Advertisement

The SCF-Xα Scattered-Wave Method with Applications to Molecules and Surfaces

  • Notker Rösch
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 24)

Abstract

Currently theoreticians in molecular science and solid state physics are confronted with a growing demand for a quantitative description of systems consisting of a large, but finite number of electrons. Experiments on systems of increasing complexity are being performed, and very often such additional information is necessary to fully interpret the measurements. Systems with a finite number of electrons may exist as isolated entities, like polyatomic molecules in the gas phase, but in most cases they are models to study more or less localized phenomena in extended systems. To mention a few examples, we may think of a molecular complex in solution, e. g. a transition metal ion surrounded by a number of ligand atoms or molecules, of impurities or defects in an otherwise perfect crystal or of an atom or molecule chemisorbed on a metal surface. The size of such a model cluster will certainly depend on the interactions between the constituent atoms. But our choice may also be influenced by the kind of question we would like to have answered and, more often than not, our computing facilities will enforce some compromise. These questions will be taken up in more detail later on and in the lectures of Prof. Lidiard and Dr. Herman.

Keywords

Spin Orbital Oxygen Sphere Discrete Variational Method High Occupied Orbital Orbital Wave Function 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. R. Hartree, Proc. Camb. Phil. Soc., 24, 9 89, 111, 426 (1928).ADSCrossRefGoogle Scholar
  2. 2.
    J.C. Slater, Phys. Rev., 32, 339 (1928).Google Scholar
  3. 3.
    C.C.J. Roothaan, Rev. Mod. Phys., 23., 69 (1951).ADSMATHCrossRefGoogle Scholar
  4. 4.
    J.C. Slater, Quantum Theory of Atomic Structure, Vol. I and II (McGraw-Hill, New York, i960).Google Scholar
  5. 5.
    J.A. Pople and D.L. Beveridge, Approximate Molecular Orbital Theory ( McGraw-Hill, New York, 1970 ).Google Scholar
  6. 6.
    C.A. Coulson and I. Fischer, Phil. Mag., 40, 386Google Scholar
  7. 7.
    T. C. Collins, in Electronic Structure of Polymers and Molecular Crystals, eds. J.-M. Andre and J. Ladik ( Plenum Press, New York, 1975 ) p. 405.Google Scholar
  8. 8.
    J.C. Slater, Phys. Rev., 8l, 385 (1951).Google Scholar
  9. 9.
    N.M. Hugenholtz, Physica, 23, 48l (1957).MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    F. Herman and S. Skillman, Atomic Structure Calculations ( Prentice Hall, Englewood Cliffs, 1963 ).Google Scholar
  11. 11.
    e. g.: Computational Methods in Band Theory, P.M. Marcus, J.F. Janak and A.R. Williams ( Plenum Press, New York, 1971 ).Google Scholar
  12. 12.
    J.W.D. Connolly, Phys. Rev., 159, 415 (1967).Google Scholar
  13. 13.
    R. Gaspar, Acta Physica Hung., 3., 263 (1954).MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    W. Kohn and L.J. Sham, Phys. Rev., l40, A1133 (1965).Google Scholar
  15. 15.
    J.C. Slater and J.H. Wood, Int. J. Quantum Chem., S4 3 (1971).Google Scholar
  16. 16.
    J.C. Slater, Adv. Quantum Chem., 6, 1 (1972).ADSCrossRefGoogle Scholar
  17. 17.
    J.C. Slater, J. Chem. Phys., 43, S228 (1965).MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    K.H. Johnson, J. Chem. Phys.,45,3085 (1966)5 int. J. Quantum Chem., SI, 361 (196T).Google Scholar
  19. 19.
    a) J. Korringa, Physica, 13, 392 (1947); b) W. Kohn and J. Rostocker, Phys. Rev., 94 1111 (1954).Google Scholar
  20. 20.
    K.H. Johnson, Adv. Quantum Chem., 7, 147 (1973).Google Scholar
  21. 21.
    P. Weinberger and K. Schwarz, in Physical Chemistry, Series Two, Vol. 1, Theoretical Chemistry, eds. A.D. Buckingham and C.A. Coulson ( Butterworths, London, 1915 ) p. 257.Google Scholar
  22. 23.
    K.H. Johnson, Ann. Rev. Phys. Chem., 26, 39 (1975).ADSCrossRefGoogle Scholar
  23. 21.
    J.C. Slater, The Self-consistent Field for Molecules and Solids, Vol. IV of: Quantum Theory of Molecules and Solids ( McGraw-Hill, New York, 1974 ).Google Scholar
  24. 25.
    F. Bloch, Z. Physik, 57, 545 (1929); P.A.M. Dirac, Proc. Camb. Phil. Soc., 26, 376 (1930).Google Scholar
  25. 26.
    E. Wigner and F. Seitz, Phys. Rev., 43, 804 (1933).Google Scholar
  26. 27.
    see also ref. k, Vol. II, app. 22, p. 323.Google Scholar
  27. 28.
