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

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.

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References in corpus (6)

• Accurate sampling using Langevin dynamics
• Efficient stochastic thermostatting of path integral molecular dynamics
• How to remove the spurious resonances from ring polymer molecular dynamics
• Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei
• 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

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