Understanding Molecular Dynamics with Stochastic Processes via Real or Virtual Dynamics

TL;DR

This paper explores the equivalence and differences between real and virtual stochastic dynamics in molecular simulations, demonstrating their properties and efficiency across various thermostats like Langevin and Andersen.

Contribution

It extends the virtual dynamics concept to other stochastic thermostats, providing analytic and numerical insights into their sampling accuracy and efficiency.

Findings

Real and virtual dynamics approach the same correlation time plateau at high collision frequencies.

Sampling accuracy and efficiency are stable over a broad range of collision frequencies.

A heuristic model is proposed to understand stochastic thermostatting processes.

Abstract

Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation [J. Chem. Phys. 147, 184104 (2017)] in principle exists in other types of stochastic thermostats as well. The recommended middle scheme [J. Chem. Phys. 147, 034109 (2017)] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation is proposed for understanding efficient stochastic thermostatting processes with molecular dynamics.