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Application of a Stochastic Path Integral Approach to the Computations of an Optimal Path and Ensembles of Trajectories

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 4)

Abstract

A stochastic path integral is used to obtain approximate long time trajectories with an almost arbitrary time step. A detailed description of the formalism is provided and an extension that enables the calculations of transition rates is discussed.

Keywords

Optimal Trajectory Langevin Equation Random Force Transition State Theory Large Time Step 
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References

  1. 1.
    J. Hofrichter, J.H. Sommer, E.R. Henry and W.A. Eaton, Proc. Natl. Acad. Sci. USA 80, 2235 (1983)CrossRefGoogle Scholar
  2. 2.
    M.E. Tuckerman, G.J. Martyna and B.J. Berne, J. Chem. Phys., 97, 1990–2001 (1992); F. Figueirido, R. Zhou, B.J. Berne and Ronald M. Levy, J. Chem. Phys. 106, 9835-9849 (1997)CrossRefGoogle Scholar
  3. 3.
    P. Derreumaux and T. Schlick, Proteins 21, 282 (1995)CrossRefGoogle Scholar
  4. 4.
    D. Okunbor and R.D. Skeel, J. Computational Chemistry, 15, 72–79 (1994)CrossRefGoogle Scholar
  5. 5.
    H. Grubmuller, H. Heller, A. Windemuth and K. Schulten, Molecular Simulations, 6, 121–142 (1991)CrossRefGoogle Scholar
  6. 6.
    L. Onsager and S. Machlup, Phys. Rev. 91, 1505 (1953); S. Machlup and L. Onsager, ibid., 91, 1512 (1953)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    R. Olender and R. Elber, J. Chem. Phys. 105, 9299 (1996)CrossRefGoogle Scholar
  8. 8.
    R. Olender and R. Elber, “Yet another look at the steepest descent path”, J. Mol. Struct. Theochem and the proceeding of the WATOC symposium, 398-399, 63–72 (1997)Google Scholar
  9. 9.
    C. Dellago, P.G. Bolhuis, F.S. Csajka, and D. Chandler, “Transition path sampling and the calculation of rate constants”, a preprint.Google Scholar
  10. 10.
    B. Oksendal, “Stochastic differential equations: An introduction with applications”, Springer-Verlag, Berlin, 1995Google Scholar
  11. 11.
    H. Risken, “The Fokker-Planck equation: Methods of solution and applications”, Springer-Verlag, Berling, 1984, chapter 3.zbMATHGoogle Scholar
  12. 12.
    C.W. Gardiner, “Handbook of stochastic methods for physics, chemistry and natural sciences”, Springer-Verlag, Berlin, 1990zbMATHGoogle Scholar
  13. 13.
    B. J. Berne, M. E. Tuckerman, J.E. Straub and A.L.R. Bug, J. Chem. Phys. 93, 5084 (1990)CrossRefGoogle Scholar
  14. 14.
    R. Elber, D. P. Chen, D. Rojewska, and R. S. Eisenberg, Biophys. J. 68, 906–924 (1995)CrossRefGoogle Scholar
  15. 15.
    H. Kleinert, “Path integrals in quantum mechanics, statistics and polymer physics”, World Scientific, Singapore, 1995, chapters 18.5 and 18.6.Google Scholar
  16. 16.
    C. Lanczos, “The Variational Principles of Mechanics”, University of Toronto Press, Toronto, 1970zbMATHGoogle Scholar
  17. 17.
    J.P. Ryckaert, G. Ciccotti and H.J.C. Berendsen, J. of Comput. Physics 23, 327 (1977)CrossRefGoogle Scholar
  18. 18.
    C.S. Peskin and T. Schlick, Communications on Pure and Applied Mathematics, XLII, 1001 (1989); G. Zhang and T. Schlick, J. Comp. Chem. 14, 121 (1993); G. Zhang and T. Schlick, J. Chem. Phys., 101, 4995 (1994)MathSciNetCrossRefGoogle Scholar
  19. 19.
    S. Glasstone, K.J. Laidler and H. Eyring, “The theory of rate processes”, McGraw-Hill, New York, 1961Google Scholar
  20. 20.
    J.P. Valleau and G.M. Torrie, “A Guide to Monte Carlo for Statistical Mechanics: 2. Byways”, in “Statistical Mechanics”, Ed. B. Berne, Plenum Press, New York, 1977CrossRefGoogle Scholar
  21. 21.
    S.F. McCormick, Editor, “Multigrid Methods”, SIAM, Philadelphia, 1987zbMATHGoogle Scholar
  22. 22.
    S. Kirkpatrick, Jr., C.D. Gelatt and M.P. Vecchi, Science 220, 671 (1983)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Department of Physical Chemistry, and Department of Biological ChemistryThe Fritz Haber Research Center, and the Wolfson Center for Applied Structural Biology, The Hebrew UniversityJerusalemIsrael
  2. 2.Department de Physique, Department de ChimieUniversite de MontrealMontrealCanada
  3. 3.Peptor LtdRehovotIsrael

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