The second self-diffusion and viscosity virial coefficients of the Lennard-Jones fluid were calculated by a detailed evaluation of the velocity and shear-stress autocorrelation functions using equilibrium molecular dynamics simulations at low and moderate densities. Accurate calculation of these coefficients required corresponding transport coefficient values with low degrees of uncertainty. These were obtained via very long simulations by increasing the number of particles and by using the knowledge of correlation functions in the Green-Kubo method in conjunction with their corresponding generalized Einstein relationships. The values of the self-diffusion and shear viscosity coefficients were evaluated for systems with reduced densities between 0.0005 and 0.05 and reduced temperatures from 0.7 to 30.0. This provided a insight into the transport coefficients beyond what could be offered by the Rainwater-Friend theory, which had not been developed for the self-diffusion coefficient.

Calculation of the Second Self-Diffusion and Viscosity Virial Coefficients of Lennard-Jones Fluid by Equilibrium Molecular Dynamics Simulations. Oderji, H.Y., Ding, H., Behnejad, H.: Physical Review E, 2011, 83[6], 061202