    T.C. Koopmans, Physica, 1, 104 (1933).Google Scholar
  28. 29.
    J.C. Slater, J.B. Mann, T.M. Wilson and J.H. Wood, Phys. Rev., l84, 672 (1969).Google Scholar
  29. 30.
    J.C. Slater, J. Chem. Phys., 57, 2389 (1972).ADSCrossRefGoogle Scholar
  30. 31.
    M. Ross, Phys. Rev., 179, 612 (1969); W. E. Rudge, Phys. Rev., l8l, 1033 (1969); L.J. Sham, Phys. Rev., Al, 169 (1970).Google Scholar
  31. 32.
    J.B. Mann, Los Alamos Sci. Lap. Rep. LA-369O (1967) and LA-369I (1968).Google Scholar
  32. 33.
    K. Schwarz, Phys. Rev., B5., 2466 (1972); Theoret. Chim. Acta., 34, 225 (1974).Google Scholar
  33. 33a.
    K. Schwarz and J.W.D. Connolly, J. Chem. Phys., 55, 4710 (1971).ADSCrossRefGoogle Scholar
  34. 34.
    I. Lindgren, Ark. Fys., 31, 59 (1966).Google Scholar
  35. 35.
    E.A. Kmetko, Phys. Rev., Al, 37 (1970).Google Scholar
  36. 36.
    J.H. Wood, Int. J. Quantum Chem., S3, 747 (1970).Google Scholar
  37. 37.
    M. Berrondo and O. Goscinski, Int. J. Quantum Chem., S3, 775 (1969).ADSCrossRefGoogle Scholar
  38. 38.
    J.C. Slater and J.H. Wood, Int. J. Quantum Chem., S4, 3 (1971).Google Scholar
  39. 39.
    R. Schrieffer, J. Vac. Sei. Technol., 13, 335 (1976).Google Scholar
  40. 40.
    P.S. Bagus and B.I. Bennett, Int. J. Quantum Chem., 9, l43 (1975).Google Scholar
  41. 41.
    O. Goscinski, B.T. Pickup and G. Purvis, Chem. Phys. Lett., 22, 167 (1973).Google Scholar
  42. 42.
    O. Goscinski, G. Howat and T. Åberg, J. Phys. B8, 11 (1975).ADSGoogle Scholar
  43. 43.
    T.M. Wilson, J.H. Wood and J.C. Slater, Phys. Rev., A2, 620 (1970).Google Scholar
  44. 44.
    P. Hohenberg and W. Kohn, Phys. Rev., 136, B86k (196k).Google Scholar
  45. 45.
    L. Hedin and S. Lundqvist, in Solid State Physics, eds. F. Seitz, D. Turnbull and H. Ehrenreich (Academic Press, New York, 1969) Vol. 23, p. 1; J. Phys. C, 4 2064 (1971).Google Scholar
  46. 46.
    O. Gunnarsson and P. Johannson, Int. J. Quantum Chem., 10, 299 (1976).Google Scholar
  47. 47.
    e. g.: J.R. Smith, in Interactions on Metal Surfaces, Topics in Applied Physics, ed. R. Gomer ( Springer, Berlin, 1975 ), Vol. k9 p. 1.Google Scholar
  48. 48.
    J.R. Sabin, J.P. Worths, and S.B. Trickey, Phys. Rev., B11, 3658 (1975); J.R. Sabin and S.B. Trickey, J. Phys. B, 8, 2593 (1975).Google Scholar
  49. 49.
    I. Lindgren and K. Schwarz, Phys. Rev., A5, 542 (1972).Google Scholar
  50. 50.
    F. Herman, J.P. Van Dyke and I.B. Ortenburger, Phys. Rev. Letters, 22, 807 (1969).ADSCrossRefGoogle Scholar
  51. 51.
    K. Schwarz, Chem. Phys., 7, 9k (1975).Google Scholar
  52. 52.
    P. Lloyd and P.V. Smith, Adv. Phys., 20, 69 (1972).Google Scholar
  53. 53.
    A.R. Williams, Int. J. Quantum Chem., S8, 89 (1974).Google Scholar
  54. 54.
    P.M. Morse and H. Feshbach, Methods of Theoretical Physics (Mc-Graw Hill, New York, 1953), Vol. I, chap. 7.Google Scholar
  55. 55.
    S.M. Blinder, in Physical Chemistry, Series Two, Vol. 1, Theoretical Chemistry, eds. A.D. Buckingham and C.A. Coulson (Butterworths, London, 1975) p.1.Google Scholar
  56. 56.
    L. Scheire and P. Phariseau, Int. J. Quantum Chem., S9, 105 (1975).CrossRefGoogle Scholar
  57. 57-.
    L. Scheire and P. Phariseau, Int. J. Quantum Chem., S8, 109 (19774).Google Scholar
  58. 58.
    L. Scheire and P. Phariseau, Physica, 74, 596 (1974).CrossRefGoogle Scholar
  59. 59.
    e. g. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962) chap. 16.Google Scholar
  60. 60.
