Advertisement

Theory of the Electronic Structure of Excited States in Small Systems with Numerical Applications to Atomic States

  • Donald R. Beck
  • Cleanthes A. Nicolaides
Chapter
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 46)

Abstract

In this lecture we discuss an approach to the understanding and efficient calculation of electron correlation of valence or inner hole excited states in atoms and small molecules. We start with the formal subshell cluster expansion of the wave-function and we analyze the various correlation effects which appear in the wave-function whose form is dictated by first order perturbation theory. I.e. only single and pair symmetry adapted correlation functions are considered. This analysis allows: 1) The formal decoupling, to a good approximation, of the subshell correlation vectors into groups and their economic computation from small Variational Configuration-Interaction (VCI) procedures. 2) The systematic optimization of the different for each group virtual one-electron functions—expressed in terms of STO’s or GTO’s—by minimizing the corresponding to each group energy functional. 3) The consequent determination of compact but accurate total wave-functions from basis sets which contain the Hartree-Fock and only a few more virtual orbitals. 4) The recognition and isolation of important for electronic spectroscopy and chemical bonding correlation effects from those which contribute mainly to total energies. 5) The recognition of the importance of triple and quadruple correlation effects for certain inner hole excited states, even in small systems. We present previously unpublished numerical results on a) the position of the H- 2P2 3P metastable state whose study supports our suggestion that variationally optimized (VO) one-electron basis sets are competitive with rij dependent basis sets in terms of fast convergence. b) The position of the H-- 2p3 4S° state which is found to be unbound. c) The pair correlations of C where reasonably accurate calculations indicate that VO-GTO virtuals are reasonably competitive with VO-STO virtuals. This suggests that the size of current molecular calculations using Gaussians can be reduced considerably at no expense of accuracy, d) The effect of electron correlation on the term structure of Ni III, of current importance in solid state physics.

