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Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics

Korol, Roman and Bou-Rabee, Nawaf and Miller, Thomas F., III (2019) Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics. Journal of Chemical Physics, 151 (12). Art. No. 124103. ISSN 0021-9606. doi:10.1063/1.5120282.

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Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD numerical integration schemes for equations of motion based on imaginary-time path integrals is the use of harmonic normal modes for the exact evolution of the free ring-polymer positions and momenta. In this work, we demonstrate that this standard practice creates numerical artifacts. In the context of conservative (i.e., microcanonical) equations of motion, it leads to numerical instability. In the context of thermostated (i.e., canonical) equations of motion, it leads to nonergodicity of the sampling. These pathologies are generally proven to arise at integration time steps that depend only on the system temperature and the number of ring-polymer beads, and they are numerically demonstrated for the cases of conventional ring-polymer MD (RPMD) and thermostated RPMD (TRPMD). Furthermore, it is demonstrated that these numerical artifacts are removed via replacement of the exact free ring-polymer evolution with a second-order approximation based on the Cayley transform. The Cayley modification introduced here can immediately be employed with almost every existing integration scheme for path-integral-based MD—including path-integral MD (PIMD), RPMD, TRPMD, and centroid MD—providing strong symplectic stability and ergodicity to the numerical integration, at no penalty in terms of computational cost, algorithmic complexity, or accuracy of the overall MD time step. Furthermore, it is shown that the improved numerical stability of the Cayley modification allows for the use of larger MD time steps. We suspect that the Cayley modification will therefore find useful application in many future path-integral-based MD simulations.

Item Type:Article
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URLURL TypeDescription
Korol, Roman0000-0001-9307-6351
Bou-Rabee, Nawaf0000-0001-9280-9808
Miller, Thomas F., III0000-0002-1882-5380
Additional Information:© 2019 Published under license by AIP Publishing. Submitted: 16 July 2019; Accepted: 26 August 2019; Published Online: 23 September 2019. We thank Jesús Sanz-Serna, Xuecheng Tao, and Eric Vanden-Eijnden for helpful discussions. N.B.-R. was supported in part by the National Science Foundation under Award No. DMS-1816378. R.K. and T.F.M. acknowledge support from the Department of Energy under Award No. DE-FOA-0001912 and the Office of Naval Research under Award No. N00014-10-1-0884.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FOA-0001912
Office of Naval Research (ONR)N00014-10-1-0884
Issue or Number:12
Record Number:CaltechAUTHORS:20190923-153207121
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Official Citation:Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics. Roman Korol, Nawaf Bou-Rabee, and Thomas F. Miller III. The Journal of Chemical Physics 151:12.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98805
Deposited By: Tony Diaz
Deposited On:23 Sep 2019 22:47
Last Modified:16 Nov 2021 17:41

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