Equilibrium and Nonequilibrium Foundations of Free Energy Computational Methods

  • C. Jarzynski
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 24)


Statistical mechanics provides a rigorous framework for the numerical estimation of free energy differences in complex systems such as biomolecules. This paper presents a brief review of the statistical mechanical identities underlying a number of techniques for computing free energy differences. Both equilibrium and nonequilibrium methods are covered.


Monte Carlo Step Free Energy Difference Heat Reservoir Thermodynamic Integration Canonical Distribution 
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  1. 1.
    D. Chandler, Introduction to Modern Statistical Mechanics, Oxford University, New York (1987).Google Scholar
  2. 2.
    D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, Academic Press, San Diego (1996).Google Scholar
  3. 3.
    M. Karplus and G.A. Petsko, Nature 347, 631 (1990).PubMedCrossRefGoogle Scholar
  4. 4.
    N. Metropolis et al, J. Chem. Phys. 21, 1087 (1953).CrossRefGoogle Scholar
  5. 5.
    T.P. Straatsma, H.J.C. Berendsen, and J.P.M. Postma, J. Chem. Phys. 85, 6720 (1986).CrossRefGoogle Scholar
  6. 6.
    D.A. Pearlman and P.A. Kollman, J. Chem. Phys. 91, 7831 (1989).CrossRefGoogle Scholar
  7. 7.
    R. Zwanzig, J. Chem. Phys. 22, 1420 (1954).CrossRefGoogle Scholar
  8. 8.
    C.H. Bennett, J. Comp. Phys. 22, 245 (1976).CrossRefGoogle Scholar
  9. 9.
    G.M. Torrie and J.P. Valleau, J. Comp. Phys. 23, 187 (1977).CrossRefGoogle Scholar
  10. 10.
    R.J. Radmer and P.A. Kollman, J. Comp. Chem. 18, 902 (1997).CrossRefGoogle Scholar
  11. 11.
    J.G. Kirkwood,  J. Chem. Phys. 3, 300 (1935).CrossRefGoogle Scholar
  12. 12.
    W.P. Reinhardt and J.E. Hunter III, J. Chem. Phys. 97, 1599 (1992).CrossRefGoogle Scholar
  13. 13.
    J.E. Hunter III, W.P. Reinhardt, and T.F. Davis, J. Chem. Phys. 99, 6856 (1993).CrossRefGoogle Scholar
  14. 14.
    L.D. Landau and E.M. Lifshitz, Statistical Physics, 3rd. ed., Part 1, section 15, Pergamon Press, Oxford (1990).Google Scholar
  15. 15.
    Moreover, the larger the system, the smaller the probability of randomly generating a trajectory which violates Eq. 32; thus, in the macroscopic limit we recover the statement that W is “strictly” greater than ΔF for irreversible processes.Google Scholar
  16. 16.
    M.A. Miller and W.P. Reinhardt, J. Chem. Phys. 113, 7035 (2000).CrossRefGoogle Scholar
  17. 17.
    J. Hermans, J. Phys. Chem. 95, 9029 (1991). See Refs. [18] and [19] for closely related results.CrossRefGoogle Scholar
  18. 18.
    R.H. Wood, W.C.F. Mühlbauer, and P.T. Thompson, J. Phys. Chem. 95, 6670 (1991).CrossRefGoogle Scholar
  19. 19.
    L.-W. Tsao, S.-Y. Sheu, and C.-Y. Mou, J. Chem. Phys. 101, 2302 (1994).CrossRefGoogle Scholar
  20. 20.
    C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).CrossRefGoogle Scholar
  21. 21.
    C. Jarzynski, Phys. Rev. E 56, 5018 (1997).CrossRefGoogle Scholar
  22. 22.
    G.E. Crooks, J. Stat. Phys. 90, 1481 (1998).CrossRefGoogle Scholar
  23. 23.
    G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. (US) 98, 3658 (2001).CrossRefGoogle Scholar
  24. 24.
    D.A. Hendrix and C. Jarzynski, J. Chem. Phys. 114, 5974 (2001).CrossRefGoogle Scholar
  25. 25.
    D. Frenkel, private communication.Google Scholar
  26. 26.
    G. Hummer, “Fast-growth thermodynamic integration: results for sodium ion hydration”, preprint.Google Scholar
  27. 27.
    H. Hu, R.H. Yun, and J. Hermans, “Reversibility of free energy simulations: slow growth may have a unique advantage. (With a note on use of Ewald summation.)”, preprint.Google Scholar
  28. 28.
    B. Roux, Comput. Phys. Comm. 91, 275 (1995).CrossRefGoogle Scholar
  29. 29.
    S. Kumar, D. Bouzida, R.H. Swendsen, P.A. Kollman, and J.M. Rosenberg, J. Comp. Chem. 13, 1011 (1992).CrossRefGoogle Scholar
  30. 30.
    See, for instance, J.R. Gullingsrud, R. Braun, and K. Schulten, J. Comp. Phys. 151, 190 (1999), and references therein.CrossRefGoogle Scholar
  31. 31.
    Dellago, C., Bolhuis, P.G., Csajka, F.S. & Chandler, D., J. Chem. Phys. 108, 1964 (1998); Bolhuis, P., Dellago, C. & Chandler, D., Faraday Discussion Chem. Soc. 110, 421 (1998); Geissler, P. L., Dellago, C. & Chandler, D., J. Phys. Chem. B103, 3706 (1999); Geissler, P.L., Dellago, C, Chandler, D., Hutter, J. & Parinello, M., Science, in press (2001).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • C. Jarzynski
    • 1
  1. 1.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA

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