Abstract
The experimental multipole electron density, ρ(r), of diopside was derived from high-resolution single-crystal diffraction at room temperature. Its topological analysis revealed predominantly ionic Si–O bonding, as found in electron density studies of other silicates. In particular, the non-bridging Si–O bonds are slightly less ionic in character than the bridging Si–O bonds. The Ca–O and Mg–O bonds are classified as pure closed-shell ionic interactions. An analysis of –∇2ρ(r) showed the presence of maxima around the oxygen atoms, associated to lone pairs domains that are involved in bonds with the surrounding ions. Calculation of atomic basins gave net charges of –1.56(12), 3.11(17), 1.79(13) and 1.88(18) e for O (averaged), Si, Ca and Mg atoms, respectively. O···O interactions between the O atoms at the vertices of the SiO4 tetrahedron were also detected from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. All these results were also confirmed by periodic restricted Hartree–Fock (RHF) calculations.
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Abramov YuA (1997) On the possibility of kinetic energy density evaluation from the experimental electron-density distribution. Acta Crystallogr A 53:264–272
Bader RFW (1994) Atoms in molecules—a quantum theory. Oxford University Press, Oxford
Bianchi R, Forni A (2005) VALTOPO: a program for the determination of atomic and molecular properties from experimental electron densities. J Appl Cryst 38:232–236
Bruno E, Carbonin S, Molin G (1982) Crystal structures of Ca-rich clinopyroxenes on the CaMgSi2O6–Mg2Si2O6 join. Tschermaks Min Petr Mitt 29:223–240
Cameron M, Papike JJ (1980) Crystal-chemistry of silicate pyroxenes. In: Prewitt CT (eds) Reviews in mineralogy. VII. Pyroxenes. Mineralogical Society of America, Washington DC, pp 5–92
Clark JR, Appleman DE, Papike JJ (1969) Crystal-chemical characterization of clinopyroxenes based on eight new structure refinements. Miner Soc Am Spec Pap 2:31–50
Clementi E, Roetti C (1974) Roothan-Hartree–Fock atomic wavefunctions. At Data Nucl Data Tables 14:177–478
Desiraju GR, Steiner T (1999) The weak hydrogen bond. Oxford University Press, New York
Downs RT, Gibbs GV, Boisen Jr MB, Rosso KM (2002) A comparison of procrystal and ab initio model representations of the electron-density distributions of minerals. Phys Chem Minerals 29:369–385
Downs RT (2003) Topology of the pyroxenes as a function of temperature, pressure, and composition as determined from the procrystal electron density. Am Mineral 88:556–566
Espinosa E, Molins E, Lecomte C (1998) Hydrogen bond strengths revealed by topological analyses of experimentally observed electron densities. Chem Phys Lett 285:170–173
Espinosa E, Alkorta I, Elguero J, Molins E (2002) From weak to strong interactions: a comprehensive analysis of the topological and energetic properties of the electron density distribution involving X–H···F–Y systems. J Chem Phys 117:5529–5542
Finger LW, Ohashi Y (1976) The thermal expansion of diopside to 800°C and a refinement of the crystal structure at 700°C. Am Mineral 61:303–310
Gatti C (1999) TOPOND−98: an electron density topological program for systems periodic in N (N=0–3) dimensions, User’s Manual, CNR-CSRSRC, Milan, http://www.istm.cnr.it/~gatti/TOPOND.ppt
Gatti C (2005) Chemical bonding in crystals: new directions. Z Kristallogr 220:399–457
Gibbs GV, Downs JW, Boisen MB (1994) The elusive SiO bond. In: Heaney PJ, Prewitt CT, Gibbs GV (eds) Reviews in mineralogy. Mineralogical Society of America, Washington DC, pp 331–368
Gibbs GV, Boisen MB, Rosso KM, Teter DM, Bukowinski MST (2000) Model structures and electron density distributions for the silica polymorph coesite at pressure: an assessment of OO bonded interactions. J Phys Chem B104:10534–10542
Gibbs GV, Boisen MB, Beverly LL, Rosso KM (2001) A computational quantum chemical study of the bonded interactions in earth materials and structurally and chemically related molecules. In: Cygan RT, Kubicki JD (eds) Reviews in mineralogy and geochemistry, vol 42. Mineralogical Society of America, Washington DC, pp 345–381
Gibbs GV, Whitten AE, Spackman MA, Stimpfl M, Downs RT, Carducci MD (2003) An exploration of theoretical and experimental electron density distributions and SiO bonded interactions for the silica polymorph coesite. J Phys Chem B 107:12996–13006