    M. Danos and L.C. Maximon, J. Math. Phys., 6, 766 (1965); R. Nozawa, J. Math. Phys., 7, l84l (1966); E.O. Steinborn and E. Filter, Theor. Chim. Acta, 38, 247, 261 (1975).MathSciNetGoogle Scholar
  61. 61.
    D.M. Brink and G.R. Satchler, Angular Momentum (Clarendon Press, Oxford, 1968), 2nd. ed.Google Scholar
  62. 62.
    L. Scheire and P. Phariseau, Int. J. Quantum Chem., 9, 887 (1975).Google Scholar
  63. 63.
    R. Kjellander, Chem. Phys., 12., 469 (1975).ADSCrossRefGoogle Scholar
  64. 64.
    R. Kjellander, Chem. Phys. Lett., 29, 270 (191k).ADSCrossRefGoogle Scholar
  65. 65.
    C.Y. Yang and S. Rabii, Phys. Rev., A12, 362 (1975); B.G. Cartling and D.M. Whitmore, Int. J. Quantum Chem., 10, 393 (1976).Google Scholar
  66. 66.
    L.F.Mattheis, Phys. Rev., 133, A1399 (1964).Google Scholar
  67. 67.
    P.O. Lowdin, Adv. Phys., 5, 1 (1956).Google Scholar
  68. 68.
    T. Loucks, Augmented Plane Wave Method ( Benjamin, New York, 1967 ).Google Scholar
  69. 69.
    J.W.D. Connolly and J.R. Sabin, J. Chem. Phys., 56, 5529 (1972).Google Scholar
  70. 70.
    U. Mitzdorf, Theor. Chim. Acta, 37, 129 (1975).Google Scholar
  71. 71.
    M.L. Sink and G.E. Juras, Chem. Phys. Lett., 20, 474 (1973).ADSCrossRefGoogle Scholar
  72. 72.
    R.F.W. Bader, Acc. Chem. Res., 8, 34 (1975).Google Scholar
  73. 73.
    J.C. Slater, Quantum Theory of Molecules and Solids, Vol. II (McGraw-Hill, New York, 1965) chap. 4.Google Scholar
  74. 74.
    S. Larsson and J.W. D. Connolly, Chem. Phys. Lett., 20, 323 (1973).Google Scholar
  75. 75.
    J.W.D. Connolly and K.H. Johnson, Chem. Phys. Lett., 10, 616 (1971).Google Scholar
  76. 76.
    J.B. Diamond, Chem. Phys. Lett., 20, 63 (1973).MathSciNetADSCrossRefGoogle Scholar
  77. 77.
    e. g. M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 196U).Google Scholar
  78. 78.
    A. Veillard: Computational Techniques in Quantum Chemistry and Molecular Physics, eds. G.H.F. Diercksen, B.T. Sutcliffe and A. Veillard ( Reidel, Dordrecht, 1975 ) p. 201.CrossRefGoogle Scholar
  79. 79.
    V. Heine, in: Solid State Physics, Vol. 24, eds. H. Ehrenreich, F. Seitz and D. Turnbull ( Academic, New York, 1970 ) p. 1.Google Scholar
  80. 80.
    F.S. Ham and B. Segall, Phys. Rev., 124, 1786 (1961).Google Scholar
  81. 81.
    N. Rosch and J. Ladik, Chem. Phys., 13, 285 (1976).Google Scholar
  82. 82.
    F.C. Smith, Jr. and K.H. Johnson, private communication.Google Scholar
  83. 83.
    J.B. Danese and J.W.D. Connolly, J. Chem. Phys., 6l, 3063 (1974).ADSCrossRefGoogle Scholar
  84. 84.
    W. von Nies sen, L.S. Cederbaum, G.H.F. Diercksen and G. Hohlneicher, Chem. Phys., 11, 399 (1975).Google Scholar
  85. 85.
    W. M Tolles and W.D. Gwinn, J. Chem. Phys., 36, 1119 (1962); K. Kimura and S.H. Bauer, J. Chem. Phys., 39, 3172 (1963).Google Scholar
  86. 86.
    a) J.I. Musher, Angew. Chem., 81, 68 (1969);CrossRefGoogle Scholar
  87. b) J.I. Musher, J. Amer. Chem. Soc., 94, 1370 (1972);Google Scholar
  88. c) V.B. Koutecky and J.I. Musher, Theor. Chim. Acta, 33, 227 (1974).CrossRefGoogle Scholar
  89. 87.
    L. Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, 1960), 3rd ed.Google Scholar
  90. 88.
    G. Dogett, Theor. Chim. Acta, l5, 344 (1969).Google Scholar
  91. 89.
    C.A. Coulson, Nature, 221, 1106 (1969).Google Scholar
  92. 90.
    R.E. Rundle, Survey Progr. Chem., 1, 8l (1963).Google Scholar
  93. 91.
    For a detailed list of references, see ref. 91 and 92.Google Scholar
  94. 92.
    N. Rösch, V.H. Smith, Jr. and M.H. Whangbo, J. Amer. Chem. Soc., 96, 5384 (197*0-Google Scholar
  95. 93.
