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Theoretical models of cluster bonding

  • D. Michael
  • P. Mingos
  • Roy L. Johnston
Conference paper
Part of the Structure and Bonding book series (STRUCTURE, volume 68)

Abstract

The theoretical models which have been used to describe the bonding in cluster compounds of the main group and transition metal elements are reviewed. The historical development of these models is outlined and special emphasis is placed on those studies which have led to the elucidation of structure-electron count correlations. Theoretical treatments of cluster bonding are based on localised, delocalised (molecular orbital) or free electron methods derived from the solution of the Schrödinger equation for a particle on a sphere. A detailed analysis of the Tensor Surface Harmonic method, as an example of a free electron model, is presented. Group theoretical consequences of the model are also presented.

Keywords

Molecular Orbital Electron Count Cluster Compound Transition Metal Cluster Tetrahedral Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1. (a)
    Muetterties, E. L.: Chem. Eng. News, 30th August, 1982, 28; (b) Transition Metal Clusters (ed. Johnson, B. F. G.) Wiley, New York 1981 and references thereinGoogle Scholar
  2. 2. (a)
    Lipscomb, W. N.: Boron Hydrides, Benjamin, New York 1963; (b) Boron Hydride Chemistry (ed. Muetterties, E. L.), Academic, New York 1975 and references therein. (c) The first boranes were characterised by Stock and coworkers: Stock A.: Hydrides of Boron and Silicon, Cornell University Press, Ithaca, New York 1933 and references therein. (d) For reviews of the related metallaboranes and metallacarboranes see: Metal Interactions with Boron Clusters (ed. Grimes, R. N.), Plenum, New York 1982; Grimes R. N.: Ace. Chem. Res. 16, 22 (1983)Google Scholar
  3. 3.
    See, for example: Weilmuenster, E. A.: Ind. Eng. Chem. 49, 1340 (1957); Martin, D. R.: J. Chem. Educ. 36, 208 (1959)CrossRefGoogle Scholar
  4. 4.
    Corbett, J. D.: Prog. Inorg. Chem. 21, 129 (1976); Corbett, J. D.: Chem. Rev. 85, 383 (1985); von Schnering, H. G.: Angew. Chem. Int. Edn. Engl. 20, 33 (1981) and references therein. For theoretical treatments of naked metal clusters see: Belin, C. H. E., Corbett, J. D., Cisar, A.: J. Amer. Chem. Soc. 99, 7163 (1977); Lohr, L. L.: Inorg. Chem. 20, 4229 (1981); Burns, R. C., Gillespie, R. J., Barnes, J. A., McGlinchey, M. J.: Inorg. Chem. 21, 799 (1982)Google Scholar
  5. 5.
    Paquette, L. A.: Acc. Chem. Res. 4, 280 (1971); Clark, T., McKervey, M. A.: Comp. Organic Chem. 1, 35 (1979); Ternansky, R. J., Balogh, D. W., Paquette, L. A.: J. Amer. Chem. Soc. 104, 4503 (1982) and references thereinCrossRefGoogle Scholar
  6. 6.
    For recent reviews of catalytic processes which may involve transition metal cluster compounds see: Whyman, R.: in Ref. 1b, Ch. 8 p. 545; Whyman, R.: Phil. Trans. R. Soc. Lond. A308, 131 (1982) and references thereinGoogle Scholar
  7. 7.
    Johnson, B. F. G., Lewis, J.: Adv. Inorg. Chem. Radiochem. 24, 225 (1981); Johnson, B. F. G., Lewis, J.: Phil. Trans. R. Soc. Lond. A308, 5 (1982)Google Scholar
  8. 8.
    Muetterties, E. L., Rhodin, T. N., Band, E., Brucker, C. F., Pretzer, W. R.: Chem. Rev. 29, 91 (1979); Muetterties, E. L., Wexler, R. M.: Survey Prog. Chem. 10, 61 (1983)CrossRefGoogle Scholar
  9. 9.
    Schmid, G.: Struct. Bond. 62, 51 (1985) and references thereinGoogle Scholar
  10. 10.
    Mingos, D. M. P., Wardle, R. W. M.: Transition Met. Chem. 10, 441 (1985) and references therein. See also: Longoni, G., Chini, P.: J. Amer. Chem. Soc. 98, 7225 (1976); Gregson, D., Howard, J. A. K., Murray, M., Spencer, J. L.: J. Chem. Soc. Chem. Commun. 716 (1981); Frost, P. W., Howard, J. A. K., Spencer, J. L., Turner, D. G.: J. Chem. Soc., Chem. Commun. 1104 (1981)CrossRefGoogle Scholar
  11. 11.
    Hall, K. P., Mingos, D. M. P.: Prog. Inorg. Chem. 32, 237 (1984) and references thereinGoogle Scholar
  12. 12.
    Schäfer, H., von Schnering, H. G.: Angew. Chem. 76, 833 (1964); Baird, M. C.: Prog. Inorg. Chem. 9, 1 (1968); McCarley, R. E.: Phil. Trans. R. Soc. Lond. A308, 141 (1982) and references thereinGoogle Scholar
  13. 13.
    Simon, A.: Angew. Chem. Int. Edn. Engl. 14, 239 (1981); Corbett, J. D.: Ace. Chem. Res. 14, 239 (1981)Google Scholar
  14. 14.
