Efficient stochastic thermostatting of path integral molecular dynamics

TL;DR

This paper introduces two efficient stochastic thermostats, PILE and GLE, for path integral molecular dynamics, improving sampling efficiency and computational performance in simulating quantum properties of condensed systems.

Contribution

The paper presents a simple stochastic PILE thermostat and applies a GLE thermostat, both exploiting frequency knowledge to enhance sampling efficiency in PIMD.

Findings

PILE performs as well as NHC with better efficiency

GLE achieves near-optimal sampling in all tested cases

Both thermostats outperform conventional methods in efficiency

Abstract

The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high-frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently-developed colored-noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nos\'e-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.