    N. Rösch, V.H. Smith, Jr. and M.H. Whangbo, Inorg. Chem. (1976) to be published.Google Scholar
  96. 94.
    W.E. Dasent, Nonexisting Compounds ( Dekker, New York, 1965 ) p. 153.Google Scholar
  97. 95.
    F.A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry (Wiley-Interscience, New York, 1972) 3rd. ed.Google Scholar
  98. 96.
    M.M. Chen and R. Hoffmann, J. Amer. Chem. Soc., 98, 1647 (1976).CrossRefGoogle Scholar
  99. 97.
    G.M. Schwenzer and H.F. Schaefer III, J. Amer. Chem. Soc., 97, 1393 (1975).Google Scholar
  100. 98.
    R.S. Mulliken, J. Chem. Phys., 23, 1833, l84l (1955).Google Scholar
  101. 99.
    a) D.W. Turner, C. Baker, A.D. Baker and C.R. Brundle, Molecular Photoelectron Spectroscopy ( Wiley, London, 1970 );Google Scholar
  102. b) A. W. Potts, H.J. Lempka, D.G. Streets and W.C. Price, Phil. Trans. Roy. Soc. London, A268, 59 (1970);Google Scholar
  103. c) R.E. LaVilla, J. Chem. Phys., 57, 899 (1972);Google Scholar
  104. d) U. Grelius, J. Electron. Spectr., 5, 985 (1974).Google Scholar
  105. 100.
    K. Siegbahn et al., ESCA Applied to Free Molecules (North-Holland, Amsterdam, 1969)Google Scholar
  106. 101.
    D.P. Santry and G. A. Segal, J. Chem. Phys., 47, 158 (1967).ADSCrossRefGoogle Scholar
  107. 102.
    a) G.L. Bendazzoli, P. Palmieri, B. Cadioli and U. Pincelli, Mol. Phys., 19, 865 (1970);Google Scholar
  108. b) F.A. Gianturco, C. Guidotti, U. Lamanna and R. Moccia, Chem. Phys. Lett., 10, 269 (1971).Google Scholar
  109. c) B. Roos, unpublished results, cited in b).Google Scholar
  110. 103.
    J.G. Fripiat, K.T. Chow, M. Boudart, J.B. Diamond and K.H. Johnson, J. Mol. Catal., 1, 59 (1975).CrossRefGoogle Scholar
  111. 104.
    B.J. Ransil and J.J. Sinai, J. Chem. Phys., 46, 4050 (1967) and unpublished calculations by A.C. Wahl cited therein.Google Scholar
  112. 105.
    W. Kutzelnigg, V. Staemmler and M. Gelus, Chem. Phys. Lett., 13, U96 (1972).Google Scholar
  113. 106.
    P. Weinberger and K. Schwarz, Theor. Chim. Acta, 38, 231 (1975).Google Scholar
  114. 107.
    P. Weinberger and D.D. Konowalow, Int. J. Quantum Chem., S7, 353 (1973).Google Scholar
  115. 108.
    J. Weber and J.W.D. Connolly, Int. J. Quantum Chem., S9, 129 (1975).CrossRefGoogle Scholar
  116. 109.
    J.B. Danese, J. Chem. Phys., 6l, 3071 (1974).Google Scholar
  117. 110.
    J. Keller, Int. J. Quantum Chem., 9, 583 (1975).Google Scholar
  118. 111.
    D.E. Ellis and G.S. Painter, in ref. 11, p. 271, 277; Phys. Rev., B2, 2887 (1970).ADSGoogle Scholar
  119. 112.
    E.J. Baerends, D.E. Ellis and P. Ros, Chem. Phys., 2, 4l (1973);Google Scholar
  120. E.J. Baerends and P. Ros, Chem. Phys., 2 52 (1973); Chem. Phys. 8, 412 (1975).Google Scholar
  121. 113.
    C.B. Haselgrove, Math. Comp., 15, 323 (l96l).Google Scholar
  122. 114.
    W. Heijser, A.T. van Kessel and E.J. Baerends, Chem. Phys. (1976), to be published.Google Scholar
  123. 115.
    H. Sambe and R.H. Felton, J. Chem. Phys., 62, 1122 (1975).ADSCrossRefGoogle Scholar
  124. 116.
    N. Rösch, W.G. Klemperer and K.H. Johnson, Chem. Phys. Lett., 23, 149 (1973).ADSCrossRefGoogle Scholar
  125. 117.
    D.A. Liberman, unpublished results.Google Scholar
  126. 118.
    F. Herman, A.R. Williams and K.H. Johnson, J. Chem. Phys., 61, 3508 (1974).Google Scholar
  127. 119.
    K.H. Johnson, F. Herman and R. Kjellander, in Electronic Structure of Polymers and Molecular Crystals, eds. J. Andre, J. Ladik and J. Delhalle ( Plenum, New York, 1975 ) p. 601.Google Scholar
  128. 120.
