Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
Search:
   
 
 
 
Previous Article
HKrF in solid krypton
A new krypton-containing compound, HKrF, has been prepared in a low-temperature Kr matrix via VUV photolysis of the HF precursor and posterior thermal mobilization of H and F atoms. All three fundamen...
Next Article
Transport coefficients at metastable densities from models of generalized hydrodynamics
The fully wave vector dependent extended mode coupling model is studied with the inclusion of an additional slow variable of the defect density for the amorphous system. We use the extremely slow rela...

Qualitative dynamics of generalized Langevin equations and the theory of chemical reaction rates

J. Chem. Phys. 116, 2516 (2002); doi:10.1063/1.1436116

Issue Date: 8 February 2002

You are not logged in to this journal. Log in

Craig C. Martens
Department of Chemistry, University of California, Irvine, Irvine, California 92697-2025
In this paper, we present an analysis of condensed phase chemical reactions from the perspective of qualitative dynamical systems theory. Our approach is based on a phenomenological phase space representation of the generalized Langevin equation (GLE). In general, the GLE with memory requires an infinite-dimensional phase space for its description. The phenomenological phase space is constructed by augmenting the physical phase plane (q,p) with additional variables defined as the convolution of the system momentum with the memory kernel and its time derivatives. The qualitative dynamics in this representation are then characterized in terms of the eigenvalues and eigenvectors of the linear system near the barrier top. The phase space decomposes into a single unstable direction and a complementary stable subspace. The rate of exponential growth along the unstable eigenvector is directly related to the rate of chemical reaction, and our linear analysis reproduces the Grote–Hynes expression for the reaction rate [R. F. Grote and J. T. Hynes, J. Chem. Phys. 73, 2715 (1980)]. In the presence of noise, the stable subspace can be identified with the stochastic separatrix, a manifold of initial conditions with a reaction probability of 0.5. Other dynamical processes, such as solvent caging, can also be given a simple geometric interpretation in terms of the qualitative dynamical analysis. ©2002 American Institute of Physics.
History: Received 13 June 2001; accepted 26 November 2001
Permalink: http://link.aip.org/link/?JCPSA6/116/2516/1
BUY THIS ARTICLE   (US$24)
Download HTML Download Sectioned HTML Download PDF (354 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 82.20.Uv
    Physical chemistry and chemical physics Chemical kinetics and dynamics Stochastic theories of rate constants
  • 82.20.Db
    Physical chemistry and chemical physics Chemical kinetics and dynamics Transition state theory and statistical theories of rate constants
  • 82.20.Pm
    Physical chemistry and chemical physics Chemical kinetics and dynamics Rate constants, reaction cross sections, and activation energies
  • 82.20.Yn
    Physical chemistry and chemical physics Chemical kinetics and dynamics Solvent effects on reactivity
  • 02.10.Ud
    Mathematical methods in physics Logic, set theory, and algebra Linear algebra
  • YEAR: 2002

