Velocity autocorrelation function and self-diffusion coefficient in large molecular dynamics models of liquid argon and water

Autocorrelation function of the particle velocity Z(t) is calculated using the molecular dynamics method in the models of liquid argon and water. The large size of the models (more than a hundred thousand particles) allowed us to trace these functions up to 50 picoseconds in argon and up to 10 picoseconds in water, and to achieve a calculation accuracy sufficient for analytical analysis of their shape. The difference in the determination of the self-diffusion coefficient using Einstein's law and the integral of Z(t) (Green-Kubo integral) is analyzed and it is shown to be 3% at best when t is of the order of several picoseconds. The asymptote of the function Z(t) in argon is close to the power law αt–3/2 predicted by hydrodynamics, but with an amplitude that depends on the time interval under consideration. In water, the asymptote of Z(t) has nothing in common with that in argon: it has α < 0 and the exponent is close to -5/2, and not to -3/2.