Skip to main content
SpringerLink
Log in

Microcanonical variational transition-state theory for reaction rates in dissipative systems

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Upper bounds for the classical escape rate of a particle trapped in a metastable well and interacting with a dissipative medium are derived based on the periodic orbits of a reduced two-degree-of-freedom Hamiltonian involving the unstable normal mode and a collective bath mode. It is shown that even in what is usually thought of as the spatial diffusion limit the reactive flux can involve an energy diffusion term due to energy transfer from the dissipative media, in addition to the standard spatial diffusion term.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Hänggi, P. Talkner, and M. Borkovec,Rev. Mod. Phys. 62:251 (1990).

    Google Scholar 

  2. J. T. Hynes, inTheory of Chemical Reaction Dynamics, M. Baer, ed. (CRC Press, Boca Raton, Florida, 1985), Vol. 4, p. 171.

    Google Scholar 

  3. B. J. Berne, M. Borkovec, and J. E. Straub,J. Phys. Chem. 92:3711 (1988).

    Google Scholar 

  4. H. A. Kramers,Physica 7:284 (1940).

    Google Scholar 

  5. V. I. Mel'nikov and S. V. Meshkov,J. Chem. Phys. 85:1018 (1986).

    Google Scholar 

  6. H. Risken,The Fokker-Planck Equation, 2nd ed. (Springer-Verlag, Berlin, 1989).

    Google Scholar 

  7. D. Beece, L. Eisenstein, H. Frauenfelder, D. Good, M. C. Marden, L. Reinisch, A. H. Reynolds, L. B. Sorenson, and K. T. Yue,Biochemistry 19:5147 (1980).

    Google Scholar 

  8. W. Doster,Biophys. Chem. 17:97 (1983).

    Google Scholar 

  9. B. J. Gertner, K. R. Wilson, and J. T. Hynes,J. Chem. Phys. 90:3537 (1989);

    Google Scholar 

  10. J. P. Bergsma, B. J. Gertner, K. R. Wilson, and J. T. Hynes,J. Chem. Phys. 86:1356 (1987).

    Google Scholar 

  11. U. Seifert and S. Dietrich,Europhys. Lett. 3:593 (1987).

    Google Scholar 

  12. H. Grabert and S. Linkwitz,Phys. Rev. A 37:963 (1988).

    Google Scholar 

  13. S. B. Zhu, J. Lee, and G. W. Robinson,J. Chem. Phys. 88:7088 (1988).

    Google Scholar 

  14. E. Turlot, D. Esteve, C. Urbina, J. M. Martinis, M. H. Devoret, S. Linkwitz, and H. Grabert,Phys. Rev. Lett. 62:1788 (1989).

    Google Scholar 

  15. R. Zwanzig,J. Stat. Phys. 9:215 (1973).

    Google Scholar 

  16. A. O. Caldeira and A. J. Leggett,Ann. Phys. 149:374 (1983); erratum,153:445 (1983).

    Google Scholar 

  17. E. Cortes, B. J. West, and K. Lindenberg,J. Chem. Phys. 82:2708 (1985).

    Google Scholar 

  18. H. Eyring,J. Chem. Phys. 3:107 (1935).

    Google Scholar 

  19. E. P. Wigner,J. Chem. Phys. 5:720 (1937).

    Google Scholar 

  20. J. C. Keck,Adv. Chem. Phys. 13:85 (1967).

    Google Scholar 

  21. J. B. Anderson,J. Chem. Phys. 58:4684 (1973).

    Google Scholar 

  22. B. H. Mahan,J. Chem. Ed. 51:709 (1974).

    Google Scholar 

  23. W. H. Miller,J. Chem. Phys. 61:1823 (1974).

    Google Scholar 

  24. W. L. Hase, inDynamics of Molecular Collisions, Part B, W. H. Miller, ed. (Plenum Press, New York, 1976), p. 121.

    Google Scholar 

  25. P. Pechukas, inDynamics of Molecular Collisions, Part B, W. H. Miller, ed. (Plenum Press, New York, 1976), p. 269.

    Google Scholar 

  26. D. G. Truhlar, A. D. Isaacson, and B. C. Garrett, inTheory of Chemical Reaction Dynamics, M. Baer, ed. (CRC Press, Boca Raton, Florida, 1985), Vol. 4, p. 1.

