Insights into the crystal chemistry of earth materials rendered by electron density distributions: Pauling's rules revisited

American Mineralogist

Volumn 99, Issue 5-6, 2014, Pages 1071-1084

  Gibbs, G V ^a   Ross, Nancy L ^a   Cox, David F ^b   Rosso, Kevin M ^c  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b State University   (United States)

^c PACIFIC NORTHWEST NATIONAL LABORATORY   (United States)

Author keywords

Bond strength; Bonded radii; Electron density distribution; Pauling

Indexed keywords

ATOMS; BOND LENGTH; BOND STRENGTH (CHEMICAL); CRYSTAL CHEMISTRY; ELECTRON DENSITY MEASUREMENT; ELECTRONEGATIVITY; ELECTRONIC DENSITY OF STATES; ELECTRONS; MOLECULES; QUANTUM THEORY; SILICATES; SILICON;

BOND CRITICAL POINTS; BOND VALENCE MODEL; BONDED INTERACTIONS; BONDED RADII; ELECTRONEGATIVE ATOMS; PAULING; QUANTUM MECHANICAL; REGRESSION EXPRESSIONS;

BOND STRENGTH (MATERIALS);

CRYSTAL CHEMISTRY; CRYSTALLOGRAPHY; ELECTRON DENSITY; OXIDE; OXYGEN; POWER LAW; QUANTUM MECHANICS; SILICATE; STABILIZATION;

EID: 84902531033     PISSN: 0003004X     EISSN: 19453027     Source Type: Journal    
DOI: 10.2138/am.2014.4660     Document Type: Article

References (101)

