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Title: Layered nested Markov chain Monte Carlo

Abstract

A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. In conclusion, the proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.

Authors:
 [1];  [1];  [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1466393
Alternate Identifier(s):
OSTI ID: 1457211
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 7; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Jackson, Nicholas E., Webb, Michael A., and de Pablo, Juan J. Layered nested Markov chain Monte Carlo. United States: N. p., 2018. Web. doi:10.1063/1.5030531.
Jackson, Nicholas E., Webb, Michael A., & de Pablo, Juan J. Layered nested Markov chain Monte Carlo. United States. doi:https://doi.org/10.1063/1.5030531
Jackson, Nicholas E., Webb, Michael A., and de Pablo, Juan J. Tue . "Layered nested Markov chain Monte Carlo". United States. doi:https://doi.org/10.1063/1.5030531. https://www.osti.gov/servlets/purl/1466393.
@article{osti_1466393,
title = {Layered nested Markov chain Monte Carlo},
author = {Jackson, Nicholas E. and Webb, Michael A. and de Pablo, Juan J.},
abstractNote = {A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. In conclusion, the proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.},
doi = {10.1063/1.5030531},
journal = {Journal of Chemical Physics},
number = 7,
volume = 149,
place = {United States},
year = {2018},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

FIG. 1. FIG. 1.: Schematic of a {M}=[1,3,3,2] L-NMCMC scheme using {U}=[U0,U1,U2,U3] as auxiliary potentials. Horizontal arrows denote moves in configuration space, whereas dotted vertical arrows denote interlayer checks according to the acceptance criterion of Eq. 10. For clarity, note that only the first interlayer check between each set of neighboring layersmore » is shown in the diagram.« less

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