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Entropy 2014, 16(1), 138-162; doi:10.3390/e16010138
Article

Time Integrators for Molecular Dynamics

Department of Mathematical Sciences, Rutgers University—Camden, 311 N 5th Street, Camden, NJ 08102, USA
Received: 19 September 2013 / Revised: 20 November 2013 / Accepted: 4 December 2013 / Published: 27 December 2013
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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Abstract

This paper invites the reader to learn more about time integrators for Molecular Dynamics simulation through a simple MATLAB implementation. An overview of methods is provided from an algorithmic viewpoint that emphasizes long-time stability and finite-time dynamic accuracy. The given software simulates Langevin dynamics using an explicit, second-order (weakly) accurate integrator that exactly reproduces the Boltzmann-Gibbs density. This latter feature comes from adding a Metropolis acceptance-rejection step to the integrator. The paper discusses in detail the properties of the integrator. Since these properties do not rely on a specific form of a heat or pressure bath model, the given algorithm can be used to simulate other bath models including, e.g., the widely used v-rescale thermostat.
Keywords: explicit integrators; Metropolis algorithm; ergodicity; weak accuracy explicit integrators; Metropolis algorithm; ergodicity; weak accuracy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Bou-Rabee, N. Time Integrators for Molecular Dynamics. Entropy 2014, 16, 138-162.

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