Acquisition of Precise Statistics in Stochastic Langevin Molecular Dynamics

Numerical simulations of atomic and molecular ensembles by Molecular Dynamics always involve discretization of time, and as the time step is increased the discrete-time behavior not only becomes increasingly different from the anticipated continuous-time dynamics, it also develops internal inconsistencies between, e.g., configurational and kinetic measures. These inconsistencies can lead to significant problems in computational statistical mechanics if the time step is challenged.

We present a new, simple simulation technique for systems in thermal equilibrium. We briefly review our stochastic Størmer-Verlet algorithm for the evolution of Langevin equations in a manner that preserves proper configurational sampling (diffusion and Boltzmann distribution) in discrete time. The resulting method, which is as simple as conventional Verlet schemes, has been numerically tested on both low-dimensional nonlinear systems as well as more complex molecular ensembles with many degrees of freedom. Additionally, we present a recent solution to the "velocity-problem", and we show a simple approach for achieving accurate measures, simultaneously for both configurational and kinetic sampling. We show exact analytic results for linear systems, and demonstrate the applicability of the method for both nonlinear and complex systems, which can be accurately simulated at any time step within the stability limit. The method 1 is in the standard form of a Verlet-type algorithm, and is therefore easy to test and apply in existing codes, including Molecular Dynamics.

1 "Accurate configurational and kinetic statistics in discrete-time Langevin systems", Molecular Physics (2019), https://doi.org/10.1080/00268976.2019.1570369