    Google Scholar 

  27. E. Pollak, inTheory of Chemical Reaction Dynamics, M. Baer, ed. (CRC Press, Boca Raton, Florida, 1985), Vol. 3, p. 123.

    Google Scholar 

  28. D. G. Truhlar, W. L. Hase, and J. T. Hynes,J. Phys. Chem. 87:2664 (1983).

    Google Scholar 

  29. S. C. Tucker and D. G. Truhlar, inNew Theoretical Concepts for Understanding Organic Reactions, J. Bertrán and I. G. Csizmadia, eds. (Kluwer Academic Press, Dordrecht, 1989), p. 291.

    Google Scholar 

  30. D. J. Chandler,J. Chem. Phys. 68:2959 (1978).

    Google Scholar 

  31. E. Pollak,J. Chem. Phys. 95:533 (1991).

    Google Scholar 

  32. E. Pollak, S. C. Tucker, and B. J. Berne,Phys. Rev. Lett. 65:1399 (1990).

    Google Scholar 

  33. E. Pollak,J. Chem. Phys. 93:1116 (1990).

    Google Scholar 

  34. S. Lee and J. T. Hynes,J. Chem. Phys. 88:6853, 6863 (1988).

    Google Scholar 

  35. B. M. Ladanyi and J. T. Hynes,J. Am. Chem. Soc. 108:585 (1986).

    Google Scholar 

  36. J. S. Langer,Ann. Phys. (N.Y.)54:258 (1969).

    Google Scholar 

  37. R. F. Grote and J. T. Hynes,J. Chem. Phys. 73:2715 (1980).

    Google Scholar 

  38. P. Hänggi and F. Mojtabai,Phys. Rev. A 26:1168 (1982).

    Google Scholar 

  39. R. S. Larson and M. D. Kostin,J. Chem. Phys. 68:4821 (1978).

    Google Scholar 

  40. O. Edholm and O. Leimar,Physica A (Utrecht)98A:313 (1979).

    Google Scholar 

  41. W. Bez and P. Talkner,Phys. Lett. A 82:313 (1989).

    Google Scholar 

  42. F. Marchesoni,Adv. Chem. Phys. 63:603 (1985).

    Google Scholar 

  43. D. Ryter,J. Stat. Phys. 49:751 (1987).

    Google Scholar 

  44. E. Pollak and P. Pechukas,J. Chem. Phys. 69:1218 (1978).

    Google Scholar 

  45. P. Pechukas and E. Pollak,J. Chem. Phys. 71:2062 (1979).

    Google Scholar 

  46. H. Mori,Prog. Theor. Phys. 33:423 (1965).

    Google Scholar 

  47. B. J. Berne and R. Pecora,Introduction to the Molecular Theory of Light Scattering (Wiley, New York, 1976).

    Google Scholar 

  48. E. Pollak,J. Chem. Phys. 85:865 (1986).

    Google Scholar 

  49. E. Pollak, H. Grabert, and P. Hänggi,J. Chem. Phys. 91:4073 (1989).

    Google Scholar 

  50. I. Rips and E. Pollak,Phys. Rev. A 41:5366 (1990).

    Google Scholar 

  51. R. Graham,J. Stat. Phys. 60:675 (1990).

    Google Scholar 

Download references

Author information

Author notes

  1. Susan C. Tucker

    Present address: Department of Chemistry, University of California, 95616, Davis, California

Authors and Affiliations

  1. Department of Chemistry, Columbia University, 10027, New York, New York

    Susan C. Tucker

  2. Chemical Physics Department, Weizmann Institute of Science, 76100, Rehovot, Israel

    Eli Pollak

Authors
  1. Susan C. Tucker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eli Pollak
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tucker, S.C., Pollak, E. Microcanonical variational transition-state theory for reaction rates in dissipative systems. J Stat Phys 66, 975–990 (1992). https://doi.org/10.1007/BF01055711

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01055711

Key words

Search

Navigation