    J. Norman, Jr., Mol. Phys., 31, 1191 (1976).Google Scholar
  129. 121.
    D.R. Salahub, R.P. Messmer and K.H. Johnson., Mol. Phys., 31, 529 (1976).Google Scholar
  130. 122.
    P.E. Cade, K.D. Sales and A.C. Wahl, J. Chem. Phys., 44, 1973 (1966).Google Scholar
  131. 123.
    A.C. Wahl, J. Chem. Phys., 41, 2600 (1964).Google Scholar
  132. 124.
    W.M. Huo, J. Chem. Phys., 43, 624 (1965).ADSCrossRefGoogle Scholar
  133. 125.
    G. Herzberg, Molecular Spectra and Molecular Structures I. Spectra of Diatomic Molecules (van Nostrand, Princeton, 1950 ).Google Scholar
  134. 126.
    M. Rosenblum, Chemistry of the Iron Group Metallocenes ( Wiley-Interscience, New York, 1965 ).Google Scholar
  135. 127.
    D.A. Brown, in: Transition Metal Chemistry, Vol. 3, ed. R.L. Carlin ( Dekker, New York, 1966 ).Google Scholar
  136. 128.
    C.J. Ballhausen and H.B. Gray, in: Chemistry of the Coordination Compounds, Vol. 1, ed. A.E. Martell (van Nostrand-Reinhold, New York, 1971 ).Google Scholar
  137. 129.
    a) E.M. Shustorovich and M.E. Dyatkina, J. Struct. Chem., 1, 109 (i960).Google Scholar
  138. b) J.P. Dahl and C.J. Ballhausen, Kgl. Danske Videnskab Selskab Mat. Fys Medd., 33, No. 5 (1961).Google Scholar
  139. c) A.T. Armstrong, D.G. Carroll and S.P. McGlynn, J. Chem. Phys., 47, 110k (1967);Google Scholar
  140. d) J.H. SchachtSchneider, R. Prins and P. Ros, Inorg. Chim. Acta, 1, k62 (1967);Google Scholar
  141. e) R.F. Kirchner, G.H. Loew and U.T. Mueller-Wester-hoff, Theor. Chim. Acta, 41, 1 (1976).Google Scholar
  142. 130.
    a) A.T. Armstrong, F. Smith, E. Elder and S.P. McGlynn, J. Chem. Phys., 46, k321 (1967);Google Scholar
  143. b) P.B. Stephenson and W.E. Winterrod, J. Chem. Phys., 52, 3308 (1970);Google Scholar
  144. c) Y.S. Sohn, D.N. Hendrickson and H.B. Gray, J. Amer. Chem. Soc., 43, 3603 (1971).Google Scholar
  145. 131.
    R. Prins, Mol. Phys., 19, 603 (1970).Google Scholar
  146. 132.
    J.W. Rabalais, L.0. Werme, T. Bergmark, L. Karlsson, M. Hussain and K. Siegbahn, J. Chem. Phys., 57, 1185 (1972).Google Scholar
  147. 133.
    S. Evans, M.L.H. Green, B. Jewitt, A.F. Orchard and C.F. Pygall, JCS Faraday II, 68, 1847 (1972).CrossRefGoogle Scholar
  148. 134.
    M.-M. Coutière, J. Demuynck and A. Veillard, Theor. Chim. Acta, 27, 281 (1972).Google Scholar
  149. 135.
    M. -M. Böhmer, A. Veillard and M. H. Wood, Chem. Phys. Lett., 29, 466 (1974)Google Scholar
  150. 136.
    P.S. Bagus, U.I. Wahlgren and J. Almlof, J. Chem. Phys., 64, 2324 (1976).Google Scholar
  151. 137.
    E.J. Baerends and P. Ros, Chem. Phys. Lett., 23, 391 (1973).Google Scholar
  152. 138.
    N. Rösch and K.H. Johnson, Chem. Phys. Lett., 24, 179 (191b).Google Scholar
  153. 139.
    R.K. Bohn and A. Haaland, J. Organometallie Chem., 5., 470 (1970); G. J. Palenik, Inorg. Chem., 9, 2424 (1970).Google Scholar
  154. 140.
    M.-M. Rohmer and A. Veillard, Chem. Phys. 11, 349 (1975).CrossRefGoogle Scholar
  155. 141..
    M.J.S. Devar, Bull. Soc. Chim. France, 18, C71 (l95l); J. Chatt and L.A. Duncanson, J. Chem. Soc., 1953, 2939.Google Scholar
  156. 142.
    C.J. Ballhausen, Introduction to Ligand Field Theory ( McGraw-Hill, New York, 1962 ).MATHGoogle Scholar
  157. 143.
    J. Demuynck and A. Veillard, Theor. Chim. Acta, 28, 24l (1973).CrossRefGoogle Scholar
  158. 144.
