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Crystal structure refinement and electron density distribution in diaspore

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Abstract

Diaspore from Dilln, Hungary, AlOOH, is orthorhombic with space group Pbnm, a=4.4007(6), b=9.4253(13), c=2.8452(3) Å, and Z=4. The crystal structure and electron distribution have been refined from 791 graphite-monochromatized MoKα data (maximum 2θ=130°) to R=0.035 (R w =0.029). Difference maps show substantial electron density ascribed to covalent bonding in the hydroxyl group, O(2)-H, but no residual density is observed along the Al-O(1,2) bonds. An analysis of the charge distribution implies net charges of +1.47(26), −1.08(16), −0.59(13) and +0.20(5) for Al, O(1), O(2) and H respectively. Semi-empirical molecular orbital calculations of the Hückel type agree with the experimentally determined atomic charge distribution and also allow a rationalization of the observed bond length variations.

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References

  • Alexander, L.E., Smith, G.S.: Single-crystal diffractometry: the improvement of accuracy in intensity measurements. Acta Crystallogr. 17, 1195–1201 (1964)

    Google Scholar 

  • Bartell, L.S., Su, L.S., Yow, H.: Lengths of phosphorus-oxygen and sulfur-oxygen bonds. An extended Hückel molecular orbital examination of Cruickshank's dπ-pπ picture. Inorg. Chem. 9, 1903–1912 (1970)

    Google Scholar 

  • Bartenev, G.M., Varisov, A.Z., Goldanskii, V.I., Prokopev, E.P., Tsyganov, A.D.: Determination of the effective charges of anions in media of the ionic type by the positron method. Russ. Chem. Rev. 41, 305–313 (1972)

    Google Scholar 

  • Basch, H., Viste, A., Gray, H.B.: Valence orbital ionization potentials from atomic spectral data. Theor. Chim. Acta (Berl.) 3, 458–464 (1965)

    Google Scholar 

  • Baur, W.H.: Computer-simulated crystal structures of observed and hypothetical Mg2SiO4 polymorphs of low and high density. Am. Mineral. 57, 709–731 (1972)

    Google Scholar 

  • Becker, P.: Interpretation of experimental charge densities. Phys. Scr. 15, 119–142 (1977)

    Google Scholar 

  • Berkovitch-Yellin, Z., Leiserowitz, L., Nader, F.: Electron density distribution in cumulenes: an X-ray study of the complex allenedicarbonylic acid-acetamide (1:1) at −150° C. Acta Crystallogr. B33, 3670–3677 (1977)

    Google Scholar 

  • Brown, I.D., Wu, K.K.: Empirical parameters for calculating cation-oxygen bond valencies. Acta Crystallogr. B32, 1957–1959 (1976)

    Google Scholar 

  • Burnham, C.W.: Refinement of the crystal structure of kyanite. Z. Kristallogr. Mineral. 118, 337–360 (1963)

    Google Scholar 

  • Busing, W.R., Levy, H.A.: A single crystal neutron diffraction study of diaspore, AlO(OH). Acta Crystallogr. 11, 798–803 (1958)

    Google Scholar 

  • Byström, A.M.: The crystal structure of ramsdellite, an orthorhombic modification of MnO2. Acta Chem. Scand. 3, 163–173 (1949)

    Google Scholar 

  • Chen, R., Trucano, P., Stewart, R.F.: The valence-charge density of graphite. Acta Crystallogr. A33, 823–828 (1977)

    Google Scholar 

  • Chiari, G., Ross, F.K., Gibbs, G.V., Peterson, R.C.: Residual electron density in calcite (accepted for publication). Trans. Am. Geophys. Union 60

  • Christensen, A.N., Jensen, S.J.: Hydrothermal preparation of α-ScOOH and of γ-ScOOH. Crystal structure of α-ScOOH. Acta Chem. Scand. 21, 121–126 (1967)

    Google Scholar 

  • Clementi, E., Raimondi, D.L.: Atomic screening constants from SCF functions. J. Chem. Phys. 38, 2686–2689 (1963)

    Google Scholar 

  • 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)

    Google Scholar 

  • Cooper, W.F., Larsen, F.K., Coppens, P., Giese, R.F.: Electron population analysis of accurate diffraction data. V. Structure and one-center charge refinement of the light-atom mineral kernite, Na2B4O6(OH)2. 3H2O. Am Mineral. 58, 21–31 (1973)

    Google Scholar 

  • Coppens, P.: Evidence for systematic errors in X-ray temperature parameters resulting from bonding effects. Acta Crystallogr. B24, 1272–1274 (1968)