1. Ahrens, L. H. (1952) The use of ionization potentials Part 1. Ionic radii of the elements. Geochimica et Cosmochimica Acta, 2, 155-169.
2. Bader, RF W. (1990) Atoms in Molecules. Oxford Science Publications, Oxford, U. K.
3. - (2009) Bond paths are not chemical bonds. Journal of Physical Chemistry A, 113, 10391-10396.
4. Bader, R. F. W., and Essén, H. (1984) The characterization of atomic interactions. The Journal of Chemical Physics, 80(5), 1943-1960.
5. Barlow, W. (1883) Probable nature of the internal symmetry of crystals. Nature, 29, 186-188.
6. - (1898) XXVI. Geometrische Untersuchung uber eine mechanische Ursache der Homogenitat der Structur und der Symmetrie; mit besonderer Anwendung auf Krystallisation und chemische Verbindung. Zeitschrift für Kristallographie und Mineralogie, 29, 433-588.
7. Bartelmehs, K. L., Gibbs, G. V, and Boisen, M. B. (1989) Bond-length and bondedradii variations in sulfide molecules and crystals containing main-group elements; a comparison with oxides. American Mineralogist, 74, 620-626.
8. 2. Naturwissenschaften, 48, 549-552.
9. - (1981) Interatomic Distance Predictions for Computer Simulation of Crystal Structures. Structure and Bonding in Crystals, 2, 31-52. Academic Press, New York.
10. Bickmore, B. R., Wander, M. F. C., Edwards, J., Maurer, J., Shepherd, K., Meyer, E., Johansen, W. J., Frank, R. A., Andros, C, and Davis, M. (2013) Electronic structure effects in the vectorial bond-valence model. American Mineralogist, 98, 340-349.
11. Bishop, K. J. M., Wilmer, C. E., Soh, S., and Grzybowski, B. A. (2009) Nanoscale forces and their uses in self-assembly. Small, 5, 1600-1630.
12. Bohórquez, H. J., and Boyd, R. J. (2009) Is the size of an atom determined by its ionization energy? Chemical Physics Letters, 480, 127-131.
13. Boisen, M. B., Gibbs, G. V, and Zhang, Z. G. (1988) Resonance bond numbers: A graph-theoretic study of bond length variations in silicate crystals. Physics and Chemistry of Minerals, 15, 409-415.
14. Bragg, W. H., and Bragg, W. L. (1913) The structure of the diamond. Proceedings of the Royal Society of London. Series A, 89, 277-291.
15. Bragg, W. L. (1913) The structure of some crystals as indicated by their diffraction of X-rays. Proceedings of the Royal Society of London. Series A, 89, 248-277.
16. - (1914) The analysis of crystals by the X-ray spectrometer. Proceedings of the Royal Society of London. Series A, 89(613), 468-489.
17. - (1920) The arrangement of atoms in crystals. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 40, 169-189.
18. - (1937) Atomic Structure of Minerals. Cornell University Press, Ithaca.
19. Brown, ID. (1981) The bond-valence method: An empirical approach to chemical structure and bonding. In M. O'Keeffe and A. Navrotsky, Eds. Structure and Bonding in Crystals, 2, p. 1-30. Academic Press, New York.
20. - (2013) A step closer to predicting the bonding geometry of crystals. American Mineralogist, 98, 1093-1094.
21. Brown, ID., and Shannon, R. D. (1973) Empirical bond-strength-bond-length curves for oxides. Acta Crystallographica Section A, 29, 266-282.
22. Burdett, J. K., and McLarnan, T. J. (1984) An orbital interpretation of Pauling's rules. American Mineralogist, 69, 601-621.
23. Burnham, C. W, and Buerger, M. J. (1961) Refinement of the crystal structure of andalusite. Zeitschrift für Kristallographie, 115, 269-290.
24. Buterakos, L. A., Gibbs, G. V, and Boisen, M. B. (1992) Bond length variation in hydronitride molecules and nitride crystals. Physics and Chemistry of Minerals, 19, 127-132.
25. Cahen, D. (1988) Atomic radii in ternary adamantines. Journal of Physics and Chemistry of Solids, 49, 103-111.
26. Casey, W. H., and Rustad, J. R. (2007) Reaction dynamics, molecular clusters, and aqueous geochemistry. Annual Review of Earth and Planetary Sciences, 35, 21-46.
27. Casey, W. H., Rustad, J. R., and Spiccia, L. (2009) Minerals as molecules-Use of aqueous oxide and hydroxide clusters to understand geochemical reactions. Chemistry-A European Journal, 15, 4496-4515.
28. Clark, J. R., Appleman, D. E., and Papike, J. J. (1969) Crystal-Chemical Characterization of Clinopyroxenes Based on Eight New Refinements. In J. J. Papike, Ed., Mineralogical Society of America Special Paper, no. 2, 31-50.