    Chevrel, R., Sergent, M., Prigent, J.: J. Solid State Chem. 3, 515 (1971); Chevel, R., Gougeon, P., Potel, M., Sergent, M.: J. Solid State Chem. 57, 25 (1985)CrossRefGoogle Scholar
  15. 15.
    Matthias, B. T., Marezio, M., Corenzwit, E., Cooper, A. S., Barz, H. E.: Science 175, 1465 (1972); Fischer, O.: Appl. Phys. 16, 1 (1978); Topics in Current Physics: Superconductivity in Ternary Compounds (eds. Fischer, O., Maple, M. B.) Springer-Verlag, Berlin 1982, 32Google Scholar
  16. 16.
    Garner, C. D.: in Ref. lb, Ch. 4 p. 235 and references thereinGoogle Scholar
  17. 17.
    See, for example: Heaton, B. T.: Phil. Trans. R. Soc. Lond. A308, 95 (1982); Green, J. C., Seddon, E. A., Mingos, D. M. P.: J. Chem. Soc., Chem. Commun. 94 (1979)Google Scholar
  18. 18.
    Raithby, P. R.: in Ref. 1b, Ch. 2 p. 5Google Scholar
  19. 19.
    Heider, H., London, F.: Z. Phys. 44, 455 (1927)CrossRefGoogle Scholar
  20. 20.
    Pauling, L.: The Nature of the Chemical Bond (3rd. Edn.), Cornell University Press, Ithaca, New York 1960Google Scholar
  21. 21.
    Mulliken, R. S.: Phys. Rev. 41, 49 (1932)CrossRefGoogle Scholar
  22. 22.
    Pauling, L., Wilson, E. B.: Introduction to Quantum Mechanics, McGraw-Hill, New York 1935 and references thereinGoogle Scholar
  23. 23.
    Wade, K.: Electron Deficient Compounds, Nelson, London 1971Google Scholar
  24. 24.
    Longuet-Higgins, H. C.: J. Chim. Phys. 46, 275 (1949)Google Scholar
  25. 25.
    Longuet-Higgins, H. C.: J. Roy. Inst. Chem. 77, 197 (1953)Google Scholar
  26. 26.
    Duffey, G. H.: J. Chem. Phys. 19, 963 (1951); 20, 195 (1952); 21, 761 (1953)CrossRefGoogle Scholar
  27. 27.
    Eberhardt, W. H., Crawford Jr., B., Lipscomb, W. N.: J. Chem. Phys. 22, 989 (1954)CrossRefGoogle Scholar
  28. 28.
    Torkington, P.: J. Chem. Phys. 19, 528 (1951)CrossRefGoogle Scholar
  29. 29.
    Lennard-Jones, J. E.: Proc. Roy. Soc. A 198, 1, 14 (1949)Google Scholar
  30. 30.
    Pople, J. A.: Quart. Rev. Chem. Soc. 11, 273 (1957)CrossRefGoogle Scholar
  31. 31.
    Switkes, E., Stevens, R. M., Lipscomb, W. N., Newton, M. D.: J. Chem. Phys. 51, 2085 (1969); Switkes, E., Lipscomb, W. N., Newton, M. D.: J. Amer. Chem. Soc. 92, 3847 (1970); Epstein, I. R., Tossell, J. A., Switkes, J. E., Stevens, R. M., Lipscomb, W. N.: Inorg. Chem. 10, 171 (1971); Marynick, D. S., Lipscomb, W. N.: J. Amer. Chem. Soc. 94, 1748 (1972); Laws, E. A., Stevens, R. M., Lipscomb, W. N.: J. Amer. Chem. Soc. 94, 4467 (1972)CrossRefGoogle Scholar
  32. 32.
    Kettle, S. F. A., Tomlinson, V.: J. Chem. Soc. (A) 2002 (1969)Google Scholar
  33. 33.
    Kettle, S. F. A., Tomlinson, V.: J. Chem. Soc. (A) 2007 (1969)Google Scholar
  34. 34. (a)
    Cotton, F. A.: Quart. Rev. Chem. Soc. 20, 389 (1966) and references therein. (b) Lewis, J.: Pure Appl. Chem. 10, 11 (1965); Chini, P.: Inorg. Chim. Acta. Rev. 2, 31 (1968); Abel, E. W., Stone, F. G. A.: Quart. Rev. Chem. Soc. 23, 325 (1969)CrossRefGoogle Scholar
  35. 35.
    Vaughan, P. A.: Proc. Natl. Acad. Sci. 36, 461 (1950)CrossRefGoogle Scholar
  36. 36.
    Sheldon, J. C.: J. Chem. Soc. 1007, 3106 (1960)CrossRefGoogle Scholar
  37. 37.
    Crossmann, L. D., Olsen, D. P., Duffey, G. H.: J. Chem. Phys. 38, 73 (1963)CrossRefGoogle Scholar
  38. 38.
    Cotton, F. A., Haas, T. E.: Inorg. Chem. 3, 10 (1964)CrossRefGoogle Scholar
  39. 39.
    Kettle, S. F. A.: Theor. Chim. Acta. 3, 211 (1965)CrossRefGoogle Scholar
  40. 40.