    Google Scholar 

  • Coppens, P.: Direct evaluation of the charge transfer in the tetrathiofulvalene-tetracyanoquinodimethane (TTF-TCNQ) complex at 100° K by numerical integration of X-ray diffraction amplitudes. Phys. Rev. Lett. 35, 98–100 (1975a)

    Google Scholar 

  • Coppens, P.: Measurement of electron densities in solids by X-ray diffraction. In: MTP Int. Rev. Sci., Physical Chemistry, Series Two, Vol. II: Chemical Crystallogr., Robertson, J.M. (ed.). London: Butterworths 1975b, pp. 21–56

    Google Scholar 

  • Coppens, P.: Experimental electron densities and chemical bonding. Angew. Chem. Int. Ed. Engl. 16, 32–40 (1977a)

    Google Scholar 

  • Coppens, P.: Overcoming the free-atom bias with modified least-squares formalisms. Is. J. Chem. 16, 159–162 (1977b)

    Google Scholar 

  • Coppens, P., Coulson, C.A.: The effect of asymmetry of the atomic charge distribution on the positions of terminal atoms as determined with X-rays. Acta Crystallogr. 23, 718–720 (1967)

    Google Scholar 

  • Coppens, P., Guru Row, T.N., Leung, P., Stevens, E.D., Becker, P.T., Wang, Y.W.: Net atomic charges and molecular dipole moments from spherical-atom X-ray refinements and the relation between atomic charge and shape. Acta Crystallogr. A35, 63–72 (1979)

    Google Scholar 

  • Coppens, P., Hamilton, W.C.: Anisotropic extinction corrections in the Zachariasen approximation. Acta Crystallogr. A26, 71–83 (1970)

    Google Scholar 

  • Coppens, P., Pautler, D., Griffin, J.F.: Electron population analysis of accurate diffraction data. II. Application of one-center formalisms to some organic and inorganic molecules. J. Am. Chem. Soc. 93, 1051–1058 (1971)

    Google Scholar 

  • Delflandre, M.: La structure cristalline du diaspore. Bull. Soc. Fr. Mineral. Cristallogr. 55, 140–165 (1932)

    Google Scholar 

  • Dent Glasser, L.S., Ingram, L.: Refinement of the crystal structure of groutite, α-MnOOH. Acta Crystallogr. B24, 1233–1236 (1968)

    Google Scholar 

  • Evans, H.T., Mrose, M.E.: A crystal chemical study of montroseite and paramontroseite. Am. Mineral. 40, 861–875 (1955)

    Google Scholar 

  • Ewing, F.J.: The crystal structure of diaspore. J. Chem. Phys. 3, 203–207 (1935)

    Google Scholar 

  • Ferraris, G., Franchini-Angela, M.: Survey of the geometry and environment of water molecules in crystalline hydrates studied by neutron diffraction. Acta Crystallogr. B28, 3572–3583 (1972)

    Google Scholar 

  • Forsyth, J.B., Hedley, I.G., Johnson, C.E.: The magnetic structure and hyperfine field of goethite (α-FeOOH). Proc. Phys. Soc. London, Sec. C 1, 179–188 (1968)

    Google Scholar 

  • 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. Geol. Soc. Am. Abstr. Progr. 10, 721 (1978)

    Google Scholar 

  • Giese, R.F., Weller, S., Datta, P.: Electrostatic energy calculations of diaspore (α AlOOH), goethite (α FeOOH) and groutite (α MnOOH). Z. Kristallogr. Mineral. 134, 275–284 (1971)

    Google Scholar 

  • Hamilton, W.C.: Significance tests on the crystallographic R factor. Acta Crystallogr. 18, 502–510 (1965)

    Google Scholar 

  • Higgins, J.B., Ribbe, P.H.: Sapphirine II. A neutron and X-ray diffraction study of (Mg-Al)VI and (Si-Al)IV ordering in monoclinic sapphirine. Contrib. Mineral. Petrol. 68, 357–368 (1979)

    Google Scholar 

  • Hill, R.J., Gibbs, G.V., Ross, F.K.: Residual electron density in hemimorphite. Acta Crystallogr. (in press, 1979)

  • Hoffmann, R.: An extended Hückel theory. I. Hydrocarbons. J. Chem. Phys. 39, 1397–1412 (1963)

    Google Scholar 

  • Hoppe, W.: Über die Kristallstruktur von α-AlOOH (Diaspor) und α-FeOOH (Nadeleisenerz). Z. Kristallogr. Mineral. 103, 73–89 (1941)

