Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics

Christoph Junghans; Danny Perez; Thomas Vogel

doi:10.1021/ct500077d

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arXiv · 1401.6184

Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics

Christoph Junghans·Danny Perez·Thomas Vogel

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Abstract

We show direct formal relationship between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)] and statistical temperature molecular dynamics [PRL 97, 050601 (2006)], the major Monte Carlo and molecular dynamics work-horses for sampling from a generalized, multicanonical ensemble. We demonstrate that statistical temperature molecular dynamics (which is formally derived from the Wang-Landau method), augmented by the introduction of kernel updates of the statistical temperature, generates dynamics which are indistinguishable from a corresponding metadynamics simulation. We also show that the use of a Gaussian kernel significantly improves the performance of statistical temperature molecular dynamics, highlighting the practical benefits of this improved formal understanding.

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Christoph Junghans, Danny Perez, Thomas Vogel. 2014-04-29. Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics. https://doi.org/10.1021/ct500077d

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