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
N. Metropolis et al. (1953) Equation of State Calculations by Fast Computing Machines. J. Chem. Phys., 21, p. 1087
S. Ulam and N. Metropolis (1949) The Monte Carlo Method. J. Am. Stat. Assoc., 44, p. 335
V. I. Manousiouthakis and M. W. Deem (1999) Strict detailed balance is unnecessary in Monte Carlo simulation. J. Chem. Phys., 110, p. 2753
A. A. Barker (1965) Monte Carlo calculations of the radial distribution functions for a proton-electron plasma. Aust. J. Phys., 18, p. 119
Understanding Molecular Simulations: from Algorithms to Applications (2nd Edition). (Academic Press, San Diego, 2002)
R. H. Swendsen and J. S. Wang (1987) Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett., 58, p. 86
D. Frenkel (2004) Speed-up of Monte Carlo simulations by sampling of rejected states. Proc. Nat. Acad. Sci., 101, p. 17571
I. Coluzza and D. Frenkel (2005) Virtual-move parallel tempering. Chem. Phys. Chem., 6(9), p. 1779
G. Boulougouris and D. Frenkel (2005) Monte Carlo sampling of a Markov web. J. Chem. Theory Comput., 1, p. 389
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Frenkel, D. (2006). Waste-Recycling Monte Carlo. In: Ferrario, M., Ciccotti, G., Binder, K. (eds) Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1. Lecture Notes in Physics, vol 703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35273-2_4
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DOI: https://doi.org/10.1007/3-540-35273-2_4
Publisher Name: Springer, Berlin, Heidelberg
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