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Dimension-free path-integral molecular dynamics without preconditioning

Korol, Roman and Rosa-Raíces, Jorge L. and Bou-Rabee, Nawaf and Miller, Thomas F., III (2020) Dimension-free path-integral molecular dynamics without preconditioning. Journal of Chemical Physics, 152 (10). Art. No. 104102. ISSN 0021-9606. doi:10.1063/1.5134810.

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Convergence with respect to imaginary-time discretization (i.e., the number of ring-polymer beads) is an essential part of any path-integral-based molecular dynamics (MD) calculation. However, an unfortunate property of existing non-preconditioned numerical integration schemes for path-integral molecular dynamics—including essentially all existing ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (T-RPMD) methods—is that for a given MD time step, the overlap between the exact ring-polymer Boltzmann–Gibbs distribution and that sampled using MD becomes zero in the infinite-bead limit. This has clear implications for hybrid Metropolis Monte Carlo/MD sampling schemes, and it also causes the divergence with bead number of the primitive path-integral kinetic-energy expectation value when using standard RPMD or T-RPMD. We show that these and other problems can be avoided through the introduction of “dimension-free” numerical integration schemes for which the sampled ring-polymer position distribution has non-zero overlap with the exact distribution in the infinite-bead limit for the case of a harmonic potential. Most notably, we introduce the BCOCB integration scheme, which achieves dimension freedom via a particular symmetric splitting of the integration time step and a novel implementation of the Cayley modification [R. Korol et al., J. Chem. Phys. 151, 124103 (2019)] for the free ring-polymer half-steps. More generally, we show that dimension freedom can be achieved via mollification of the forces from the external physical potential. The dimension-free path-integral numerical integration schemes introduced here yield finite error bounds for a given MD time step, even as the number of beads is taken to infinity; these conclusions are proven for the case of a harmonic potential and borne out numerically for anharmonic systems that include liquid water. The numerical results for BCOCB are particularly striking, allowing for nearly three-fold increases in the stable time step for liquid water with respect to the Bussi–Parrinello (OBABO) and Leimkuhler (BAOAB) integrators, while introducing negligible errors in the calculated statistical properties and absorption spectrum. Importantly, the dimension-free, non-preconditioned integration schemes introduced here preserve ergodicity and global second-order accuracy, and they remain simple, black-box methods that avoid additional computational costs, tunable parameters, or system-specific implementations.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Korol, Roman0000-0001-9307-6351
Rosa-Raíces, Jorge L.0000-0003-2311-2948
Bou-Rabee, Nawaf0000-0001-9280-9808
Miller, Thomas F., III0000-0002-1882-5380
Additional Information:© 2020 Published under license by AIP Publishing. Submitted: 1 November 2019; Accepted: 9 February 2020; Published Online: 11 March 2020. The authors thank Andreas Eberle and Ondrej Marsalek for helpful discussions. N.B.-R. acknowledges support from the National Science Foundation under Award No. DMS-1816378 and the Alexander von Humboldt Foundation. R.K., J.L.R.-R., 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
Alexander von Humboldt FoundationUNSPECIFIED
Department of Energy (DOE)DE-FOA-0001912
Office of Naval Research (ONR)N00014-10-1-0884
Issue or Number:10
Record Number:CaltechAUTHORS:20191216-155842954
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Official Citation:Dimension-free path-integral molecular dynamics without preconditioning. Roman Korol, Jorge L. Rosa-Raíces, Nawaf Bou-Rabee, and Thomas F. Miller III. The Journal of Chemical Physics 152:10; doi: 10.1063/1.5134810
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100316
Deposited By: Tony Diaz
Deposited On:17 Dec 2019 00:03
Last Modified:16 Nov 2021 17:53

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