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

Abstract

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 thermostatted (i.e., canonical) equations of motion, it leads to non-ergodicity of the sampling. These pathologies are generally proven to arise at integration timesteps 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 molecular dynamics (RPMD) and thermostatted 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 molecular dynamics - 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 timestep. Furthermore, it is shown that the improved numerical stability of the Cayley modification allows for the use of larger MD timesteps. We suspect that the Cayley modification will therefore find useful application in many future path-integral-based MD simulations.

arXiv comment12 pages, 7 figures. Condition (37) is tightened (due to a sign error fix)

References in corpus (13)

• Canonical sampling through velocity-rescaling
• Nuclear quantum effects enter the mainstream
• Efficient stochastic thermostatting of path integral molecular dynamics
• How to remove the spurious resonances from ring polymer molecular dynamics
• Robust and efficient configurational molecular sampling via Langevin Dynamics
• Accelerating the convergence of path integral dynamics with a generalized Langevin equation
• A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
• Efficient methods and practical guidelines for simulating isotope effects
• 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
• Sampling diffusive transition paths
• Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory

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