    Simon, A., von Schnering, H. G., Wohrle, H.: Z. Anorg. Allg. Chem. 339, 155 (1965); Simon, A., von Schnering, H. G., Schäfer, H.: Z. Anorg. Allg. Chem. 361, 235 (1968)CrossRefGoogle Scholar
  41. 41.
    Kettle, S. F. A.: J. Chem. Soc. (A) 1013 (1966)Google Scholar
  42. 42.
    Maxwell, L. R., Hendricks, S. B., Mosley, V. M.: J. Chem. Phys. 3, 699 (1935)CrossRefGoogle Scholar
  43. 43.
    Kettle, S. F. A.: Theor. Chim. Acta. 4, 150 (1966)CrossRefGoogle Scholar
  44. 44.
    Sidgwick, N. V.: Electronic Theory and Valence, Clarendon Press, Oxford 1927; Craig, D. P., Doggett, G.: J. Chem. Soc. 4189 (1963); Tolman, C. A.: Chem. Soc. Rev. 1, 337 (1972)Google Scholar
  45. 45.
    Sidgwick, N. V., Powell, H. E.: Proc. Roy. Soc. A 176, 153 (1940)Google Scholar
  46. 46.
    Corey, E. R., Dahl, L. F., Beck, W.: J. Amer. Chem. Soc. 85, 1202 (1963)CrossRefGoogle Scholar
  47. 47.
    Kettle, S. F. A.: J. Chem. Soc. (A) 314 (1967)Google Scholar
  48. 48.
    Schulman, J. M., Fischer, C. R., Solomon, P., Venanzi, T. J.: J. Amer. Chem. Soc. 100, 2949 (1978)CrossRefGoogle Scholar
  49. 49.
    Heilbronner, E., Jones, T. B., Krebs, A., Maisch, D.-D., Maier, G., Pocklington, J., Schmelzer, A.: J. Amer. Chem. Soc. 102, 564 (1980)CrossRefGoogle Scholar
  50. 50.
    Mingos, D. M. P.: Nature Phys. Sci. 236, 99 (1972)Google Scholar
  51. 51.
    Gillespie, R. J.: Chem. Soc. Rev. 8, 315 (1979) and references thereinCrossRefGoogle Scholar
  52. 52.
    Gillespie, R. J., Nyholm, R. S.: Quart. Rev. Chem. Soc. 11, 339 (1957); Gillespie, R. J.: Molecular Geometry, Van Nostrand-Reinhold, Princeton, New Jersey 1972CrossRefGoogle Scholar
  53. 53.
    Burns, R. C., Gillespie, R. J., Luk, W.-C., Slim, D. R.: J. Chem. Soc., Chem. Commun. 791 (1976); Inorg. Chem. 18, 3086 (1979)Google Scholar
  54. 54.
    Wei, C.-H., Dahl, L. F.: J. Amer. Chem. Soc. 88, 1821 (1966); Strouse, C. E., Dahl, L. F.: Discuss. Faraday Soc. 47, 93 (1969); Stevenson, D. L., Wei, C.-H., Dahl, L. F.: J. Amer. Chem. Soc. 93, 6027 (1971); Strouse, C. E.. Dahl, L. F.: J. Amer. Chem. Soc. 93, 6032 (1971)CrossRefGoogle Scholar
  55. 55.
    McGlinchey, M. J., Tal, Y.: Chemical Applications of Topology and Graph Theory, Studies in Phys. and Theor. Chem. 28, 124 (1983)Google Scholar
  56. 56. (a)
    King, R. B., Rouvray, D. H.: J. Amer. Chem. Soc. 99, 7834 (1977). (b) King, R. B.: Inorg. Chim. Acta. 49, 237 (1981); 57, 79 (1982); 116, 99, 109, 119, 125 (1986). (c) King, R. B.: Polyhedron 1, 132 (1982)CrossRefGoogle Scholar
  57. 57.
    King, R. B.: J. Amer. Chem. Soc. 91, 7211 (1969); 92, 6455, 6460 (1970); 94, 95 (1972)CrossRefGoogle Scholar
  58. 58.
    Teo B. K.: Inorg. Chem. 23, 1251 (1984); Teo, B. K., Longoni, G., Chung, F. R. K.: Inorg. Chem. 23, 1258 (1984)CrossRefGoogle Scholar
  59. 59.
    O'Neill, M. E., Wade, K.: Inorg. Chem. 21, 461 (1982)CrossRefGoogle Scholar
  60. 60.
    Pipal, J. R., Grimes, R. N.: Inorg. Chem. 18, 257 (1979)CrossRefGoogle Scholar
  61. 61.
    Bowser, J. R., Bonny, A., Pipal, J. R., Grimes, R. N.: J. Amer. Chem. Soc. 101, 6229 (1979)CrossRefGoogle Scholar
  62. 62.
    Mulliken, R. S.: J. Chem. Phys. 3, 375 (1935)CrossRefGoogle Scholar
  63. 63.
    Longuet-Higgins, H. C.: Quart. Rev. Chem. Soc. 11, 121 (1957)CrossRefGoogle Scholar
  64. 64.
