Two methods to calculate corrected collective diffusion coefficients in zeolites are compared. The meaning of the center-of-mass coordinate that occurs in the usual Einstein expression for the corrected diffusivity is discussed. The use of unfolded particle trajectories in the expression is shown to be only valid for periodic systems and only if the entire box is taken as the control volume. A wave vector-dependent Einstein expression is derived, equivalent to the Green–Kubo form that was derived in an earlier study [J. Chem. Phys. 113, 6875 (2000)]. The box size dependence of the diffusivities calculated from the usual Einstein equation is reproduced for small k-values when the new expression is applied to a large box.
Tepper, H. L., & Briels, W. J. (2002). Comments on the use of the Einstein equation for transport diffusion: Application to argon in AIP04-5. Journal of chemical physics, 116(21), 9464-9474. https://doi.org/10.1063/1.1473821