On the system size dependence of the diffusion coefficients in MD simulations: A simple correction formula for pure dense fluids

A practical correction formula relating the self-diffusion coefficient of dense liquids from molecular dynamics simulations with periodic boundary conditions to the self-diffusion coefficient in the thermodynamic limit is discussed. This formula applies to pure dense fluids and has a very simple form $D=D_0(1-\gamma N^{-1\mathrm{/}3})$, where $D_0$ is the self-diffusion coefficient in the thermodynamic limit and $N$ is the number of particles in the simulation. The numerical factor $\gamma$ depends on the geometry of the simulation cell. Remarkably, $\gamma \simeq 1.0$ for the most popular cubic geometry. The success of this formula is supported by results from MD simulations, including very recent simulations with a ``magic’’ simulation geometry.