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Waste-Recycling Monte Carlo

  • D. Frenkel
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 703)

Abstract

The Metropolis (Markov Chain) Monte Carlo method is simple and powerful. Since 1953, many extensions of the original Markov Chain Monte Carlo method have been proposed, but they are all based on the original Metropolis prescription that only states belonging to the Markov Chain should be sampled. In particular, if trial moves to a potential target state are rejected, that state is not included in the sampling. I will argue that the efficiency of effectively all Markov Chain MC schemes can be improved by including the rejected states in the sampling procedure. Such an approach requires only a trivial (and cheap) extension of existing programs. I will demonstrate that the approach leads to improved estimates of the energy of a system and that it leads to better estimates of free-energy landscapes.

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References

  1. 1.
    N. Metropolis et al. (1953) Equation of State Calculations by Fast Computing Machines. J. Chem. Phys., 21, p. 1087CrossRefADSGoogle Scholar
  2. 2.
    S. Ulam and N. Metropolis (1949) The Monte Carlo Method. J. Am. Stat. Assoc., 44, p. 335zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    V. I. Manousiouthakis and M. W. Deem (1999) Strict detailed balance is unnecessary in Monte Carlo simulation. J. Chem. Phys., 110, p. 2753CrossRefADSGoogle Scholar
  4. 4.
    A. A. Barker (1965) Monte Carlo calculations of the radial distribution functions for a proton-electron plasma. Aust. J. Phys., 18, p. 119ADSGoogle Scholar
  5. 5.
    Understanding Molecular Simulations: from Algorithms to Applications (2nd Edition). (Academic Press, San Diego, 2002)Google Scholar
  6. 6.
    R. H. Swendsen and J. S. Wang (1987) Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett., 58, p. 86CrossRefADSGoogle Scholar
  7. 7.
    D. Frenkel (2004) Speed-up of Monte Carlo simulations by sampling of rejected states. Proc. Nat. Acad. Sci., 101, p. 17571CrossRefADSGoogle Scholar
  8. 8.
    I. Coluzza and D. Frenkel (2005) Virtual-move parallel tempering. Chem. Phys. Chem., 6(9), p. 1779Google Scholar
  9. 9.
    G. Boulougouris and D. Frenkel (2005) Monte Carlo sampling of a Markov web. J. Chem. Theory Comput., 1, p. 389CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • D. Frenkel
    • 1
  1. 1.FOM Institute for Atomic and Molecular Physics (AMOLF)AmsterdamThe Netherlands

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