System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions

We study the system-size dependence of translational diffusion coefficients and viscosities in molecular dynamics simulations under periodic boundary conditions. Simulations of water under ambient conditions and a Lennard-Jones (LJ) fluid show that the diffusion coefficients increase strongly as the system size increases. We test a simple analytic correction for the system-size effects that is based on hydrodynamic arguments. This correction scales as N-1/3, where N is the number of particles. For a cubic simulation box of length L, the diffusion coefficient corrected for system-size effects is D-0 = D-PBC + 2.837297k(B)T/(6.7pietaL), where D-PBC is the diffusion coefficient calculated in the simulation, k(B) the Boltzmann constant, T the absolute temperature, and eta the shear viscosity of the solvent. For water, LJ fluids, and hard-sphere fluids, this correction quantitatively accounts for the system-size dependence of the calculated self-diffusion coefficients. In contrast to diffusion coefficients, the shear viscosities of water and the LJ fluid show no significant system-size dependences.