Molecular-dynamics calculations of the velocity autocorrelation function: Hard-sphere results

The velocity autocorrelation function for the hard-sphere fluid is computed for ten values of the volume ranging from 25 to 1.6 times the close-packed volume $V_0$ for systems of from 108 to 4000 hard spheres, using a Monte Carlo, molecular-dynamics technique. The results are compared with the theoretical predictions of the mode-coupling theory, modified to take into account the finite size of the system and the periodic boundary conditions. The data are found to be in good agreement with the theory, evaluated using Enskog values for the transport coefficients, for values of the time greater than roughly 15 to 30 mean free times (depending on density), for volumes as small as 2$V_0$. The higher-density results do not agree with the theory, unless the actual transport coefficients (evaluated using molecular dynamics) are used in the theory. The latter version of the theory, however, fails to fit the data at lower densities, except at very long times. To answer the recent critique by Fox, the data are further compared with the theory over time intervals for which the molecular-dynamics trajectories retain some measure of accuracy. The agreement between the data and the theory is largely unaffected, except at a volume 1.8$V_0$ for which there is a marginally significant difference at very long times only.