    Longuet-Higgins, H. C., de V. Roberts, M.: Proc. Roy. Soc. A 230, 110 (1955)Google Scholar
  65. 65. (a)
    Hoffmann, R., Lipscomb, W. N.: J. Chem. Phys. 36, 2179 (l962). (b) Hoffmann, R., Lipscomb, W. N.: J. Chem. Phys. 36, 3489 (1962); 37, 2872 (1962)CrossRefGoogle Scholar
  66. 66.
    Mulliken, R. S.: J. Chem. Phys. 23, 1833, 2343 (1955)CrossRefGoogle Scholar
  67. 67.
    Hoffmann, R.: J. Chem. Phys. 39, 1397 (1963)CrossRefGoogle Scholar
  68. 68.
    Klanberg, F., Muetterties, E. L.: Inorg. Chem. 5, 1955 (l966); Eatin, D. R., Guggenberger, L. J., Muetterties, E. L.: Inorg. Chem. 6, 1271 (1967); Guggenberger, L. J.: Inorg. Chem. 7, 2260 (1968); Guggenberger L. J.: Inorg. Chem. 8, 2771 (1969)CrossRefGoogle Scholar
  69. 69.
    Dixon, D. A., Kleier, D. A., Halgren, T. A., Hall, J. H, Lipscomb, W. N.: J. Amer. Chem. Soc. 99, 6226 (1977); Dewar, M. J. S., McKee, M. L.: Inorg. Chem. 17, 1569 (1978);19, 2662 (1980); Guest, M. F., Hillier, I. H.: Mol. Phys. 26, 435 (1973)CrossRefGoogle Scholar
  70. 70.
    Williams, R. E.: Prog. Boron Chem. 2, 51 (1970)Google Scholar
  71. 71.
    Williams, R. E.: Inorg. Chem. 10, 210 (1971); Williams, R. E.: Adv. Inorg. Chem. Radiochem. 18, 67 (1976)CrossRefGoogle Scholar
  72. 72. (a)
    Wade, K.: J. Chem. Soc., Chem. Commun. 792 (1971). (b) See also: Wade, K.: Adv. Inorg. Chem. Radiochem. 18, 1 (1976); Wade, K.: in Ref. 1b, Ch. 3 p. 193Google Scholar
  73. 73.
    Rudolph, R. W., Pretzer, W. R.: Inorg. Chem. 11, 1974 (1972); Rudolph, R. W.: Acc. Chem. Res. 9, 446 (1976)CrossRefGoogle Scholar
  74. 74.
    Johnston, R. L., Mingos, D. M. P.: Inorg. Chem. 25, 1661 (1986)CrossRefGoogle Scholar
  75. 75.
    Albano, V., Chini, P., Scatturin, V.: J. Chem. Soc., Chem. Commun. 163 (1968)Google Scholar
  76. 76.
    Johnson, B. F. G., Johnston, R. D., Lewis, J.: J. Chem. Soc., Chem. Commun. 1057 (1967); Mason R., Robinson, W.: J. Chem. Soc., Chem. Commun. 468 (1968)Google Scholar
  77. 77.
    Albano, V., Bellon, P. L., Chini, P., Scatturin, V.: J. Organomet. Chem. 16, 461 (1969)CrossRefGoogle Scholar
  78. 78.
    Braterman, P. S.: Struct. Bond. 10, 57 (1972)Google Scholar
  79. 79.
    Churchill, M. R., Wormwald, J., Knight, J., Mays, M. J.: J. Chem. Soc. Chem. Commun. 458 (1970)Google Scholar
  80. 80.
    Braye, E. H., Dahl, L. F., Hubel, W., Wampler, D. L.: J. Amer. Chem. Soc. 84, 4633 (1962)CrossRefGoogle Scholar
  81. 81.
    Wade, K.: Inorg. Nucl. Chem. Lett. 8, 559, 563, 823 (1972); Wade, K.: Nature Phys. Sci. 240, 71 (1972)CrossRefGoogle Scholar
  82. 82.
    Mason, R., Thomas, K. M., Mingos, D. M. P.: J. Amer. Chem. Soc. 95, 3802 (1973)CrossRefGoogle Scholar
  83. 83.
    Evans, J.: J. Chem. Soc., Dalton Trans. 18, 35 (1978)Google Scholar
  84. 84.
    Mingos, D. M. P.: J. Chem. Soc., Dalton Trans. 133 (1974)Google Scholar
  85. 85.
    Lauher, J. W.: J. Amer. Chem. Soc. 100, 5305 (1978)CrossRefGoogle Scholar
  86. 86.
    Halpern, J.: Discuss. Faraday Soc. 46, 7 (1968)CrossRefGoogle Scholar
  87. 87.
    Foust, A. S., Foster, M. S., Dahl, L. F.: J. Amer. Chem. Soc. 91, 5631 (1969)CrossRefGoogle Scholar
  88. 88.
    Ellis, J. E.: J. Chem. Educ. 53, 2 (1976)CrossRefGoogle Scholar
  89. 89.
    Herder, W. R., Klanberg, F., Muetterties, E. L.: Inorg. Chem. 6, 1696 (1967)CrossRefGoogle Scholar
  90. 90.