    R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry ( Verlag Chemie, Weinheim, 1971 ).Google Scholar
  159. 145.
    e. g. N. Rösch and R. Hoffmann, Inorg. Chem., 13, 2654 (1974); M. Elian and R. Hoffmann, Inorg. Chem., 14, 365 (1975); J.W. Lauher and R. Hoffmann, J. Amer. Chem. Soc., 98, 1729 (1976); R. Hoffmann, J.M. Howell and A. Rossi, J. Amer. Chem. Soc., 98, 2484 (1976).Google Scholar
  160. 146.
    J.C. Slater and K.H. Johnson, Physics Today, October, 1974, p. 3k.Google Scholar
  161. 147.
    S. Larsson, E.K.Viinikka, M.L. de Sequeira and J.W.D. Connolly, Int. J. Quantum Chem., S8, 1U5 (1974).Google Scholar
  162. 148.
    J.W.D. Connolly, H. Siegbahn, U. Gelius and C. Nordling, J. Chem. Phys., 58, U265 (1973).Google Scholar
  163. 149.
    N. Rösch and V.H. Smith, Jr., work in progress.Google Scholar
  164. 150.
    S. Larsson and J.W.D. Connolly, J. Chem. Phys., 60, 1514 (1974); S. Larsson, Theor. Chira. Acta, 39, 173 (1975).Google Scholar
  165. 151.
    L. Noodleman, J. Chem. Phys., 64, 2343 (1976).Google Scholar
  166. 152.
    D. Dill and J.L. Dehmer, J. Chem. Phys., 6l, 692 (1974); J.L. Dehmer and D. Dill, Phys. Rev. Lett., 35., 213 (1975).Google Scholar
  167. 153.
    J.W. Davenport, Phys. Rev. Lett., 36, 945 (1976).Google Scholar
  168. 154.
    R.P. Messmer, L.V. Interrante and K.H. Johnson, J. Amer. Chem. Soc., 96, 38147 (1974).CrossRefGoogle Scholar
  169. 155.
    N. Rösch, R.P. Messmer and K.H. Johnson, J. Amer. Chem. Soc., 96, 3855 (1974).Google Scholar
  170. 156.
    K.H. Johnson and U. Wahlgren, Int. J. Quantum Chem., S6, 243 (1972).Google Scholar
  171. 157.
    A.P. Mortola, J.W. Moskowitz and N. Rösch, Int. J. Quantum Chem., S8, l6l (1974).CrossRefGoogle Scholar
  172. 158.
    C.Y. Yang, K.H. Johnson, R.H. Holm and J.G. Norman, Jr., J. Amer. Chem. Soc., 97, 6596 (1975).Google Scholar
  173. 159.
    K. Schwarz and N. Rösch, J. Phys. C, 9, L433 (1976); N. Rösch and K. Schwarz, to be published.Google Scholar
  174. 160.
    T.E. Fischer, Physics, Today, 27, No. 5, 23 (1974).Google Scholar
  175. 161.
    Ed. E. Drauglis and R.I. Jaffee, The Physical Basis for Heterogeneous Catalysis, Proceedings of the Batelle Institute Materials Science Colloquium Gstaad 1974 ( Plenum, New York, 1975 ).Google Scholar
  176. 162.
    D. A. Micha, Adv. Chem. Phys., 30, 7 (1975); W.H. Miller, ibid. p. 77.Google Scholar
  177. 163.
    R.B. Bernstein and R.D. Levine, Adv. At. Mol. Phys., 11, 216 (1975).Google Scholar
  178. 164.
    Various articles in Physics Today, 28, No. 4 (1975).Google Scholar
  179. 165.
    Interactions on Metal Surfaces, ed. R. Gomer, Topics in Applied Physics, Vol. 5 (Springer, Berlin, 1975).Google Scholar
  180. 166.
    Electronic Structure and Reactivity of Metal Surfaces, Proceedings of the NATO Advanced Study Institute at Namur 1975 (Plenum, New York, 1976).Google Scholar
  181. 167.
    T.N. Rhodin and D.S.Y. Tong, Physics Today, 28, No. 10 (1975).Google Scholar
  182. 168.
    A.M. Bradshaw, L.S. Cederbaum and W. Domcke, Structure and Bonding,Vol. 24 ( Springer, Berlin, 1975 ).Google Scholar
  183. 169.
    a)J.E. Demuth, D.W. Jepsen and P.M. Marcus, Phys. Rev. Lett., 31, 540 (1973); Surf. Sci., 45, 433 (1975);Google Scholar
  184. b) C.B. Duke, N.O. Lipari and G.E. Laramore, J. Vac. Sci. Technol., 11, 180 (1974); 12, 222 (1975);Google Scholar
  185. c) J.E. Demuth and T.N. Rhodin, Surf. Sci., 45, 249 (1974).Google Scholar
  186. 170.
    D. Menzel, J. Vac. Sci. Technol., 12, 313 (1075).ADSCrossRefGoogle Scholar
  187. 171.
    a) J.R. Schrieffer, J. Vac Technol., 9, 561 (1972); 13, 335 (1976).Google Scholar
  188. b) A. Clark, The Chemisorptive Bond ( Academic, New York, 1974 )Google Scholar
  189. 172.
