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Computer Simulation of LiquidsSecond Edition$
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Michael P. Allen and Dominic J. Tildesley

Print publication date: 2017

Print ISBN-13: 9780198803195

Published to Oxford Scholarship Online: November 2017

DOI: 10.1093/oso/9780198803195.001.0001

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Advanced Monte Carlo methods

Advanced Monte Carlo methods

Chapter:
(p.297) 9 Advanced Monte Carlo methods
Source:
Computer Simulation of Liquids
Author(s):

Michael P. Allen

Dominic J. Tildesley

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198803195.003.0009

This chapter describes the ways in which the Monte Carlo importance sampling method may be adapted to improve the calculation of ensemble averages, particularly those associated with free energy differences. These approaches include umbrella sampling, non-Boltzmann sampling, the Wang–Landau method, and nested sampling. In addition, a range of special techniques have been developed to accelerate the simulation of flexible molecules, such as polymers. These approaches are illustrated with scientific examples and program code. The chapter also explains the analysis of such simulations using techniques such as weighted histograms, and acceptance ratio calculations. Practical advice on selection of methods, parameters, and the direction in which to make comparisons, are given. Monte Carlo methods for modelling phase equilibria and chemical reactions at equilibrium are described.

Keywords:   Non-Boltzmann-sampling, umbrella-sampling, Wang–Landau, weighted-histogram-analysis-method, multistate-Bennett-acceptance-ratio, configuration-biased-Monte-Carlo, smart-Monte-Carlo, force-bias, Gibbs-ensemble, concerted-rotation-Monte-Carlo

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