    Corbett, J. D.: Inorg. Chem. 7, 198 (1968)CrossRefGoogle Scholar
  91. 91. (a)
    Elian, M., Hoffmann, R.: Inorg. Chem. 14, 1058 (1975). (b) Elian, M., Chen, M. M. L., Mingos, D. M. P., Hoffmann, R.: Inorg. Chem 15, 1148 (1976)CrossRefGoogle Scholar
  92. 92.
    Hoffmann, R.: Nobel Lecture 1981, Science 211, 995 (1981); Hoffmann, R.: Angew. Chem. Int. Edn. Engl. 21, 711 (1982)Google Scholar
  93. 93.
    Stone, F. G. A.: Angew. Chem. Int. Edn. Engl. 23, 89 (1984) and references thereinCrossRefGoogle Scholar
  94. 94.
    DeKock, R. L., Fehlner, T. P.: Polyhedron 1, 521 (1982)CrossRefGoogle Scholar
  95. 95.
    Greenwood, N. N., Savory, C. G., Grimes, R. N., Sneddon, L. G., Davison, A., Wreford, S. S.: J. Chem. Soc., Chem. Commun. 718 (1974)Google Scholar
  96. 96.
    Miller, V. R., Weiss, R., Grimes, R. N.: J. Amer. Chem. Soc. 99, 5646 (1977)CrossRefGoogle Scholar
  97. 97.
    Brint, R. P., Pelin, K., Spalding, T. R.: Inorg. Nucl. Chem. Lett. 16, 391 (1980); Brint, R. P., Spalding, T. R.: J. Chem. Soc., Dalton Trans. 1236 (1980)CrossRefGoogle Scholar
  98. 98.
    Woolley, R. G.: Inorg. Chem. 24, 3525 (1985)CrossRefGoogle Scholar
  99. 99.
    Woolley, R. G.: Nouv. J. Chim. 5, 219, 227, 441 (1981); Woolley, R. G.: in Ref. lb, Ch. 9 p. 607; Woolley, R. G.: Inorg. Chem. 24, 3519 (1985)Google Scholar
  100. 100.
    Nicholls, J. N.: Polyhedron 3, 1307 (1984); Herrmann, W. A.: Angew. Chem. Int. Edn. Eng]. 25, 56 (1986) and references thereinCrossRefGoogle Scholar
  101. 101.
    Mingos, D. M. P., Forsyth, M. L: J. Chem. Soc., Dalton Trans. 610 (1977)Google Scholar
  102. 102.
    Albano, V. G., Bellon, P. L., Ciani, G. F.: J. Chem. Soc., Chem. Commun. 1024 (1969)Google Scholar
  103. 103.
    Evans, D. G., Mingos, D. M. P.: Organometallics 2, 435 (1983)CrossRefGoogle Scholar
  104. 104.
    Goudsmit, R. J., Johnson, B. F. G., Lewis, J., Raithby, P. R., Whitmire, K. H.: J. Chem. Soc., Chem. Commun. 640 (1982)Google Scholar
  105. 105.
    McPartlin, M., Eady, C. R., Johnson, B. F. G., Lewis, J.: J. Chem. Soc., Chem. Commun. 883 (1976)Google Scholar
  106. 106.
    McPartlin, M.: Polyhedron 3, 1279 (1984); McPartlin, M., Mingos, D. M. P.: Polyhedron 3, 1321 (1984)CrossRefGoogle Scholar
  107. 107.
    Evans, D. G., Mingos, D. M. P.: J. Organomet. Chem. 240, 321 (1982)CrossRefGoogle Scholar
  108. 108.
    Mingos, D. M. P.: J. Chem. Soc., Dalton Trans. 601 (1977)Google Scholar
  109. 109.
    Mingos, D. M. P.: J. Chem. Soc., Dalton Trans. 1163 (1976)Google Scholar
  110. 110.
    Nyholm, R. S.: Proc. Chem. Soc. Lond. 273 (1961); Pyykkö, P., Desclaux, J.-P.: Acc. Chem. Res. 12, 276 (1979)Google Scholar
  111. 111.
    van Koten, G., Noltes, J. G.: in Comprehensive Organometallic Chemistry (eds. Wilkinson, G., Stone, F. G. A., Abel, E. W.,) Pergamon, Oxford 1982, Vol. 2 p. 709; Noltes, J. G.: Phil. Trans. R. Soc. Lond. A308, 35 (1982). For a theoretical treatment of bridged copper clusters see: Mehrotra, P. K., Hoffmann, R.: Inorg. Chem. 17, 2187 (1978)Google Scholar
  112. 112.
    See, for example: Briant, C. E., Smith, R. G., Mingos, D. M. P.: J. Chem. Soc., Chem. Commun. 586 (1984)Google Scholar
  113. 113.
    Evans, D. G., Mingos, D. M. P.: J. Organomet. Chem. 232, 171 (1982); 295, 389 (1985)CrossRefGoogle Scholar
  114. 114.
    Johnson, B. F. G., Kaner, D. A., Lewis, J., Raithby, P. R.: J. Organoment. Chem. 215, C33 (1981); Johnson, B. F. G., Kaner, D. A., Lewis, J., Raithby, P. R., Taylor, M. J.: J. Chem. Soc., Chem. Commun. 314 (1982); Green, M., Orpen, A. G., Salter, I. D., Stone, F. G. A.: J. Chem. Soc., Chem. Commun. 813 (1982); Lehrer, H., Matt, D., Pregosin, P. S., Venanzi, L. M., Albinati, A.: J. Amer. Chem. Soc. 104, 6825 (1982)CrossRefGoogle Scholar
  115. 115.