Keywords

Excited State Pair Correlation Term Structure Small System Cluster Expansion 
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. Beck and C.A. Nicolaides, Int. J. Qu. Chem. S8, 17, (1973).Google Scholar
  2. 2.
    D.R. Beck and C.A. Nicolaides, Int. J. Qu. Chem. S10, 119, (1976).Google Scholar
  3. 3.
    R.J. Buenker and S.D. Peyerimhoff, Theor. Chim. Acta 35, 33, (1974).CrossRefGoogle Scholar
  4. 4.
    R.J. Buenker and S.D. Peyerimhoff, this volume.Google Scholar
  5. 5.
    G. Das and A.C. Wahl, J. Chem. Phys. 50, 3532, (1972)CrossRefGoogle Scholar
  6. 5a.
    S.L. Guberman, J. Chem. Phys. 67, 1125 (1977).CrossRefGoogle Scholar
  7. 6.
    R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. Letts. 34, 225, (1975).CrossRefGoogle Scholar
  8. 7.
    C. Froese-Fischer, Comp. Phys. Comm. 4, 107, (1972).CrossRefGoogle Scholar
  9. 8.
    H.J. Silverstone, J. Chem. Phys. 67, 4172, (1977).CrossRefGoogle Scholar
  10. 9.
    C.A. Nicolaides and D.R. Beck, Chem. Phys. Letts. 36, 79, (1975).CrossRefGoogle Scholar
  11. 10.
    D.R. Beck and C.A. Nicolaides, Phys. Letts. 65A, 293, (1978).CrossRefGoogle Scholar
  12. 11.
    C.A. Nicolaides and D.R. Beck, “Time Dependence, Complex Scaling and the Calculation of Resonances in Many-Electron Systems”, to be published in the Volume “Complex Scaling in the Spectral Theory of the Hamiltonian”, ed. by P.O. Löwdin (Int. J. Qu, Chem. supplement volume 1978).Google Scholar
  13. 12.
    B. Kahn and G.E. Uhlenbeck, Physica 5, 399, (1938); the term “linked cluster” apparently first appeared in this article.CrossRefGoogle Scholar
  14. 13.
    V. Fock, M. Vesselov and M. Petrashen, J. Exp. Theor. Phys. (U.S.S.R.) 10, 723, (1940).Google Scholar
  15. 14.
    F. Iwamoto and M. Yamada, Prog. Theor. Phys. 17, 543, (1957).CrossRefGoogle Scholar
  16. 15.
    W. Brenig, Nucl. Phys. 4, 363, (1957).CrossRefGoogle Scholar
  17. 16.
    R. Brout, Phys. Rev. 111, 1324, (1958).CrossRefGoogle Scholar
  18. 17.
    O. Sinanoglu, J. Chem. Phys. 36, 706, (1962).CrossRefGoogle Scholar
  19. 18.
    L. Szasz, Phys. Rev. 126, 169, (1962).CrossRefGoogle Scholar
  20. 19.
    H.J. Silverstone and O. Sinanoğlu, J. Chem. Phys. 44, 1898, 3608, (1966).CrossRefGoogle Scholar
  21. 20.
    J. Cizek, J. Chem. Phys. 45, 4256, (1966)CrossRefGoogle Scholar
  22. 20a.
    J. Cizek, Adv. Chem. Phys. 14, 35, (1969).CrossRefGoogle Scholar
  23. 21.
    R.K. Nesbet, Phys. Rev. 155, 56, (1957).CrossRefGoogle Scholar
  24. 22.
    C. Møller and M.S. Plesset, Phys. Rev. 46, 618, (1934).CrossRefGoogle Scholar
  25. 23.
    O. Sinanoğlu, Proc. R. Soc. (london) A260, 379, (1961).Google Scholar
  26. 24.
    C.F. Bender and E.R. Davidson, Phys. Rev. 183, 23, (1969).CrossRefGoogle Scholar
  27. 25.
    A.N. Weiss, Phys. Rev. A3, 126, (1971).Google Scholar
  28. 26.
    J.W. Viers, F.E. Harris and H.F. Schaefer III, Phys. Rev. A1, 24, (1970).Google Scholar
  29. 27.
    C.F. Bunge, Chem. Phys. Letts. 42, 141, (1976).CrossRefGoogle Scholar
  30. 28.
    F. Sasaki and M. Yoshimine, Phys. Rev. A9, 26, (1974).Google Scholar
  31. 29.
    CM. Moser and R.K. Nesbet, Phys. Rev. A6, 1710, (1972).Google Scholar
  32. 30.
    R. Ahlrichs, H. Lischka, B. Zurawski and W. Kutzelnigg, J. Chem. Phys. 63, 4685, (1975)CrossRefGoogle Scholar
  33. 30a.
    W. Meyer, J. Chem. Phys. 58, 1017, (1973) and references therein.CrossRefGoogle Scholar
