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A generalized class of strongly stable and dimension-free T-RPMD integrators

Rosa-Raíces, Jorge L. and Sun, Jiace and Bou-Rabee, Nawaf and Miller, Thomas F., III (2021) A generalized class of strongly stable and dimension-free T-RPMD integrators. Journal of Chemical Physics, 154 (2). Art. No. 024106. ISSN 0021-9606.

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Recent work shows that strong stability and dimensionality freedom are essential for robust numerical integration of thermostatted ring-polymer molecular dynamics (T-RPMD) and path-integral molecular dynamics, without which standard integrators exhibit non-ergodicity and other pathologies [R. Korol et al., J. Chem. Phys. 151, 124103 (2019) and R. Korol et al., J. Chem. Phys. 152, 104102 (2020)]. In particular, the BCOCB scheme, obtained via Cayley modification of the standard BAOAB scheme, features a simple reparametrization of the free ring-polymer sub-step that confers strong stability and dimensionality freedom and has been shown to yield excellent numerical accuracy in condensed-phase systems with large time steps. Here, we introduce a broader class of T-RPMD numerical integrators that exhibit strong stability and dimensionality freedom, irrespective of the Ornstein–Uhlenbeck friction schedule. In addition to considering equilibrium accuracy and time step stability as in previous work, we evaluate the integrators on the basis of their rates of convergence to equilibrium and their efficiency at evaluating equilibrium expectation values. Within the generalized class, we find BCOCB to be superior with respect to accuracy and efficiency for various configuration-dependent observables, although other integrators within the generalized class perform better for velocity-dependent quantities. Extensive numerical evidence indicates that the stated performance guarantees hold for the strongly anharmonic case of liquid water. Both analytical and numerical results indicate that BCOCB excels over other known integrators in terms of accuracy, efficiency, and stability with respect to time step for practical applications.

Item Type:Article
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URLURL TypeDescription Paper
Rosa-Raíces, Jorge L.0000-0003-2311-2948
Bou-Rabee, Nawaf0000-0001-9280-9808
Miller, Thomas F., III0000-0002-1882-5380
Additional Information:© 2021 Published under license by AIP Publishing. Submitted: 10 November 2020; Accepted: 7 December 2020; Published Online: 8 January 2021. This work was supported in part by the U.S. Department of Energy (Grant No. DE-SC0019390) and the National Institutes of Health (Grant No. R01GM125063). N.B.-R. acknowledges support by the Alexander von Humboldt foundation and the National Science Foundation (Grant No. DMS-1816378). Authors' Contributions: J.L.R.-R. and J.S. contributed equally to this work. Data Availability: The data that support the findings of this study are available from the corresponding author upon reasonable request.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0019390
Alexander von Humboldt FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20201203-151032238
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106901
Deposited By: George Porter
Deposited On:03 Dec 2020 23:59
Last Modified:15 Jan 2021 22:03

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