Göttlicher S, Vegas A (1988) Electron-density distribution in magnesite (MgCO3). Acta Cryst Sect B 44:362–367
Hehre WJ, Ditchfield R, Stewart RF, Pople JA (1970) Self-consistent molecular orbital methods. IV. Use of the Gaussian expansion of slater-type orbitals. Extension to second-row molecules. J Chem Phys 51:2769–2773
Ivanov YuV, Belokoneva EL, Protas J, Hansen NK, Tsirelson VG (1998) Multipole analysis of the electron density in topaz using X-ray diffraction data. Acta Cryst B 54:774–781
Kampermann SP, Sabine TM, Craven BM, McMullan RK (1995) Hexamethylenetetramine: extinction and thermal vibrations from neutron diffraction at six temperatures. Acta Crystallogr A 51:489–497
Kirfel A, Krane HG, Blaha P, Schwarz K, Lippmann T (2001) Electron-density distribution in stishovite, SiO2: a new high-energy synchrotron-radiation study. Acta Crystallogr A 57:663–677
Koga T, Saito M, Hoffmeyer RE, Thakkar AJ (1994) Contracted Gaussian basis sets for sodium through to argon. J Mol Struct (Theochem) 306:249–260
Levien L, Prewitt CT (1981) High-pressure structural study of diopside. Am Mineral 66:315–323
Luaña V, Costales A, Mori-Sánchez P, Pendás AM (2003) Ions in crystals: the topology of the electron density in ionic materials. 4. The danburite (CaB2Si2O8) case and the occurrence of oxide–oxide bond paths in crystals. J Phys Chem B107:4912–4921
Merli M, Cámara F (2003) Topological analysis of the electron density of the clinopyroxene structure by the maximum entropy method: an exploratory study. Eur J Mineral 15:903–911
Oganov AR, Gillan MJ, Price GD (2005) Structural stability of silica at high pressures and temperatures. Phys Rev B71:064104-1–064104-7
Pietro WJ, Levi BA, Hehre WJ, Stewart RF (1980) Molecular orbital theory of the properties of inorganic and organometallic compounds. I. STO-NG basis sets fir third-row main-group elements. Inorg Chem 19:2225–2229
Pilati T, Demartin F, Gramaccioli CM (1996) Lattice-dynamical evaluation of the atomic displacement parameters of minerals and its implications: the example of diopside. Am Mineral 81:811–821
Poirier R, Kari R, Csizmadia IG (1985) Handbook of Gaussian basis sets. Elsevier, Amsterdam, p 477
Prencipe M, Tribaudino M, Pavese A, Hoser A, Reehuis M (2000) A single-crystal neutron-diffraction investigation of diopside at 10 K. Can Mineral 38:183–189
Rossi G, Oberti R, Dal Negro A, Molin GM, Mellini M (1987) Residual electron density at the M2 site in C2/c clinopyroxenes: relationships with bulk chemistry and sub-solidus evolution. Phys Chem Mineral 14:514–520
Sabine TM (1992) The flow of radiation in a real crystal. International tables for crystallography, vol C. Kluwer, Dordrecht, pp 530–536
Sasaki S, Fujino K, Takéuchi Y, Sadanaga R (1980) On the estimation of atomic charges by the X-ray method for some oxides and silicates. Acta Cryst A 36:904–915
Saunders VR, Dovesi R, Roetti C, Causà M, Harrison NM, Orlando R, Zicovich-Wilson CM (1998) CRYSTAL98 user’s manual. University of Torino, Torino
Stewart RF (1976) Electron population analysis with rigid pseudoatoms. Acta Crystallogr A 32:565–574
Thakkar AJ, Koga T, Saito M, Hoffmeyer RE (1993) Double and quadruple zeta contracted gaussian basis sets for hydrogen through neon. Int J Quantum Chem Quantum Chem Symposium27:343–354
Tsirelson VG, Evdokimova OA, Belokoneva EL, Urusov VS (1990) Electron density distribution and bonding in silicates. Phys Chem Minerals 17:275–292
Tsirelson VG, Avilov AS, Abramov YuA, Belokoneva EL, Kitaneh R, Feil D (1998) X-ray and electron diffraction study of MgO. Acta Cryst B 54:8–17
Zhang L, Ahsbahs H, Hafner SS, Kutoglu A (1997) Single-crystal compression and crystal structure of clinopyroxene up to 10 Gpa. Am Mineral 82:245–258
Zhurova EA, Tsirelson VG, Stash AI, Pinkerton AA (2002) Characterizing the oxygen–oxygen interaction in the dinitramide anion. J Am Chem Soc 124:4574–4575
Acknowledgment
We gratefully thank Prof. J. Gibbs for a stimulating discussion about the Espinosa classification of the atomic interactions.
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Bianchi, R., Forni, A. & Oberti, R. Multipole-refined charge density study of diopside at ambient conditions. Phys Chem Minerals 32, 638–645 (2005). https://doi.org/10.1007/s00269-005-0039-9
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DOI: https://doi.org/10.1007/s00269-005-0039-9