29. Coulson, C. A. (1955) The contributions of wave mechanics to chemistry. Journal of the Chemical Society, 2069-2084.
30. Cremer, D., and Kraka, E. (1984) A Description of the Chemical Bond in Terms of Local Properties of Electron Density and Energy. Croatica Chemica Acta, 57, 1259-1281.
31. Criscenti, L. J., Kubicki, J. D., and Brantley, S. L. (2006) Silicate glass and mineral dissolution: Calculated reaction paths and activation energies for hydrolysis of a Q (3) Si by H3O+ using ab initio methods. Journal of Physical Chemistry A, 110, 198-206.
32. Donnay, G. (1969) Further use for the Pauling-bond concept. Carnegie Institute of Washington Yearbook, 68, 292-295.
33. 2O in crystal structures determined by X-ray. American Mineralogist, 55, 1003-1015.
34. Downs, R. T., Andalman, A., and Hudacsko, M. (1996) The coordination numbers of Na and K atoms in low albite and microcline as determined from a procrystal electron-density distribution. American Mineralogist, 81, 1344-1349.
35. Downs, R. T., Gibbs, G. V, Boisen, M. B. Jr., and Rosso, KM. (2002) A comparison of procrystal and ab initio model representations of the electron-density distributions of minerals. Physics and Chemistry of Minerals, 29, 369-385.
36. Fajans, K. (1931) Radioelements and Isotopes, Chemical Forces. Cornell University Press, Ithaca.
37. Feynman, R. P (1939) Forces in molecules. Physical Review, 56, 340.
38. Friedrich, W, Knipping, P., and Von Laue, M. (1912) Sitzungsberiche der math? ematisch-physikalischen Klasse der Königlich. Bayererischen Akademie der Wissenschaften zu München, 302-322.
39. Fyfe, WS. (1954) The problem of bond type. American Mineralogist, 39, 991-1004.
40. Gatti, C. (1997) TOPOND96 User's Manual. CNR-CSRSRC, Milano, Italy.
41. - (2005) Chemical bonding in crystals: new directions. Zeitschrift für Kristallographie, 220, 399-457.
42. Gibbs, G. V. (1982) Molecules as models for bonding in silicates. American Mineralogist, 67, 421-450.
43. Gibbs, G. V, Finger, L. W., and Boisen, M. B. (1987) Molecular mimicry of the bond length-bond strength variations in oxide crystals. Physics and Chemistry of Minerals, 14, 327-331.
44. Gibbs, G. V, Spackman, M. A., and Boisen, M. B. (1992) Bonded and promolecule radii for molecules and crystals. American Mineralogist, 77, 741-750.
45. Gibbs, G. V, Boisen, M. B., Beverly, L. L., and Rosso, KM. (2001) A computational quantum chemical study of the bonded interactions in earth materials and structurally and chemically related molecules. In R. T. Cygan and J. D. Kubicki, Eds., Molecular Modeling Theory: Applications in the Geosciences, vol. 42, p. 345-381. Reviews in Mineralogy, Mineralogical Society of America, Chantilly, Virginia.
46. Gibbs, G. V, Whitten, A. E., Spackman, M. A., Stimpfl, M., Downs, R. T, and Carducci, M. D. (2003) An exploration of theoretical and experimental electron density distributions and SiO bonded interactions for the silica polymorph coesite. Journal of Physical Chemistry B, 107, 12996-13006.
47. Gibbs, G. V, Cox, D. F, and Rosso, KM. (2004) A connection between empirical bond strength and the localization of the electron density at the bond critical points of the Si-O bonds in silicates. Journal of Physical Chemistry A, 108, 7643-7645.
48. Gibbs, G. V, Downs, R. T, Cox, D. F, Ross, N. L., Boisen, M. B., and Rosso, KM. (2008a) Shared and closed-shell O-O interactions in silicates. Journal of Physical Chemistry A, 112, 3693-3699.
49. Gibbs, G. V., Downs, R. T., Cox, D. F., Ross, N. L., Prewitt, C. T., Rosso, K. M., Lippmann, T., and Kirfel, A. (2008b) Bonded interactions and the crystal chemistry of minerals: A review. Zeitschrift für Krisstallographie, 223, 1-40.
50. 4 olivine and selected organic metal complexes: Comparison with properties calculated for non-transition and transition metal M-O bonded interactions for silicates and oxides. Journal of Physical Chemistry A, 112, 8811-8823.
51. Gibbs, G. V., Wallace, A. F, Cox, D. F, Dove, P. M., Downs, R. T., Ross, N. L., and Rosso, K. M. (2009a) Role of directed van der Waals bonded interactions in the determination of the structures of molecular arsenate solids. Journal of Physical Chemistry A, 113, 736-749.
