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

Abstract

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 (PIMD), without which standard integrators exhibit non-ergodicity and other pathologies [J. Chem. Phys. 151, 124103 (2019); 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.

arXiv commentJorge L. Rosa-Raíces and Jiace Sun contributed equally to this work

References in corpus (21)

• Canonical sampling through velocity-rescaling
• Competing quantum effects in the dynamics of a flexible water model
• Nuclear quantum effects enter the mainstream
• Nuclear quantum effects in water
• Efficient stochastic thermostatting of path integral molecular dynamics
• i-PI 2.0: A Universal Force Engine for Advanced Molecular Simulations
• Ab initio thermodynamics of liquid and solid water
• How to remove the spurious resonances from ring polymer molecular dynamics
• Accelerating the convergence of path integral dynamics with a generalized Langevin equation
• Rational Construction of Stochastic Numerical Methods for Molecular Sampling
• Boltzmann-conserving classical dynamics in quantum time-correlation functions: Matsubara dynamics
• A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
• Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics
• Randomized Hamiltonian Monte Carlo
• A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics
• Geometric integrators and the Hamiltonian Monte Carlo method
• Fine Tuning Classical and Quantum Molecular Dynamics using a Generalized Langevin Equation
• Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics
• Dimension-free path-integral molecular dynamics without preconditioning
• Path integral evaluation of equilibrium isotope effects
• Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions

Cited by in corpus (3)

• New Stable and Fast Ring-Polymer Molecular Dynamics for Calculating Bimolecular Rate Coefficients with Example of OH + CH_4
• Efficient Sampling of Thermal Averages of Interacting Quantum Particle Systems with Random Batches
• Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy