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Quantum scattering via the S-matrix version of the Kohn variational principle

J. Chem. Phys. 88, 6233 (1988); doi:10.1063/1.454462

Issue Date: 15 May 1988

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John Z. H. Zhang, Shih-I. Chu, and William H. Miller
Department of Chemistry, University of California, and Material Chemical Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
The S-matrix version of the Kohn variational principle is used to obtain a very effective method for quantum scattering calculations. The approach is especially useful for the nonlocal (i.e., exchange) interactions that arise in chemically reactive scattering (and also in electron–atom/molecule scattering). The particular version developed in this paper has a more general structure than an earlier one by Miller and Jansen op de Haar [J. Chem. Phys. 86, 6213 (1987)], and applications to an elastic scattering problem, and also to three-dimensional H+H2 reactive scattering, show that it is also more useful in practice. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
History: Received 17 November 1987; accepted 26 January 1988
Permalink: http://link.aip.org/link/?JCPSA6/88/6233/1
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KEYWORDS and PACS

Keywords
PACS
  • 34.10.+x
    Atomic and molecular collision processes and interactions General theories and models (including statistical theories, transition state, stochastic and trajectory models, etc.)
  • 34.40.+n
    Atomic and molecular collision processes and interactions Elastic scattering of atoms and molecules
  • 82.30.Cf
    Physical chemistry Specific chemical reactions; reaction mechanisms Atom and radical reactions; chain reactions
  • YEAR: 1988

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
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REFERENCES (21)
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  1. For a general discussion of rearrangement scattering, see, for example, A. Messiah, Quantum Mechanics (Wiley, New York, 1962), Vol. II, p. 832, and references therein.
  2. For a recent review, see R. B. Walker and J. C. Light, Annu. Rev. Phys. Chem. 31, 401 (1980).
  3. W. H. Miller, J. Chem. Phys. 50, 407 (1969).
  4. Approaches to reactive scattering that do not involve nonlocal interactions are the hyperspherical coordinate method, see, for example, (a) A. Kuppermann and P. G. Hipes, J. Chem. Phys. 84, 5962 (1986);
    5. (b) C. A. Parker, R. T. Pack, B. J. Archer, and R. B. Walker, Chem. Phys. Lett. 137, 564 (1987); the matching-on-a-surface method;
    (c) A. Kuppermann and G. C. Schatz, J. Chem. Phys. 62, 2502 (1975); and the use of a reaction coordinate, see, for example,
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  5. B. R. Johnson, National Resource for Computation in Chemistry, NRCC Proceedings No. 5 (University of California, Berkeley, 1979), p. 86.
  6. W. H. Miller and B. M. D. D. Jansen op de Haar, J. Chem. Phys. 86, 6213 (1987).
  7. (a) J. E. Adams and W. H. Miller, J. Chem. Phys. 83, 1505 (1979);
    8. (b) M. R. Hermann and W. H. Miller, Chem. Phys. 109, 163 (1986).
  8. D. W. Schwenke, K. Hang, D. G. Truhlar, Y. Sun, J. Z. H. Zhang, and D. J. Kouri, J. Phys. Chem. 91, 6080 (1987);
    9. J. Z. H. Zhang, D. J. Kouri, K. Hang, D. W. Schwenke, Y. Shima, and D. G. Truhlar, J. Chem. Phys. 88, 2492 (1988).
  9. J. Z. H. Zhang and W. H. Miller, Chem. Phys. Lett. 140, 329 (1987).
  10. (a) J. Nuttall and H. L. Cohen, Phys. Rev. 188, 1542 (1969);
    11. (b) F. A. McDonald and J. Nuttall, Phys. Rev. C 6, 121 (1972);
    (c) R. T. Baumel, M. C. Crocker, and J. Nuttall, Phys. Rev. A 12, 486 (1975).
  11. W. Kohn, Phys. Rev. 74, 1763 (1948).
    12. See also, T.-Y. Wu and T. Ohmura, Quantum Theory of Scattering (Prentice-Hall, Englewood Cliffs, NJ, 1962), pp. 57–68.
  12. See O. H. Crawford, J. Chem. Phys. 55, 2571 (1971) for an early application of the Kohn variational principle to the S matrix. In this work, however, a finite radius is introduced, as in the R-matrix approach, that separates the internal and external regions of configuration space, and the logarithmic derivative of the wave function is matched at this radius.
  13. R. K. Nesbet, Variational Methods in Electron-Atom Scattering Theory (Plenum, New York, 1980), pp. 30–50.
  14. See, for example, D. J. Kouri and F. S. Levin, Ann. Phys. (N. Y.) 83, 316 (1974).
  15. C. W. McCurdy, T. N. Rescigno, and B. I. Schneider, Phys. Rev. A. 36, 2061 (1987).
  16. See, for example, T.-Y. Wu and T. Ohmura, Quantum Theory of Scattering (Prentice-Hall, Englewood Cliffs, NJ, 1962), p. 64. See Ref. 7 for some applications to reactive scattering.
  17. A. D. Isaacson, C. W. McCurdy, and W. H. Miller, Chem. Phys. 34, 311 (1978).
  18. A. J. F. Siegert, Phys. Rev. 56, 750 (1939).
  19. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (U. S. GPO, Washington, D.C., 1964), p. 437.
  20. G. Staszewska and D. G. Truhlar, Chem. Phys. Lett. 130, 341 (1986).
  21. B. M. D. D. Jansen op de Haar (unpublished calculations).

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