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The prediction and interpretation of bond lengths in crystals

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Part of the book series: Structure and Bonding ((STRUCTURE,volume 71))

Abstract

The concept of bond valence and its correlation with bond length are reviewed. It is shown how to augment bond valence sums at an atom with other constraints so that bond lengths can be predicted for a given topology. These constraints can be read directly from the connectivity matrix for the structure. The physical reasons for the constraints are analysed, and this analysis leads in turn to a reformulation of Pauling's electrostatic valence sum rule. The apparent valences of atoms, calculated as a sum of bond valences derived from bond lengths, are often significantly different from the actual valences. It is demonstrated that such observations are often diagnostic of non-bonded repulsions. Limitations and possible extensions of the method are outlined.

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References

  1. Brown ID (1978) Chem. Soc. Rev. 7: 359

    Article  CAS  Google Scholar 

  2. Brown ID (1981) In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals II. Academic, New York

    Google Scholar 

  3. O'Keeffe M, Hyde BG (1985) Structure and Bonding 61: 79

    Google Scholar 

  4. Pauling L (1947) J. Amer. Chem. Soc. 69: 542

    Article  CAS  Google Scholar 

  5. Byström A, Wilhelmi K-A (1951) Acta Chem. Scand. 5: 1003

    Article  Google Scholar 

  6. Bragg WL (1920) Phil. Mag. 40: 169

    CAS  Google Scholar 

  7. Slater JC (1965) Quantum Theory of Molecules and Solids 2, McGraw-Hill, New York

    Google Scholar 

  8. Shannon RD, Prewitt CT (1969) Acta Crystallogr. B25: 925

    Google Scholar 

  9. O'Keeffe M (1981) In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals I. Academic, New York

    Google Scholar 

  10. Pauling L (1960) The nature of the chemical bond, Cornell University Press, Ithaca

    Google Scholar 

  11. Adamson A (1979) A textbook of physical chemistry, Academic, New York

    Google Scholar 

  12. Johnston HS (1966) Gas phase reaction theory, Ronald, New York

    Google Scholar 

  13. Zachariasen WH (1963) Acta Crystallogr. 16: 385

    Article  CAS  Google Scholar 

  14. Brown ID, Altermatt D (1985) Acta Crystallogr. B41: 244

    CAS  Google Scholar 

  15. Brown ID (1977) Acta Crystallogr. B33: 1305

    CAS  Google Scholar 

  16. Mackay AL, Finney JL (1973) J. Appl. Crystallogr. 6: 284

    Article  CAS  Google Scholar 

  17. Horiuchi H, Sawamoto H (1981) Amer. Mineral. 66: 568

    CAS  Google Scholar 

  18. O'Keeffe M, Hyde BG (1978) Acta Crystallogr. B34: 3519

    Google Scholar 

  19. Laurent Y, Guyader J, Roult G (1981) Acta Crystallogr. B37: 911

    CAS  Google Scholar 

  20. Marezio M (1965) Acta Crystallogr. B37: 481

    Article  Google Scholar 

  21. Hesse K-F (1977) Acta Crystallogr. B33: 901

    CAS  Google Scholar 

  22. Völlenkle H, Wittmann J (1968) Mh. Chem. 99: 244

    Google Scholar 

  23. O'Keeffe M, Hansen S (1988) J. Am. Chem. Soc. 110: 1506

    Article  Google Scholar 

  24. Harris LA, Yakel HL (1969) Acta Crystallogr. B25: 1647

    Google Scholar 

  25. Geller S (1960) J. Chem. Phys. 33: 676

    Article  CAS  Google Scholar 

  26. Marezio M, Remeika JP (1967) J. Chem. Phys. 46: 1862

    Article  CAS  Google Scholar 

  27. Daniel F, Moret J, Phillippot E, Maurin M (1977) J. Solid State Chem. 22: 113

    Article  CAS  Google Scholar 