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (49)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. R. Kubo, Rep. Prog. Phys. 29, 255 (1966).
  2. R. Zwanzig, J. Stat. Phys. 9, 215 (1973).
  3. P. Hanggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
  4. A. Nitzan, Adv. Chem. Phys. 70, 489 (1988).
  5. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983).
  6. E. P. Wigner, Trans. Faraday Soc. 34, 29 (1938).
  7. J. C. Keck, Adv. Chem. Phys. 13, 85 (1967).
  8. P. Pechukas, in Dynamics of Molecular Collisions, Part B, edited by W. H. Miller (Plenum, New York, 1976), p. 269.
  9. E. Pollak, in Theory of Chemical Reaction Dynamics, edited by M. Baer (CRC, Boca Raton, 1985), Vol. 3.
  10. H. A. Kramers, Physica (Utrecht) 7, 284 (1940).
  11. New Trends in Kramers' Reaction Rate Theory, edited by P. Talkner and P. Hanggi (Kluwer, Dordrecht, 1995).
  12. R. F. Grote and J. T. Hynes, J. Chem. Phys. 73, 2715 (1980).
  13. P. Hanggi and F. Mojtabai, Phys. Rev. A 26, 1168 (1982).
  14. Y. I. Dakhnovskii and A. A. Ovchinnikov, Phys. Lett. A 113, 147 (1985).
  15. E. Pollak, J. Chem. Phys. 85, 865 (1986).
  16. A. M. Levine, M. Shapiro, and E. Pollak, J. Chem. Phys. 88, 1959 (1988).
  17. E. Pollak, H. Grabert, and P. Hanggi, J. Chem. Phys. 91, 4073 (1989).
  18. E. Pollak, S. C. Tucker, and B. J. Berne, Phys. Rev. Lett. 65, 1399 (1990).
  19. E. Pollak, J. Chem. Phys. 95, 533 (1991).
  20. E. Pollak, A. M. Berezhkovskii, and Z. Schuss, J. Chem. Phys. 100, 334 (1994).
  21. P. Talkner and H.-B. Braun, J. Chem. Phys. 88, 7537 (1988).
  22. A. M. Berezhkovskii, E. Pollak, and V. Y. Zitserman, J. Chem. Phys. 97, 2422 (1992).
  23. L. Farkas, Z. Phys. Chem. 125, 236 (1927).
  24. B. J. Gertner, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 90, 3537 (1989).
  25. B. J. Berne, in Activated Barrier Theory, edited by P. Hanggi and G. Fleming (World Scientific, Singapore, 1993).
  26. J. C. Keck, Adv. At. Mol. Phys. 8, 39 (1972).
  27. D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, Oxford, 1987).
  28. D. J. Tannor and D. Kohen, J. Chem. Phys. 100, 4932 (1994).
  29. D. Kohen and D. J. Tannor, J. Chem. Phys. 103, 6013 (1995).
  30. R. Abraham and J. E. Marsden, Foundations of Mechanics, 2nd ed. (Addison–Wesley, Redwood City, 1985).
  31. R. H. Abraham and C. D. Shaw, Dynamics: The Geometry of Behavior, 2nd ed. (Addison–Wesley, Redwood City, 1992).
  32. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer-Verlag, Berlin, 1992).
  33. Coping with Chaos, edited by E. Ott, E. Sauer, and J. A. Yorke (Wiley, New York, 1994).
  34. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 1997).
  35. F. Takens, Detecting Strange Attractors in Turbulence (Springer-Verlag, Berlin, 1981).
  36. M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys. 17, 232 (1945).
  37. H. Mori, Prog. Theor. Phys. 34, 399 (1965).
  38. M. Ferrario and P. Grigolini, J. Math. Phys. 20, 2567 (1979).
  39. F. Marchesoni and P. Grigolini, J. Chem. Phys. 78, 6287 (1983).
  40. M. M. Dygas, B. J. Mathkowsky, and Z. Schuss, J. Chem. Phys. 84, 3731 (1986).
  41. J. E. Straub, M. Borkovec, and B. J. Berne, J. Chem. Phys. 84, 1788 (1986).
  42. A. Frishman and E. Pollak, J. Chem. Phys. 98, 9532 (1993).
  43. V. I. Arnol'd, Ordinary Differential Equations, 3rd ed. (Springer, Berlin, 1992).
  44. D. Ryter, Physica A 142, 103 (1987).
  45. D. Ryter, J. Stat. Phys. 49, 751 (1987).
  46. M. M. Klosek, B. J. Mathkowsky, and Z. Schuss, Ber. Bunsenges. Phys. Chem. 95, 331 (1991).
  47. G. R. Haynes, G. A. Voth, and E. Pollak, J. Chem. Phys. 101, 7811 (1994).
  48. C. C. Martens (unpublished).
  49. W. Kaplan, Advanced Mathematics for Engineers (Addison–Wesley, Reading, 1981).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics