Frequency-dependent hydrodynamic finite size correction in molecular simulations reveals the long-time hydrodynamic tail

TL;DR

This paper develops a frequency-dependent hydrodynamic correction for molecular simulations to accurately reveal long-time hydrodynamic tails, addressing finite-size effects in dynamic property calculations.

Contribution

It introduces an analytical correction method for periodic boundary effects, enabling the observation of long-time tails in velocity autocorrelation functions from small simulation boxes.

Findings

Long-time hydrodynamic tails are observable after applying the correction.

Finite-size effects significantly distort dynamic properties in simulations.

The correction method works for both water and Lennard-Jones fluids.

Abstract

Finite-size effects are challenging in molecular dynamics simulations because they have significant effects on computed static and dynamic properties, in particular diffusion constants, friction coefficients and time- or frequency-dependent response functions. We investigate the influence of periodic boundary conditions on the velocity autocorrelation function and the frequency-dependent friction of a particle in a fluid and show that the long-time behavior (starting at the picosecond timescale) is significantly affected. We develop an analytical correction allowing to subtract the periodic boundary condition effects. By this we unmask the power-law long-time tails of the memory kernel and the velocity autocorrelation function in liquid water and a Lennard-Jones fluid from rather small simulation boxes.