — olivine and spinel. Chem Minerals (in press)

  • Klahn B (1983) The relations between the valence angles of sp3-hybridized central atoms for all possible local symmetries. J Molec Struc 104:49–77

    Google Scholar 

  • Klein C, Hurlburt CS (1985) Manual of Mineralogy, 20th edn. (after J.D. Dana). Wiley, New York

    Google Scholar 

  • Kuczkowsky RL, Suenram RD, Lovas FD (1981) Microwave spectrum, structure, and dipole moment of sulfuric acid. J Am Chem Soc 103:2561–2566

    Google Scholar 

  • Louisnathan SJ, Hill RF, Gibbs GV (1977) Tetrahedal bond length variations in sulfates. Phys Chem Minerals 1:53–69

    Google Scholar 

  • Narasimham PSL, Rao KJ (1978) Phase diagram and glass formation in the K2SO4-ZnSO4 system. J Non-Cryst Solids 27:225–246

    Google Scholar 

  • Navrotsky A, Geisinger KL, McMillan P, Gibbs GV (1985) The tetrahedral framework in glasses and melts-Inferences from molecular orbital calculations and implications for structure, thermodynamics, and physical properties. Phys Chem Minerals 11:284–298

    Google Scholar 

  • O'Keeffe M, Gibbs GV (1985) Ab initio MO calculations on cyclodisiloxanes and other Si-X-Si-X rings and the problem of “silica-w”. J Phys Chem 89:4574–4577

    Google Scholar 

  • Newton MD (1981) Theoretical probes of bonding in the siloxyl group. In: O'Keeffe M, Navrotsky A (eds) Structure and Bonding in Crystals, Vol 1. Academic Press, New York

    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 silioxanes. Phys Chem Minerals 6:221–246

    Google Scholar 

  • O'Keeffe M, Domenges B, Gibbs GV (1985) Ab initio molecular orbital calculations on phosphates: comparison with silicates. J Phys Chem 89:2304–2309

    Google Scholar 

  • Shannon RD (1981) Bond distances in sulfides and a preliminary table of sulfide crystal radii. In: O'Keeffe M, Navrotsky A (eds) Structure and Bonding in Crystals, Vol. 2. Academic Press, New York

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • Stull DR, Prophet H (eds) (1971) JANAF Thermochemical Tables, 2nd ed. National Bureau of Standards, Washington, DC

    Google Scholar 

  • Sundar HGK, Rao KJ (1980) Glass formation in the ternary sulphate system K2SO4-Na2SO4-ZnSO4. J Chem Soc Faraday I 76:1617–1626

    Google Scholar 

  • Tossell JA (1983) A qualitative molecular orbital study of the stability of polyanions in mineral structures. Phys Chem Minerals 9:115–123

    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

    Google Scholar 

  • Tossell JA, Gibbs GV (1978) 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 A34:463–472

    Google Scholar 

  • Warren BE (1972) X-ray studies of the structure of glass. Soviet Phys Crystallogr 16:1106–1113

    Google Scholar 

  • Yamaguchi Y, Frisch MJ, Gaw JF, Schaefer III HF, Binkley JS (1986) Analytic evaluation and basis set dependence of intensities of infrared spectra. J Chem Phys 84:2262–2278

    Google Scholar 

  • Yu PY, Mak TCW (1978) Refinement of the crystal structure of anhydrous sulfuric acid. J Cryst Molec Struc 8:193–199

    Google Scholar 

  • Zhang ZG, Boisen Jr MB, Finger LW, Gibbs GV (1985) Molecular mimicry of the geometry and charge density distribution of polyanions in borate minerals. Am Mineral 70:1238–1247

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lindsay, C.G., Gibbs, G.V. A molecular orbital study of bonding in sulfate molecules: Implications for sulfate crystal structures. Phys Chem Minerals 15, 260–270 (1988). https://doi.org/10.1007/BF00307515

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00307515

Keywords

Navigation