    Mingos, D. M. P.: Pure Appl. Chem. 52, 705 (1980)Google Scholar
  116. 116.
    Briant, C. E., Theobald, B. R. C., White, J. W., Bell, L. K., Mingos, D. M. P., Welch, A. J.: J. Chem. Soc., Chem. Commun. 201 (1981)Google Scholar
  117. 117.
    Mingos, D. M. P.: Phil. Trans. R. Soc. Lond. A308, 75 (1982); Hall, K. P., Gilmour, D. I., Mingos, D. M. P.: J. Organomet. Chem. 268, 275 (1984); Mingos, D. M. P.: Polyhedron 3, 1289 (1984)Google Scholar
  118. 118.
    Mingos, D. M. P.: J. Chem. Soc., Chem. Commun. 706 (1983)Google Scholar
  119. 119.
    Mingos, D. M. P.: Acc. Chem. Res. 17, 311 (1984)CrossRefGoogle Scholar
  120. 120.
    Mingos, D. M. P., Evans, D. G.: J. Organomet. Chem. 251, C13 (1983)CrossRefGoogle Scholar
  121. 121.
    Chini, P.: J. Organomet. Chem. 200, 37 (1980)CrossRefGoogle Scholar
  122. 122.
    Lauber, J. W.: J. Amer. Chem. Soc. 101, 2604 (1979)CrossRefGoogle Scholar
  123. 123.
    Ciani, G., Sironi, A.: J. Organomet. Chem. 197, 233 (1980)CrossRefGoogle Scholar
  124. 124.
    Slovokhotov, Yu. L., Struchkov, Yu. T.: Russ. Chem. Rev., 54, 323 (1985)CrossRefGoogle Scholar
  125. 125.
    Hume-Rothery, W.: The Metallic State, Oxford University Press, New York, 1931, p. 328Google Scholar
  126. 126.
    Teo, B. K.: J. Chem. Soc., Chem. Commun. 1362 (1983)Google Scholar
  127. 127. (a)
    Messmer, R. P., Knudson, S. K., Johnson, K. H., Diamond, J. B., Yang, C. Y.: Phys. Rev. B: Solid State 13, 1396 (1976). (b) Yang, C. Y., Johnson, K. H., Salahub, D. R., Kaspar, J., Messmer, R. P.: Phys. Rev. B: Solid State 24, 5673 (1981)Google Scholar
  128. 128. (a)
    Mingos, D. M. P.: J. Chem. Soc., Chem. Commun. 1352 (1985). (b) Mingos, D. M. P.: Chem. Soc. Rev., 15, 31 (1986)Google Scholar
  129. 129.
    Vollenbroek, F. A., van der Berg, J. P., van der Velden, J. W. A., Bout, J. J.: Inorg. Chem. 19, 2685 (1980)CrossRefGoogle Scholar
  130. 130.
    Burdett, J. K.: Prog. Solid State Chem. 15, 173 (1985)CrossRefGoogle Scholar
  131. 131.
    Mingos, D. M. P.: Anglo-Japanese Advanced Research Meeting: Molecular Basis of Transition Metal Catalysis, April 1985, Abstracts, p. 9Google Scholar
  132. 132.
    Shustorovich, E.: N.A.T.O. A.S.I. Ser., Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry (Ed. Veillard, A.,) Reidel, Dordrecht (NL) 1986, 445; Shustorovich, E.: Surf. Sci. Rep. 6, 1 (1986)Google Scholar
  133. 133.
    Benfield, R. E., Edwards, P. P., Stacy, A. M.: J. Chem. Soc., Chem. Commun. 525 (1982); Benfield, R. E., Edwards, P. P., Nelson, W. J. H., Vargas, M. D., Johnson, D. C., Sienko, M. J.: Nature 314, 231 (1985); Teo, B. K., DiSalvo, F. J., Waszczak, J. V., Longoni, G., Ceriotti, A.: Inorg. Chem. 25, 2262 (1986)Google Scholar
  134. 134.
    Benfield, R. E.: unpublished work, mentioned at the Dalton/A.C.S. meeting: Clusters in the Solid State, Birmingham (U.K.) 1986Google Scholar
  135. 135.
    Pimental, G. C., Pitzer, K. S.: J. Chem. Phys. 17, 882 (1949)CrossRefGoogle Scholar
  136. 136.
    See, for example: DeKock, R. L., Gray, H. B.: Chemical Structure and Bonding, Benjamin/ Cummings, Menlo Park (California) 1980, p. 419Google Scholar
  137. 137.
    Bayliss, N. S.: J. Chem. Phys. 16, 287 (1948); Kuhn, H.: J. Chem. Phys. 16, 840 (1948); Platt, J. R.: J. Chem. Phys. 22, 1448 (1954); Wheland, G. R.: Resonance in Organic Chemistry, Wiley, New York 1955CrossRefGoogle Scholar
  138. 138.
    Lu, C.-S., Donohue, J.: J. Amer. Chem. Soc. 66, 818 (1944)CrossRefGoogle Scholar
  139. 139.