    M. Nevns, Phys. Rev., Bl, 3304 (1970).Google Scholar
  190. 173.
    a) D.M. Nevns, Phys. Rev., 178, 1123 (1969);Google Scholar
  191. b) G. Doyen and G. Ertl, Surf. Sci., 43, 197 (1974);Google Scholar
  192. c) W. Brenig and K. Schönhammer, Z. Phys., 267, 201 (1974).Google Scholar
  193. 174.
    L. Einstein, Surf. Sci., 45, 713 (1974).Google Scholar
  194. 175.
    C. Bond, Discuss. Faraday Soc., 41, 200 (1966).Google Scholar
  195. 176.
    L.W. Anders, R.S. Hansen and L.S. Bartell, J. Chem. Phys., 59, 5277 (1973); 62, 1641 (1975);Google Scholar
  196. b) D.J.M. Fassaert, H. Verbeek and A. van der Avoird, Surf. Sci., 29, 501 (1972);Google Scholar
  197. c) A.B. Anderson and R. Hoffmann, J. Chem. Phys., 61, 4545 (1974);Google Scholar
  198. d) A.B. Anderson, J. Chem. Phys., 64, 4046 (1976).Google Scholar
  199. 177.
    a) G. Blyholder, JCS Chem. Comm., 1973, 625;Google Scholar
  200. b) G. Blyholder, J. Vac. SCi. Technol., 11, 865 (1974).ADSGoogle Scholar
  201. 178.
    L.S. Cederbaum, W. Domcke, W. von Niessen and W. Brenig, Z. Phys., B21, 3811 (1975);Google Scholar
  202. b) C.W. Bauschlicher, Jr., C.F. Bender, H.F. Schaefer III and P.S. Bagüs, Chem. Phys., 15., 227 (1976).Google Scholar
  203. 179.
    D. E. Ellis, H. Adachi and F.W. Averill, to be published.Google Scholar
  204. 180.
    K. H. Johnson and R.P. Messmer, J. Vac. Sci. Technol., 11, 236 (1974).Google Scholar
  205. 181.
    a) T. B. Grimley and C. Pisani, J. Phys. C, 7, 2831 (1974);ADSCrossRefGoogle Scholar
  206. b) T.B. Grimley, in ref. l66;Google Scholar
  207. c) A. van der Avoird, S.P. Liebmann and D.J.M. Fassaert, Phys. Rev., B10, 1230 (1974);Google Scholar
  208. 181.
    d) E.A. Hyman, Phys. Rev., B11, 3739 (1975);Google Scholar
  209. e) R.H. Paulson and T..N. Rhodin, Surf. Sci., 55., 61 (1976).Google Scholar
  210. 182.
    W. Kohn, Phys. Rev., B11, 3756 (1975); N. Kar and P. P. Soven, Phys. Rev., B11, 3761 (1975).Google Scholar
  211. 183.
    R.H. Paulson and J.R. Schrieffer, Surf. Sci., 48, 329 (1975).Google Scholar
  212. 184.
    a) S.C. Ying, J.R. Smith and W. Kohn, Phys. Rev., B11, 1U83 (1975);ADSGoogle Scholar
  213. b) L.M. Kahn and S.C. Ying, Solid State Commun., 16, 799 (1975).Google Scholar
  214. c) N.D. Lang and A.R. Williams, Phys. Rev. Lett., 34, 531 (1975)Google Scholar
  215. d) O. Gunnarsson and H. Hjelmberg, Phys. Scripta, 11, 97 (1975).ADSCrossRefGoogle Scholar
  216. 185.
    N. Rösch and D. Menzel, Chem. Phys., 13, 243 (1976).Google Scholar
  217. 186.
    a) J.W.D. Connolly, Phys. Rev., 159, 4l5 (1967);ADSCrossRefGoogle Scholar
  218. b) J.F. Janak, A.R. Williams and V.L. Moruzzi, Phys. Rev., B11, 1522 (1975);Google Scholar
  219. c) N.E. Christensen, Phys. Stat. Solidi, 31, 635 (1969).Google Scholar
  220. 187.
    S. Hüfner, G.K. Wertheim, N.V. Sunitz and M.M. Traum, Solid State Commun., 11, 329 (1972).Google Scholar
  221. 188.
    a) D.E. Eastman, J. Physique, CI, 293 (1971);Google Scholar
  222. b) D.E. Eastman and J.K. Cashion, Phys. Rev. Lett., 24, 310 (1970);Google Scholar
  223. c) A.D. MacLachlan, J. Liesegang, R.C.G. Leckey and J.G. Jenkin, Phys. Rev., Bll, 2877 (1975).Google Scholar
  224. 189.
    R.P. Messmer, S.K. Knudson, K.H. Johnson, J.B. Diamond and C.Y. Yang, Phys. Rev., B13, 1396 (1976).Google Scholar
  225. 190.
    J. Callaway and C.S. Wang, Phys. Rev., B7, 1096 (1973).ADSGoogle Scholar
  226. 191.