52. Gibbs, G. V., Wallace, A. F, Cox, D. F, Downs, R. T., Ross, N. L., and Rosso, K. M. (2009b) Bonded interactions in silica polymorphs, silicates, and siloxane molecules. American Mineralogist, 94, 1085-1102.
53. Gibbs, G. V., Wallace, A. F, Downs, R. T., Ross, N. L., Cox, D. F, and Rosso, K. M. (2011) Thioarsenides: a case for long-range Lewis acid-base-directed van der Waals interactions. Physics and Chemistry of Minerals, 38, 267-291.
54. Gibbs, G. V., Wang, D., Hin, C, Ross, N. L., Cox, D. F, Crawford, T. D., Spackman, M. A., and Angel, R. J. (2012) Properties of atoms under pressure: Bonded interactions of the atoms in three perovskites. The Journal of Chemical Physics, 137, 164313.
55. Gibbs, G. V., Ross, N. L., Cox, D. F, Rosso, KM., Iversen, B. B., and Spackman, M. A. (2013a) Bonded radii and the contraction of the electron density of the oxygen atom by bonded interactions. The Journal of Physical Chemistry A, 117, 1632-1640.
56. Gibbs, G. V., Ross, N. L., Cox, D. F, Rosso, KM., Iversen, B. B., and Spackman, M. A. (2013b) Pauling bond strength, bond length and electron density distribution. Physics and Chemistry of Minerals, 41, 17-25.
57. Goldschmidt, VM. (1954) Geochemistry, 736 p. Clarendon Press, Oxford.
58. Hoffmann, R. (1988) Solids and Surfaces: A Chemist's View of Bonding in Extended Structures, 142 p. VCH, New York.
59. Hüttig, G. F (1920) Notiz zur geometrie der koordinationzahl. Zeitschrift für Anor? ganische und Allgemeine Chemie, 113, 24-26.
60. Johnson, O. (1973) Ionic radii for spherical potential ions. I. Inorganic Chemistry, 12, 780-785.
61. Johnson, W. R., Kolb, D., and Huang, K. N. (1983) Electric dipole, quadrupole, and magnetic-dipole susceptibilities and shielding factors for closed-shell ions of the He, Ne, Ar, Ni (Cu+), Kr, Pb, and Xe isoelectronic sequences. Atomic Data and Nuclear Data Tables, 28, 333-340.
62. 2: a new high-energy synchrotron-radiation study. Acta Crystallographica Section A, 57, 663-677.
63. 4, determined with synchrotron single crystal X-ray diffraction data. Physics and Chemistry Minerals, 32, 301-313.
64. Muller, O., and Roy, R. R. (1974) The Major Ternary Structure Families. Springer-Verlag, New York.
65. Nicoll, J. S., Gibbs, G. V., Boisen, M. B., Downs, R. T., and Bartelmehs, K. L. (1994) Bond length and radii variations in fluoride and oxide molecules and crystals. Physics and Chemistry of Minerals, 20, 617-624.
66. Novak, G. A., and Gibbs, G. V. (1971) The crystal chemistry of the silicate garnets. American Mineralogist, 56, 791-825.
67. Oganov, A. R., Gillan, M. J., and Price, G. D. (2005) Structural stability of silica at high pressures and temperatures. Physical Review B (Condensed Matter and Materials Physics), 71(6), 064104.
68. O'Keeffe, M., and Hyde, B. G. (1981) The role of nonbonded forces in crystals. In M. O'Keeffe and A. Navrotsky, Eds., Structure and Bonding in Crystals, p. 222-254. Academic Press, New York.
69. Parr, R. G., and Yang, W (1989) Density-functional theory of atoms and molecules, 333 p. Oxford University Press, U. K.
70. Pauling, L. (1927) The sizes of ions and the structure of ionic crystals. Journal of the American Chemical Society, 49, 765-790.
71. - (1929) The principles determining the crystal structure of complex ionic crystals. Journal of the American Chemical Society, 51, 1010-1026.
72. - (1939) The Nature of the Chemical Bond. Cornell University Press, Ithaca.
73. - (1948) The modern theory of valency. Journal of the Chemical Society (Resumed), 0, 1461-1467.
74. - (1960) The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry. Cornell University Press, Ithaca.
75. Pelmenschikov, A., Leszczynski, J., and Pettersson, L. G. M. (2001) Mechanism of dissolution of neutral silica surfaces: Including effect of self-healing. Journal of Physical Chemistry A, 105, 9528-9532.
76. Pyykko, P. (2012) Refitted tetrahedral covalent radii for solids. Physical Review B, 85 (2).
77. Rickard, D., and Luther, G. W. (2006) Metal sulfide complexes and clusters. In D. J. Vaughan, Ed., Sulfide Mineralogy and Geochemistry, vol. 61, p. 421-504. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Chantilly, Virginia.