    Chapman, D., Waddington, T. C.: Trans. Faraday Soc. 58, 1679 (1962)CrossRefGoogle Scholar
  140. 140.
    Hoffmann, R., Gouterman, M.: J. Chem. Phys. 36, 2189 (1962)CrossRefGoogle Scholar
  141. 141.
    Bethe, H. A.: Ann. Physic. 3, 133 (1929); Van Vleck, J. H.: J. Chem. Phys. 3, 807 (1935); Griffith, J. S.: The Theory of Transition Metal Ions, Cambridge University Press, Cambridge 1961; Ballhausen, C. J.: Ligand Field Theory, McGraw-Hill, New York 1962Google Scholar
  142. 142.
    Waddington, T. C.: Trans. Faraday Soc. 63, 1313 (1967)CrossRefGoogle Scholar
  143. 143.
    Hoffmann, D. K., Ruedenberg, K., Verkade, J. G.: Struct. Bond. 33, 57 (1977)CrossRefGoogle Scholar
  144. 144.
    Mulliken, R. S.: Rev. Mod. Phys. 2, 60, 506 (1930); 4, 40 (1932)CrossRefGoogle Scholar
  145. 145. (a1)
    Stone, A. J.: Mol. Phys. 41, 1339 (1980). (b) Stone, A. J.: Inorg. Chem. 20, 563 (1981). (c) Stone, A. J., Alderton, M. J.: Inorg. Chem. 21, 2297 (1982). (d) Stone, A. J.: Polyhedron 3, 2051 (1984)CrossRefGoogle Scholar
  146. 146.
    Brink, D. M., Satchler, G. R.: Angular Momentum (2nd. Edn.), Oxford University Press, Oxford 1971Google Scholar
  147. 147.
    Eckart, C.: Phys. Rev. 36, 878 (1930)CrossRefGoogle Scholar
  148. 148.
    Hilckel, E.: Z. Physik. 70, 204 (1931); 72, 310 (1931); 76, 628 (1932)CrossRefGoogle Scholar
  149. 149.
    Brint, P., Cronin, J. P., Seward, E.: J. Chem. Soc., Dalton Trans. 675 (1983)Google Scholar
  150. 150.
    Fowler, P. W., Porterfield, W. W.: Inorg. Chem. 24, 3511 (1985)CrossRefGoogle Scholar
  151. 151.
    Johnston, R. L., Mingos, D. M. P.: J. Organomet. Chem. 280, 419 (1985)CrossRefGoogle Scholar
  152. 152.
    Johnston, R. L., Mingos, D. M. P.: J. Organomet. Chem. 280, 407 (1985)CrossRefGoogle Scholar
  153. 153.
    Biggs, N. L.: Algebraic Graph Theory, Cambridge University Press, London 1974Google Scholar
  154. 154.
    Redmond, D. B., Quinn, C. M., McKiernan, J. G. R.: J. Chem. Soc., Faraday Trans. II 79, 1791 (1983); Inorg. Chem. 22, 2310 (1983); J. Chem. Educ. 61, 569, 572 (1984)CrossRefGoogle Scholar
  155. 155.
    McDonnell Jr., P. W.: Introduction to Map Making, Marcell Dekker, New York 1979Google Scholar
  156. 156. (a)
    Fowler, P. W.: Polyhedron 4, 2051 (1985). (b) Fowler, P. W., Woolrich, J.: Chem. Phys. Lett. 127, 84 (1986)CrossRefGoogle Scholar
  157. 157. (a)
    Johnston, R. L., Mingos, D. M. P.: J. Chem. Soc., Dalton Trans. 647 (1987). (b) Johnston, R. L., Mingos, D. M. P.: J. Chem. Soc., Dalton Trans., 1445 (1981)Google Scholar
  158. 158.
    Altmann, S. L.: Induced Representations in Crystals and Molecules, Academic Press, New York 1977Google Scholar
  159. 159.
    Ceulemans, A.: Mol. Phys. 54, 161 (1985)CrossRefGoogle Scholar
  160. 160.
    See, for example: Cotton, F. A.: Chemical Applications of Group Theory (2nd Edn.), Wiley, New York 1971Google Scholar
  161. 161.
    Maier, G., Pfriem, S., Schafter, U., Matusch, R.: Angew. Chem. 90, 652 (1978)Google Scholar
  162. 162.
    Atoji, M., Lipscomb, W. N.: Acta Crystallogr. 6, 547 (1953)CrossRefGoogle Scholar
  163. 163.
    Brown, L. D., Lipscomb, W. N.: Inorg. Chem. 16, 2989 (1977); Bicerano, G., Marynick, D. S., Lipscomb, W. N.: Inorg. Chem. 17, 2041, 3443 (1978)CrossRefGoogle Scholar
  164. 164.
    Johnston, R. L., Mingos, D. M. P.: Polyhedron 5, 2059 (1986)CrossRefGoogle Scholar
  165. 165.