    J.L. Carter and J.H. Sinfelt, J. Catal., 10, 134 (1968).Google Scholar
  227. 192.
    R. O. Jones, P.J. Jennings and G.S. Painter, Surf. Sci., 53, 409 (1975).Google Scholar
  228. 193.
    R.C. Baetzold and R.E. Mack, J. Chem. Phys., 62, 1513 (1975).ADSCrossRefGoogle Scholar
  229. 194.
    a) R.C. Baetzold, J. Catal., 29, 129 (1973).Google Scholar
  230. b) G. Blyholder, Surf. Sci., 42, 249 (197*0.Google Scholar
  231. 195.
    R.P. Messmer and G.O. Watkins, Phys. Rev., B7, 2568 (1973).Google Scholar
  232. 196.
    R.P. Messmer and D•R. Salahub, Int. J. Quant. Chem., S10 (1976).Google Scholar
  233. 197.
    D.E. Eastman and J.K. Cashion, Phys. Rev. Lett., 27, 1520 (1971).Google Scholar
  234. 198.
    a) H.H. Madden, J. Küppers and G. Ertl, J. Chem. Phys., 58, 3401 (1973); K. Christmann, J. Küppers and G. Ertl, J. Chem. Phys., 60, 4719 (1974);Google Scholar
  235. b) F.A. Cotton, A.K. Fischer and G. Wilkinson, J. Amer. Chem. Soc., 8l, 800 (1959).Google Scholar
  236. 199.
    J.C. Tracy, J. Chem. Phys., 56, 2736 (1972).ADSCrossRefGoogle Scholar
  237. 200.
    G. Blyholder, J. Phys. Chem., 68, 2772 (I96U).Google Scholar
  238. 201.
    I.P. Batra and O. Robaux, J. Vac. Sci. Technol., 12, 242 (1975).ADSCrossRefGoogle Scholar
  239. 202.
    a) D.E. Eastman and J.E. Demuth, Jpn. J. Appl. Phys. Suppl. 2, 847 (1974);Google Scholar
  240. b) T. Gustafsson, E.W. Plummer, D.E. Eastman and J.L. Freeouf, Solid State Commun., 17, 391 (1975);Google Scholar
  241. c) J.C. Fuggle, M. Steinkilberg and D. Menzel, Chem. Phys., 11, 307 (1975);Google Scholar
  242. d) P.M. Williams, P. Butcher, J. Wood and K. Jacobi, to be published;Google Scholar
  243. e) P.R. Norton, R.L. Tapping and J.W. Goodale, Chem. Phys. Lett., 4l, 247 (1976).Google Scholar
  244. 203.
    I.P. Batra and P.S. Bagus, Solid State Commun., l6, 1097 (1975).Google Scholar
  245. 204.
    I.P. Batra and C.R. Brundle, Surf. Sci., 57., 12 (1976).Google Scholar
  246. 205.
    a) A.M. Bradshaw, D. Menzel and M. Steinkilberg, JCS Faraday Disc., 58, 46 (1974);Google Scholar
  247. b) S.J. Atkinson, C.R. Brundle and M.W. Roberts, ibid., 62;Google Scholar
  248. c) S. Evans, E.L. Evans, D.E. Parrey, M.J. Fricker, M.J. Walters and J.M. Thomas, ibid., 97;Google Scholar
  249. d) H. Conrad, G. Ertl, J. Küppers and E.E. Latta, ibid., ll6.Google Scholar
  250. 206.
    H.A. Engelhardt, A.M. Bradshaw and D. Menzel, Surf. Sci., 40, 410 (1973); H.A. Engelhardt and D. Menzel, Surf. Sci., to be published.Google Scholar
  251. 207.
    W. Heiland, F. Iberl, E. Taglauer and D. Menzel, Surf. Sci., 53, 383 (1975).Google Scholar
  252. 208.
    J.C. Fuggle and D. Menzel, Surf. Sci., 53, 21 (1975).Google Scholar
  253. 209.
    a) I.P. Batra and O. Robaux, Surf. Sci., 49, 653 (1975);ADSCrossRefGoogle Scholar
  254. 209.
    b) S.J. Niemczyk, J. Vac. Sci. Technol., 12, 246 (1975).Google Scholar
  255. 210.
    H. Conrad, G. Erti, J. Küppers and E.E. Latta, private communication.Google Scholar
  256. 211.
    T.N. Rhodin and D.L. Adams, in Adsorption of Gases on Solids, Vol. 6, Treatise on Solid State Chemistry, ed. N.B. Hannay (Plenum, New York, 1975 ).Google Scholar
  257. 212.
    H. Conrad, G. Erti, J. Küppers and E. E. Latta, Solid State Commun., 17, 497 (1975).ADSCrossRefGoogle Scholar
  258. 213.
    R.P. Messmer, C.W. Tucker and K.H. Johnson, Surf. Sci., 42, 341 (1974).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • Notker Rösch
    • 1
  1. 1.Lehrstuhl für Theoretische ChemieTechnische Universität MünchenGermany

Personalised recommendations