78. Rosso, K. M. (2001) Structure and reactivity of semiconducting mineral surfaces: Convergence of molecular modeling and experiment. In R. T. Cygan and J. D. Kubicki, Eds., Molecular Modeling Theory: Applications in the Geosciences, vol. 42, p. 199-271. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Chantilly, Virginia.
79. Rosso, K. M., and Vaughan, D. J. (2006a) Reactivity of sulfide mineral surfaces. In D. J. Vaughan, Ed., Sulfide Mineralogy and Geochemistry, vol. 61, p. 557-607. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Chantilly, Virginia.
80. - (2006b) Sulfide mineral surfaces. In D. J. Vaughan, Ed., Sulfide Mineralogy and Geochemistry, vol. 61, 505-556. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Chantilly, Virginia.
81. Rustad, J. R. (2001) Molecular models of surface relaxation, hydroxylation, and surface charging at oxide-water interfaces. In R. T. Cygan and J. D. Kubicki, Eds., Molecular Modeling Theory: Applications in the Geosciences, vol. 42, p. 169-197. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Chantilly, Virginia.
82. Saunders, V. R., Dovesi, R., Roetti, C., Causa, M., Harrison, N. M., Orlando, R., and Apra, E. (1998) CRYSTAL98 User's Manual. University of Torino, Italy.
83. Shannon, R. D. (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica, A, 32, 751-67.
84. - (1981) Bond distances in sulfides and a preliminary table of sulfide crystal radii. In M. O'Keeffe and A. Navrotsky, Eds., Structure and Bonding in Crystals, vol. 2, p. 53-70. Academic Press, New York.
85. Shannon, R. D., and Fischer, R. X. (2006) Empirical electronic polarizabilities in oxides, hydroxides, oxyfluorides, and oxychlorides. Physical Review B, 73, 235111.
86. Shannon, R. D., and Prewitt, C. T. (1969) Effective ionic radii in oxides and fluorides. Acta Crystallographica, B, 25, 925-946.
87. Sherman, J. (1932) Crystal energies of ionic compounds and thermochemical applications. Chemical Reviews, 11, 93-170.
88. Slater, J. C. (1964) Atomic radii in crystals. Journal of Chemical Physics, 41(10), 3199-3204.
89. - (1965) Quantum Theory of Molecules and Solids: Symmetry and Energy Bands in Crystals. McGraw Hill, New York.
90. Smith, J. V. (1953) Reexamination of the crystal structure of melilite. American Mineralogist, 38, 643-661.
91. Tamada, O., Gibbs, G. V., Boisen, M. B., and Rimstidt, J. D. (2012) Silica dissolution catalyzed by NaOH: Reaction kinetics and energy barriers simulated by quantum mechanical strategies. Journal of Mineralogical and Petrological Sciences, 107(2), 87-98.
92. Tosi, M. P. (1964) Cohesion of ionic solids in the born model. In S. Frederick and T. David, Eds., Solid State Physics, vol. 16, p. 1-120. Academic Press, New York.
93. Tosi, M. P., and Fumi, F. G. (1964) Ionic sizes and born repulsive parameters in the NaCl-type alkali halides-II: The generalized Huggins-Mayer form. Journal of Physics and Chemistry of Solids, 25, 45-52.
94. Wallace, A. F., Gibbs, G. V., and Dove, P. M. (2010) Influence of ion-associated water on the hydrolysis of Si-O bonded interactions. Journal of Physical Chemistry A, 114, 2534-2542.
95. Warren, B. E. (1929) The structure of tremolite. Zeitschrift für Kristallographie, 72, 42-57.
96. 2. Zeitschrift für Kristallographie, 69, 168-93.
97. Wasasjerna, J. A. (1923) Radii of ions. Societas Scientiarum Fennica Commentaries Physico-Mathematicae, 38, 1-25.
98. Zachariasen, W. (1963) The crystal structure of monoclinic metaboric acid. Acta Crystallographica, 16, 385-389.
99. - (1954) Crystal chemical studies of the 5f-series of elements. XXIII. On the Crystal chemistry of uranyl compounds and of related compounds of transuranic elements. Acta Crystallographica, 7, 795-799.
100. Zachariasen, W. H., and Plettinger, H. A. (1959) Crystal chemical studies of the 5fseries of elements. XXV. The crystal structure of sodium uranyl acetate. Acta Crystallographica, 12, 526-530.
101. Zhang, Y. X., and Cherniak, D. J. (2010) Diffusion in minerals and melts introduction. In Y. X. Zhang and D. J. Cherniak, Eds., Diffusion in Minerals and Melts, vol. 72, p. 1-4. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Chantilly, Virginia.