  28. Wagner TR, O'Keeffe M (1988) J. Solid State Chem. 73: 211

    Article  CAS  Google Scholar 

  29. Baur W (1981) In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals II. Academic, New York

    Google Scholar 

  30. Donnay G, Allmann R (1970) Amer. Mineral. 55: 1003

    CAS  Google Scholar 

  31. Ribbe PH, Gibbs GV (1971) Amer. Mineral. 56: 24

    CAS  Google Scholar 

  32. Pauling L (1928) Proc. Nat. Acad. Sci. U.S.A. 14: 603

    Article  CAS  Google Scholar 

  33. Bart JCJ, Ragaini V (1979) Inorg. Chim. Acta 36: 261

    Article  CAS  Google Scholar 

  34. Le Page Y, Strobel P (1982) J. Solid State Chem. 47: 6

    Article  Google Scholar 

  35. Trömel M (1983) Acta Crystallogr. B39: 664

    Google Scholar 

  36. Domengés B, McGuire NK, O'Keeffe M (1985) J. Solid State Chem. 56: 94

    Article  Google Scholar 

  37. Robin MB, Day P (1967) Adv. Inorg. Chem. Radiochem. 10: 247

    Article  CAS  Google Scholar 

  38. Hámos LV, Stscherbina W (1931) Nacr. Ges. Wiss. Gotting. Math. Phys. Kl. Fachgruppen 232

    Google Scholar 

  39. Ruby SL, Shirane G (1961) Phys. Rev. 123: 1239

    Article  CAS  Google Scholar 

  40. Morosin B, Baughman RJ, Ginley DS, Butler MA (1978) J. Appl. Cryst. 11: 121

    Article  CAS  Google Scholar 

  41. Bartell LS (1962) Tetrahedron 17: 177

    Article  CAS  Google Scholar 

  42. McGuire NK, O'Keeffe M (1984) J. Solid State Chem. 54: 49

    Article  CAS  Google Scholar 

  43. O'Keeffe M, Hyde BG (1984) Nature 309: 411

    Article  Google Scholar 

  44. O'Keeffe M, Stuart JA (1983) Inorg. Chem. 22: 177

    Article  Google Scholar 

  45. Zachariasen WH (1978) J. Less-Common Mets. 62: 1

    Article  CAS  Google Scholar 

  46. Adelbert P, Traverse JP (1979) Mat. Res. Bull. 14: 303

    Article  Google Scholar 

  47. Bämighausen H, Schulter G (1985) aJ. Less-Common Mets. 110: 385

    Article  Google Scholar 

  48. Beall GW, Milligan WO, Wolcott HA (1977) J. Inorg. Nucl. Chem. 39: 65

    Article  CAS  Google Scholar 

  49. Caro P (1972) In: Roth RS, Schneider SJ (eds) Solid state chemistry, N.B.S. Spec. Publ. 364, Washington, p. 367

    Google Scholar 

  50. Barbier J, Hyde BG (1985) Acta Crystallogr. B41: 383

    CAS  Google Scholar 

  51. Burdett JK (1980) Molecular shapes, Wiley, New York

    Google Scholar 

  52. O'Keeffe M (1979) Acta Crystallogr. A35: 776

    Google Scholar 

  53. Halot D, Flahaut J (1971) C. R. Acad. Sci. Paris C272: 465

    Google Scholar 

  54. Imanov IM, Ragimli NA, Semiletov SA (1975) Soviet Phys. Crystallogr. 19: 466 [trans. of Krystallografiya 19: 751 (1974)]

    Google Scholar 

  55. Page L, Adams NI (1931) Principles of electricity, Van Nostrand, New York

    Google Scholar 

  56. Gibbs GV, Boisen MB (1987) Mat. Res. Soc. Symp. Proc. 73: 515

    Google Scholar 

  57. Burdett JK (1988) Chem. Revs. 88: 3

    Article  CAS  Google Scholar 

  58. Brown ID, Wu KK (1976) Acta Crystallogr. B32: 1957

    CAS  Google Scholar 

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© 1989 Springer-Verlag

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O'Keeffe, M. (1989). The prediction and interpretation of bond lengths in crystals. In: Stereochemistry and Bonding. Structure and Bonding, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50775-2_5

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  • DOI: https://doi.org/10.1007/3-540-50775-2_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50775-8

  • Online ISBN: 978-3-540-46083-1

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