  34. 31.
    F.W. Byron and C.J. Joachain, Phys. Rev. 157, 7, (1967).CrossRefGoogle Scholar
  35. 32.
    C. Froese-Fischer and K.M.S. Saxena, Phys. Rev. A9, 1498, (1974).Google Scholar
  36. 33.
    H.P. Kelly and A. Ron, Phys. Rev. A4, 11, (1971).Google Scholar
  37. 34.
    J. Paldus, J. Cizek and I. Shavitt, Phys. Rev. A1, 50, (1972).Google Scholar
  38. 35.
    R.J. Buenker, S.D. Peyerimhoff and W. Butscher, Mol. Phys. 35, 771, (1978).CrossRefGoogle Scholar
  39. 36.
    R.E. Knight, Phys. Rev. 183, 45, (1969).CrossRefGoogle Scholar
  40. 37.
    A. Pipano and I. Shavitt, Int. J. Qu. Chem. II, 741, (1968).CrossRefGoogle Scholar
  41. 38.
    C. Froese-Fischer, J. Phys. B6, 1933, (1973).Google Scholar
  42. 39.
    H.P. Kelly, Phys. Rev. 144, 39, (1966).CrossRefGoogle Scholar
  43. 40.
    I. Oksüz and O. Sinanoğlu, Phys. Rev. 181, 42 (1969).CrossRefGoogle Scholar
  44. 41.
    C.A. Nicolaides and D.R. Beck, J. Phys. B6, 535, (1973).Google Scholar
  45. 42.
    D.R. Beck and O. Sinanoğlu, Phys. Rev. Letts. 28, 945, (1972).CrossRefGoogle Scholar
  46. 43.
    H.F. Schaeffer III, J. Chem. Phys. 55, 176, (1971).CrossRefGoogle Scholar
  47. 44.
    C.A. Nicolaides and D.R. Beck, J. Chem. Phys. 66, 1982, (1977).CrossRefGoogle Scholar
  48. 45.
    D.R. Beck and C.A. Nicolaides, Phys. Letts. 61A, 227, (1977).CrossRefGoogle Scholar
  49. 46.
    C.A. Nicolaides and D.R. Beck, J. Phys. B9, 1259, (1976).Google Scholar
  50. 47.
    R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. Letts. 36, 415, (1975).CrossRefGoogle Scholar
  51. 48.
    E.R. Cooper and H.P. Kelly, Phys. Rev. A7, 38, (1973).Google Scholar
  52. 49.
    E.R. Davidson, in “The World of Quantum Chemistry”, eds. R. Dandel and B. Pullman, Reidel Publ. Co. Dordrecht, (1974).Google Scholar
  53. 50.
    A. Mennier, B. Levy and G. Berthier, Int. J. Qu. Chem. 10, 1061, (1976).CrossRefGoogle Scholar
  54. 51.
    F. Sasaki, Int. J. Qu. Chem. S11, 125, (1977).Google Scholar
  55. 52.
    R.J. Bartlett and I. Shavitt, Int. J. Qu. Chem. S11, 165, (1977).Google Scholar
  56. 53.
    T.A. Carlson and M.O. Krause, Phys. Rev. Letts. 17, 1079, (1966).CrossRefGoogle Scholar
  57. 54.
    Y. Komninos, D.R. Beck and C.A. Nicolaides, unpublished.Google Scholar
  58. 55.
    L.E. McMurchie and E.R. Davidson, J. Chem. Phys. 66, 2959, (1977).CrossRefGoogle Scholar
  59. 56.
    R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. 8, 324, (1975).CrossRefGoogle Scholar
  60. 57.
    J. Reader, Phys. Rev. A7, 1431, (1973).Google Scholar
  61. 58.
    D.A. Shirley et.al., “Electron-Correlation Satellites in Electron Spectroscopy”, preprint, presented at the 2nd Int. Conf. on Inner Shell Ionization Phenomena, Preiburg, (1976).Google Scholar
  62. 59.
    E.K. Viinikka and Y. Ohrn, Phys. Rev. B11, 4168, (1975).Google Scholar
  63. 60.
    L.E. Nitzsche and E.R. Davidson, J. Chem. Phys. 68, 3103, (1978).CrossRefGoogle Scholar
  64. 61.
    C.C. J. Roothaan and P.S. Bagus, Methods of Comp. Phys. 2, B. Alder, S. Fernbach and M. Rotenberg, eds. Acad. Press (1963).Google Scholar
  65. 62.
    E.A. McCullough, Jr., J. Chem. Phys. 62, 3991, (1975).CrossRefGoogle Scholar
  66. 63.
    C.A. Nicolaides, Phys. Rev. A6, 2078, (1972)Google Scholar
  67. 63a.
    C.A. Nicolaides, Nucl Inst. Methods 110, 231 (1973).CrossRefGoogle Scholar
  68. 64.
    D.R. Beck and C.A. Nicolaides, Phys. Rev. Letts, submitted May 1978.Google Scholar
