A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat

TL;DR

This paper presents a new simple and accurate algorithm for thermostatting path integral molecular dynamics using the Langevin equation, improving efficiency and accuracy over existing methods.

Contribution

The paper introduces a novel splitting algorithm for PIMD with the Langevin thermostat that outperforms previous methods in efficiency and accuracy.

Findings

Increases simulation time intervals by a factor of 4-6 for same accuracy

Demonstrates effectiveness on realistic systems like water and hydrogen

Provides error analysis for both the new and existing algorithms

Abstract

We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation (PILE) thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4~6 or more for achieving the same accuracy. In addition, supplemental material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.