In light of the recently developed complete GJ set of single random variable stochastic, discrete-time Størmer–Verlet algorithms for statistically accurate simulations of Langevin equations [N. Grønbech-Jensen, Mol. Phys. 118, e1662506 (2020)], we investigate two outstanding questions: (1) Are there any algorithmic or statistical benefits from including multiple random variables per time step and (2) are there objective reasons for using one or more methods from the available set of statistically correct algorithms? To address the first question, we assume a general form for the discrete-time equations with two random variables and then follow the systematic, brute-force GJ methodology by enforcing correct thermodynamics in linear systems. It is concluded that correct configurational Boltzmann sampling of a particle in a harmonic potential implies correct configurational free-particle diffusion and that these requirements only can be accomplished if the two random variables per time step are identical. We consequently submit that the GJ set represents all possible stochastic Størmer–Verlet methods that can reproduce time step-independent statistics of linear systems. The second question is thus addressed within the GJ set. Based on numerical simulations of complex molecular systems, as well as on analytic considerations, we analyze apparent friction-induced differences in the stability of the methods. We attribute these differences to an inherent, friction-dependent discrete-time scaling, which depends on the specific method. We suggest that the method with the simplest interpretation of temporal scaling, the GJ-I/GJF-2GJ method, be preferred for statistical applications.
Skip Nav Destination
CHORUS
Article navigation
7 October 2020
Research Article|
October 01 2020
The challenge of stochastic Størmer–Verlet thermostats generating correct statistics
Joshua Finkelstein;
Joshua Finkelstein
a)
1
Department of Mathematics, Temple University
, Philadelphia, Pennsylvania 19122, USA
Search for other works by this author on:
Chungho Cheng;
Chungho Cheng
2
Department of Mechanical and Aerospace Engineering, University of California
, Davis, California 95616, USA
Search for other works by this author on:
Giacomo Fiorin
;
Giacomo Fiorin
3
Institute for Computational Molecular Science, Temple University
, Philadelphia, Pennsylvania 19122, USA
4
National Heart, Lung and Blood Institute
, Bethesda, Maryland 20892, USA
Search for other works by this author on:
Benjamin Seibold
;
Benjamin Seibold
1
Department of Mathematics, Temple University
, Philadelphia, Pennsylvania 19122, USA
Search for other works by this author on:
Niels Grønbech-Jensen
Niels Grønbech-Jensen
b)
2
Department of Mechanical and Aerospace Engineering, University of California
, Davis, California 95616, USA
5
Department of Mathematics, University of California
, Davis, California 95616, USA
b)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
a)
Present address: Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
b)Author to whom correspondence should be addressed: [email protected]
Note: This paper is part of the JCP Special Topic on Classical Molecular Dynamics (MD) Simulations: Codes, Algorithms, Force Fields, and Applications.
J. Chem. Phys. 153, 134101 (2020)
Article history
Received:
June 18 2020
Accepted:
September 14 2020
Citation
Joshua Finkelstein, Chungho Cheng, Giacomo Fiorin, Benjamin Seibold, Niels Grønbech-Jensen; The challenge of stochastic Størmer–Verlet thermostats generating correct statistics. J. Chem. Phys. 7 October 2020; 153 (13): 134101. https://doi.org/10.1063/5.0018962
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
DeePMD-kit v2: A software package for deep potential models
Jinzhe Zeng, Duo Zhang, et al.
CREST—A program for the exploration of low-energy molecular chemical space
Philipp Pracht, Stefan Grimme, et al.
Rubber wear: Experiment and theory
B. N. J. Persson, R. Xu, et al.
Related Content
Bringing discrete-time Langevin splitting methods into agreement with thermodynamics
J. Chem. Phys. (November 2021)
Kinetic energy definition in velocity Verlet integration for accurate pressure evaluation
J. Chem. Phys. (April 2018)
On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm
J. Chem. Phys. (November 2007)
Stability of velocity-Verlet- and Liouville-operator-derived algorithms to integrate non-Hamiltonian systems
J. Chem. Phys. (October 2018)
Constant pressure and temperature discrete-time Langevin molecular dynamics
J. Chem. Phys. (November 2014)