  69. 65.
    C.A. Nicolaides and D.R. Beck, this volume.Google Scholar
  70. 66.
    E.R. Davidson and L.Z. Stenkamp, Int. J. Qu. Chem. S10, 21 (1976).Google Scholar
  71. 67.
    L.A. Yaffe and W.A. Goddard III, Phys. Rev. A13, 1682, (1976).Google Scholar
  72. 68.
    J. Hinze and C.C.J. Roothaan, Supp. Prog. Theor. Phys. 40, 37, (1967).CrossRefGoogle Scholar
  73. 69.
    W.J. Hunt and W.A. Goddard III, Chem. Phys. Letts. 3, 414, (1969).CrossRefGoogle Scholar
  74. 70.
    E.R. Davidson, “Reduced Density Matrices in Quantum Chemistry”, Acad. Press (N.Y.) (1976);Google Scholar
  75. 70b.
    C.F. Bender and E.R. Davidson J. Phys. Chem. 70, 2675 (1966).CrossRefGoogle Scholar
  76. 71.
    C. Edmiston and M. Krauss, J. Chem. Phys. 45, 1833 (1966).CrossRefGoogle Scholar
  77. 72.
    e.g. D.R. Beck, J. Chem. Phys. 51, 2171 (1969).CrossRefGoogle Scholar
  78. 73.
    D.R. Beck and C.A. Nicolaides, unpublished.Google Scholar
  79. 74.
    D.R. Beck, C.A. Nicolaides and J.I. Musher, Phys. Rev. A10, 1522 (1974).Google Scholar
  80. 75.
    C.A. Nicolaides and D.R. Beck, Can. J. Phys. 53, 1224 (1975).CrossRefGoogle Scholar
  81. 76.
    H.F. King et. al., J. Chem. Phys. 47, 1936 (1967).CrossRefGoogle Scholar
  82. 77.
    H.F. Schaefer and F.E. Harris, J. Comp. Phys. 3, 217 (1968).CrossRefGoogle Scholar
  83. 78.
    A. Bunge, J. Chem. Phys. 53, 20, (1970).CrossRefGoogle Scholar
  84. 79.
    D.R. Beck and H. Odabasi, Ann. Phys. 67, 274, (1971).CrossRefGoogle Scholar
  85. 80.
    G.W.F. Drake, Phys. Rev. Letts. 24, 126, (1970).CrossRefGoogle Scholar
  86. 81.
    R. Schnitzer and M. Auber, J. Chem. Phys. 64, 2466 (1976).CrossRefGoogle Scholar
  87. 82.
    W. Aberth, J. Chem. Phys. 65, 4329 (1976)CrossRefGoogle Scholar
  88. 82a.
    M.L. Vestal, J. Chem. Phys. 65 p. 4331Google Scholar
  89. 82b.
    J. Durup, ibid. p. 4331Google Scholar
  90. 82c.
    R. Schnitzer and M. Aubar, ibid. p. 4432.Google Scholar
  91. 83.
    J.F. Liebman, D.L. Yeager and J. Simons, (Chem. Phys. Letts. 48, 227, (1977)) have added an attractive external potential to introduce binding, in their study of shape resonances.CrossRefGoogle Scholar
  92. 84.
    S. Huzinaga and A. Hart-Davis, Phys. Rev. 8A, 1734 (1973). Positive eigenvalues were also obtained in certain HF calculations of He- compound states (C.A. Nicolaides, Phys. Rev. A6, 2078 (1972); C.A. Nicolaides, unpublished).Google Scholar
  93. 85.
    D.R. Yarkony, H.F. Schaefer, III, and C.F. Bender, J. Chem. Phys. 64, 981 (1976).CrossRefGoogle Scholar
  94. 86.
    C.F. Bunge and A.V. Bunge, “Calculations of Atomic Electron Affinities”, preprint.Google Scholar
  95. 87.
    A.B. Kunz, this volume; Phys. Rev. B7, 5369 (1973).Google Scholar
  96. 88.
    D.R. Beck and C.A. Nicolaides, this volume.Google Scholar
  97. 89.
    C. Froese-Fischer, Can. J. Phys. 49, 1205 (1971).CrossRefGoogle Scholar
  98. 90.
    C.E. Moore, “Atomic Energy Levels Vol II”, NBS circular 467 (1952).Google Scholar
  99. 91.
    R.L. Kelly and L.J. Palumbo, “Atomic and Ionic Emission Lines below 2000 Å”, NRL Reprint 7 599 (1973).Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978

Authors and Affiliations

  • Donald R. Beck
    • 1
  • Cleanthes A. Nicolaides
    • 1
  1. 1.Theoretical Chemistry InstituteNational Hellenic Research FoundationAthens 501/1Greece

Personalised recommendations