Progress Toward the Application of Complex Coordinate and Complex Basis Function Techniques to Molecular Resonance Calculations

  • C. William McCurdy


In this talk I will discuss some recent developments in complex coordinate and basis function techniques which are beginning to make possible the application of these techniques to the treatment of molecular resonance phenomena. I will avoid any detailed discussion of the history of successful applications to atomic resonances and atomic photoionization. That history is in itself sufficient to furnish material for a review.1 Instead I will concentrate mainly on the discussion of two problems which have, until recently, slowed the development of generalizations of complex coordinate and basis function approaches suitable for molecular resonance calculations.


Photoionization Cross Section Momentum Represen Complex Scaling Molecular Resonance Electron Repulsion Integral 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I give here only a very abbreviated bibliography of papers dealing with the atomic applications: J. Nuttall and H. L. Cohen, Phys. Rev. 188, 1542 (1969);Google Scholar
  2. G. Doolen, J. Nuttall and R. Stagat, Phys. Rev. A10, 1612 (1974);CrossRefGoogle Scholar
  3. G. D. Doolen, J. Phys. B 8, 525 (1975);CrossRefGoogle Scholar
  4. R. A. Bain, J. N. Bardsley, B. R. Junker and C. V. Sukumar, J. Phys. B 7, 2189 (1974)Google Scholar
  5. T. Rescigno and V. McKoy, Phys. Rev. Al2, 552 (1975);Google Scholar
  6. A. P. Hickman, A. D. Isaacson, and W. H. Miller, Chem. Phys. Lett. 37, 63 (1976).CrossRefGoogle Scholar
  7. Also see: International Journal of Quantum Chemistry 14 number 4 (October 1978) which is devoted entirely to complex scaling and contains articles on computational aspects of the problem as well as more rigorous mathematical discussions.Google Scholar
  8. 2.
    E. Balslev and J. M. Combes, Commun. Math. Phys. 22, 280 (1971)CrossRefGoogle Scholar
  9. 3.
    C. W. McCurdy and T. N. Rescigno, Phys. Rev. Letts. 41, 1364 (1978).CrossRefGoogle Scholar
  10. 4.
    R. Yaris, John Bendler, Ronald A. Lovett, Carl M. Bender and Peter A. Fedders, Phys. Rev. A18, 1816 (1978).CrossRefGoogle Scholar
  11. 5.
    T. N. Rescigno and V. McKoy, Phys. Rev. Al2, 552 (1975);Google Scholar
  12. T. N. Rescigno, C. W. McCurdy and V. McKoy, J. Chem. Phys. 64, 422 (1976).CrossRefGoogle Scholar
  13. 6.
    J. E. Avron and I. Herbst. Commun. Math. Phys. 52, 239 (1977);CrossRefGoogle Scholar
  14. C. Cerjan, R. Hedges, C. Holt, W. P. Reinhardt, K. Scheibner and J. J. Wendoloski, Int. J. Quant. Chem. 14, 393 (1978) and references therein;Google Scholar
  15. I. W. Herbst and B. Simon, Phys. Rev. Letts. 41, 67 (1978).CrossRefGoogle Scholar
  16. 7.
    I am indebted to W. P. Reinhardt for pointing this fact out to me.Google Scholar
  17. 8.
    B. Simon, Phys. Letters, accepted for publication.Google Scholar
  18. 9.
    T. N. Rescigno, C. W. McCurdy and A. E. Orel, Phys. Rev. A17, 1931 (1978).CrossRefGoogle Scholar
  19. 10.
    T. N. Rescigno and W. P. Reinhardt, Phys. Rev. A8, 2828 (1973).CrossRefGoogle Scholar
  20. 11.
    B. R. Junker and C. L. Huang, Phys. Rev. A18, 313 (1978).CrossRefGoogle Scholar
  21. 12.
    W. H. Miller, C. A. Slocomb and H. F. Schaefer, J. Chem. Phys. 56, 1347 (1972).CrossRefGoogle Scholar
  22. 13.
    A. D. Isaacson and W. H. Miller, Chem. Phys. Letts., to appear.Google Scholar
  23. 14.
    I. Shavitt, in Methods in Computational Physics, edited by B. Alder, S. Fernbach, and M. Rotenberg ( Academic, New York 1963 ), Vol. 2, p. 1.Google Scholar
  24. 15.
    A. D. Isaacson, C. W. McCurdy and W. H. Miller, Chemical Physics 34, 311 (1978).CrossRefGoogle Scholar
  25. 16.
    N. Bardsley and B. Junker, J. Phys. B 5, L 178 (1972).Google Scholar
  26. 17.
    J. E. Avron and I. Herbst, Commun. Math. Phys. 52, 239, (1977).CrossRefGoogle Scholar
  27. 18.
    I. W. Herbst and B. Simon, Phys. Rev. Lett. 41, 67 (1978).CrossRefGoogle Scholar
  28. 19.
    C. W. McCurdy, work in progress. It may be possible to combine complex scaling in the Hamiltonian with contour rotations in all matrix elements to produce a practical version of “exterior complex scaling.”Google Scholar
  29. 20.
    Simon has discussed some unsolved mathematical problems in a rigorous overview of complex scaling. See B. Simon, Int. J. Quant. Chem. 14, 529 (1978).Google Scholar

Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • C. William McCurdy
    • 1
  1. 1.Department of ChemistryThe Ohio State UniversityColumbusUSA

Personalised recommendations