    Google Scholar 

  • Hoppe, W.: Über die Kristallstruktur von α-AlOOH (Diaspor) II. (Fourieranalyse). Z. Kristallogr. Mineral. 104, 11–17 (1942)

    Google Scholar 

  • Hornstra, J., Stubbe, B.: PW 1100 Data Processing Program. Eidhoven: Holland Philips Res. Lab. 1972

    Google Scholar 

  • International Tables for X-ray Crystallography. Vol. IV. Ibers, J.A., Hamilton, W.C. (eds.). Birmingham, England: Kynoch 1974

    Google Scholar 

  • Iwata, M.: X-ray determination of the electron distribution in crystals of [Co(NH3)6][Cr(CN)6] at 80K. Acta Crystallogr. B33, 59–69 (1977)

    Google Scholar 

  • Johnson, C.K.: ORTEP-II: A FORTRAN thermal-ellipsoid plot program for crystal structure illustrations. Oak Ridge, Tennessee: U.S. Natl. Tech. Inf. Serv. Pub. ORNL-5138 1976

    Google Scholar 

  • Kurki Suonio, K.: Analysis of crystal atoms on the basis of X-ray diffraction. Bari, Italy: Ital. Crystallogr. Assoc. Meeting 1971

  • Marumo, F., Isobe, M., Akimoto, S.: Electron-density distributions in crystals of γ-Fe2SiO4 and γ-Co2SiO4. Acta Crystallogr. B33, 713–716 (1977)

    Google Scholar 

  • Mulliken, R.S.: Electronic population analysis on LCAO-MO molecular wave functions. J. Chem. Phys. 23, 1833–1846 (1955)

    Google Scholar 

  • Pauling, L.: The modern theory of valence. J. Chem. Soc. (Lond.), 1461–1467 (1948)

  • Pauling, L.: The Nature of the Chemical Bond. 3rd edn. New York: Cornell University Press 1960

    Google Scholar 

  • Sasaki, S., Fu**o, K., Takéuchi, Y., Sadanaga, R.: X-ray determination of the electron distributions in olivines and pyroxenes. Abstract S21, XIth IUCr Congress, Warsaw 1978

  • Sheldrick, G.M.: SHELX 76: Program for crystal structure determination. Cambridge University 1976

  • Shintani, H., Sato, S., Saito, Y.: Electron-density distribution in rutile crystals. Acta Crystallogr. B31, 1981–1982 (1975)

    Google Scholar 

  • Slater, J.C.: Quantum theory of molecules and solids. Vol. 2. New York: McGraw-Hill 1965

    Google Scholar 

  • Steele, I.M., Pluth, J.J., Ito, J.: Crystal structure of synthetic LiScSiO4 olivine and comparison with isotypic Mg2SiO4. Z. Kristallogr. Mineral. 147, 119–127 (1978)

    Google Scholar 

  • Stevens, E.D., Coppens, P.: A priori estimates of the errors in experimental electron densities. Acta Crystallogr. A32, 915–917 (1976)

    Google Scholar 

  • Stewart, R.F.: Valence structure from X-ray diffraction data: an L-shell projection method. J. Chem. Phys. 53, 205–213 (1970)

    Google Scholar 

  • Stewart, R.F., Davidson, E.R., Simpson, W.T.: Coherent X-ray scattering for the hydrogen atom in the hydrogen molecule. J. Chem. Phys. 42, 3175–3187 (1965)

    Google Scholar 

  • Takané, K.: Crystal structure of diaspore. Proc. Imp. Acad. Tokyo 9, 113–116 (1933)

    Google Scholar 

  • Thomas, J.O.: Hydrogen bond studies. CXXII. A neutron diffraction and X-N deformation-electron-density study of dimethylammonium hydrogen oxalate, (CH3)2NH2HC2O4, at 298K. Acta Crystallogr. B33, 2867–2876 (1977)

    Google Scholar 

  • Toriumi, K., Ozima, M., Akaogi, M., Saito, Y.: Electron-density distribution in crystals of CoAl2O4. Acta Crystallogr. B34, 1093–1096 (1978)

    Google Scholar 

  • Urusov, V.S.: Heats of sublimation and estimates of effective atomic charges in essentially ionic crystals. Zh. Strukt. Khim. 7, 439–444 (1966)

    Google Scholar 

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

    Google Scholar 

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Hill, R.J. Crystal structure refinement and electron density distribution in diaspore. Phys Chem Minerals 5, 179–200 (1979). https://doi.org/10.1007/BF00307552

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