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Semiclassical vibrational eigenvalues of H<sup> + </sup><sub>3</sub>, D<sup> + </sup><sub>3</sub>, and T<sup> + </sup><sub>3</sub> by the adiabatic switching method
The adiabatic switching method is used to calculate the semiclassical vibrational eigenvalues of H + 3" align="middle"/>, D + 3" align="middle"/>, and T + 3" align="middle"/>. The results are in good ...
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A CASSCF-CCI study of the valence and lower excited states of the benzene molecule
Ab initio complete active space (CAS) SCF and contracted CI calculations have been carried out for all valence and the lower Rydberg states of the benzene molecule. The CASSCF active space comprised 1...

Basis set methods for describing the quantum mechanics of a ``system'' interacting with a harmonic bath

J. Chem. Phys. 86, 1451 (1987); doi:10.1063/1.452234

Issue Date: 1 February 1987

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Nancy Makri and William H. Miller
Department of Chemistry, University of California, and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
The case of a system (e.g., a one-dimensional reaction coordinate) coupled to a ``bath'' of many harmonic oscillators is treated by quantum mechanical basis set methods. By choosing the basis set for the bath to incorporate the coupling explicitly, it is shown how the bath can then be eliminated to obtain an effective Hamiltonian matrix for only the system. Numerical calculations are carried out which show that, even in the zeroth version of the approach, the effect on the system (e.g., the tunneling splitting in a double-well potential) of coupling to the bath is described well, even when the effect is extremely large. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
History: Received 19 August 1986; accepted 16 October 1986
Permalink: http://link.aip.org/link/?JCPSA6/86/1451/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ca
    Classical and quantum physics: mechanics and fields Quantum theory; quantum mechanics Formalism
  • YEAR: 1987

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ISSN:
0021-9606 (print)   1089-7690 (online)
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REFERENCES (16)
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  1. For reviews see (a) W. H. Miller, J. Phys. Chem. 87, 3811 (1983);
  2. (b) W. H. Miller, in The Theory of Chemical Reaction Dynamics, edited by D. C. Clary (Reidel, Boston, 1986), pp. 27–45.
  3. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
  4. (a) W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983);
    5. (b) R. Jaquet and W. H. Miller, J. Phys. Chem. 89, 2139 (1985);
    (c) Y. Yamashita and W. H. Miller, J. Chem. Phys. 82, 5475 (1985).
  5. (a) A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983);
    6. (b) S. Chakravarty and A. J. Leggett, Phys. Rev. Lett. 52, 5 (1984);
    (c) H. Grabert and U. Weiss, ibid. 54, 1605 (1985);
    (d) A. T. Dorsey, M. P. A. Fisher, and M. S. Wartak, Phys. Rev. A 33, 1117 (1986).
  6. (a) D. Thirumalai and B. J. Berne, J. Chem. Phys. 79, 5029 (1983);
    7. (b) D. Thirumalai, E. J. Bruskin, and B. J. Berne, ibid. 79, 5063 (1983);
    (c) D. Thirumalai and B. J. Berne, ibid. 81, 2512 (1984).
  7. (a) J. D. Doll, J. Chem. Phys. 81, 3536 (1984);
    8. (b) D. L. Freeman, R. D. Coalson, and J. D. Doll, J. Stat. Phys. 43, 931 (1986).
  8. (a) E. C. Behrmann, G. A. Jongeward, and P. G. Wolynes, J. Chem. Phys. 79, 6277 (1983);
    9. (b) R. W. Hall and P. G. Wolynes, J. Stat. Phys. 43, 935 (1986).
  9. (a) D. Chandler and P. Wolynes, J. Chem. Phys. 74, 4078 (1981);
    10. (b) M. Sprik, M. L. Klein, and D. Chandler, ibid. 83, 3042 (1985);
    (c) M. Sprik, R. W. Impey, and M. L. Klein, ibid. 83, 5802 (1985);
    (d) C. D. Jonah, C. Romeo, and A. Rahman, Chem. Phys. Lett. 123, 209 (1986);
    (e) R. J. Rossky, J. Schnitker, and R. A. Kuharski, J. Stat. Phys. 43, 949 (1986);
    (f) A. Wallquist, D. Thirumalai, and B. J. Berne, J. Chem. Phys. 85, 1583 (1986).
  10. J. W. Tromp and W. H. Miller, J. Phys. Chem. 90, 3482 (1986).
  11. I. P. Hamilton and J. C. Light, J. Chem. Phys. 84, 306 (1986).
  12. R. Silbey and R. A. Harris, J. Chem. Phys. 80, 2615 (1984).
  13. (a) J. Bicerano, H. F. Schaefer, and W. H. Miller, J. Am. Chem. Soc. 105, 2550 (1983);
    14. (b) T. Carrington, Jr. and W. H. Miller, J. Chem. Phys. 84, 4364 (1986).
  14. This is also done by most of the authors in Ref. 4.
  15. See, for example, E. C. Kemble, The Fundamental Principles of Quantum Mechanics (Dover, New York, 1958), pp. 394–396.
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    18. 19, 287 (1962).

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