    Bould, J., Greenwood, N. N., Kennedy, J. D., McDonald, W. S.: J. Chem. Soc., Chem. Commun. 465 (1982). For further examples of hypercloso (or iso-closo) metallaboranes see: Baker, R. T.: Inorg. Chem. 25, 109 (1986); Kennedy, J. D.: Inorg. Chem. 25, 111 (1986); Kennedy, J. D.: Prog. Inorg. Chem. 32, 519 (1984); 34, 211 (1986); Greenwood, N. N.: Chem. Soc. Rev. 13, 353 (1984) and references therein For a discussion of the bonding in these molecules see: Johnston, R. L., Mingos, D. M. P.: Inorg. Chem. 25, 3321 (1986); Johnston, R. L.: D. Phil. Thesis, University of Oxford 1986Google Scholar
  166. 166.
    Hoffmann, R., Schilling, B. E. R., Bau, R., Kaesz, H. D., Mingos, D. M. P.: J. Amer. Chem. Soc. 100, 6088 (1978); Schilling, B. E. R., Hoffmann, R.: J. Amer. Chem. Soc. 101, 3456 (1979)CrossRefGoogle Scholar
  167. 167. (a)
    Bullett, D. W.: Phys. Rev. Lett. 39, 664 (1977); Chang, K. W., Woolley, R. G.: J. Phys. C 12, 2745 (1979). (b) Seifert, G., Mrosan, E., Midler, H.: Phys. Status Solidi B 89, 553 (1978); Cotton, F. A., Stanley, G. G.: Chem. Phys. Lett. 58, 450 (1978), Johnson, K. H.: Crit. Rev. Solid State Mater. Sci. 7, 101 (1978); Messmer, R. P.: Surf. Sci. 106, 225 (1981); Case, D. A.: Annu. Rev. Phys. Chem. 33, 151 (1982)CrossRefGoogle Scholar
  168. 168.
    Demuynck, J., Rohmer, M.-M., Strich, A., Veillard, A.: J. Chem. Phys. 75, 3443 (1981)CrossRefGoogle Scholar
  169. 169.
    Hall, M. B., Fenske, R. F.: Inorg. Chem. 11, 768 (1972); Teo, B. K., Hall, M. B., Fenske, R. F., Dahl, L. F.: J. Organomet. Chem. 70, 413 (1974); Cheskey, P. T., Hall, M. B.: Inorg. Chem. 20, 4419 (1981); Sherwood Jr., D. E., Hall, M. B.: Inorg. Chem. 21, 3458 (1982); Sherwood Jr., D. E., Hall, M. B.: Organometallics 1, 1519 (1982)CrossRefGoogle Scholar
  170. 170.
    See, for example: Korol'kov, D. V., Miessner, H.: Z. Phys. Chem. 253, 25 (1973)Google Scholar
  171. 171.
    Manning, M. C., Trogler, W. C.: Coord. Chem. Rev. 38, 89 (1981)CrossRefGoogle Scholar
  172. 172.
    Andersen, O. K., Woolley, R. G.: Mol. Phys. 26, 905 (1973); Andersen, O. K.: Phys. Rev. B: Solid State 12, 3060 (1975); Andersen, O. K., Klose, W., Nohl, H.: Phys. Rev. B: Solid State 17, 1209 (1978)CrossRefGoogle Scholar
  173. 173.
    See, for example: Albright, T. A., Burdett, J. K., Whangbo, M.-H.: Orbital Interactions in Chemistry, Wiley, New York 1984, Ch. 13 p. 229; Hoffmann, R., Zheng, C.: N.A.T.O. A.S.I. Ser., Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry (Ed. Veillard, A.), Reidel, Dordrecht (NL) 1986, p. 425; Burdett, J. K., Canadell, E., Hughbanks, T.: J. Amer. Chem. Soc. 108, 3971 (1986); Burdett, J. K.: Struct. Bond., 65, 29 (1987)Google Scholar
  174. 174.
    Wei, C.-H., Dahl, L. F.: J. Amer. Chem. Soc. 91, 1351 (1969)CrossRefGoogle Scholar
  175. 175.
    Benfield, R. E., Johnson, B. F. G.: Top. Stereochem. 12, 253 (1981) and references thereinGoogle Scholar
  176. 176.
    Kepert, D. L., Williams, S. C.: J. Organomet. Chem. 217, 235 (1981)CrossRefGoogle Scholar
  177. 177.
    Mingos, D. M. P.: Inorg. Chem. 21, 464 (1982)CrossRefGoogle Scholar
  178. 178.
    Lauher, J. W.: J. Amer. Chem. Soc. 108, 1521 (1986)CrossRefGoogle Scholar
  179. 179.
    Clare, B. W., Favas, M. C., Kepert, D. L., May, A. S.: Adv. Dynamic Stereochem. 1, 1 (1985) and references thereinGoogle Scholar
  180. 180.
    Berkert, U., Allinger, N. L.: Molecular Mechanics, American Chemical Society, Washington 1982Google Scholar
  181. 181.
    Evans, D. G.: D. Phil. Thesis, University of Oxford 1984 and references thereinGoogle Scholar
  182. 182.
    Evans, D. G.: J. Chem. Soc., Chem. Commun. 675 (1983)Google Scholar
  183. 183.
    Minot, C., Criado-Sancho, M.: Nouv. J. Chim. 8, 537 (1984)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • D. Michael
    • 1
  • P. Mingos
    • 1
  • Roy L. Johnston
    • 1
  1. 1.Inorganic Chemistry LaboratoryUniversity of OxfordOxfordUK

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