Velocity correlations in the molecular dynamics ensemble: Computation of the distinct diffusion coefficients

The theory of the correction for the difference in the fluctuations among the different ensembles is applied to derive the time correlation function formula required to compute the distinct diffusion coefficients in the barycentric reference frame by molecular dynamics. In the process it is found that the dynamical variables in the time correlation function of any mass transport coefficient of any reference frame are the same in the canonical as in the molecular dynamics ensemble. The result agrees with the accepted formulas for computing the kinetic part of the mutual diffusion coefficient in a binary mixture of nonelectrolytes and for computing the electrical conductivity in molten salts and electrolyte solutions. The static velocity correlations in the molecular dynamics ensemble are analyzed without recourse to the other ensembles. In sharp contrast with the ensembles which are not constrained with respect to the total momentum, the laboratory-frame velocities of two different particles at the same time are found to be correlated. The result obtained is equivalent to the initial value of the canonical time correlation function of the barycentric distinct diffusion coefficients derived in the preceding paper.