Self-diffusion Green-Kubo expression

This expression is a Green-Kubo-like expression for the quantum selfdiffusion constant in CMD. Working backwards from its usual derivation shows that the self-diffusion constant can also be obtained from the long-time behavior of the slope of the centroid mean-squared displacement ... 

The search for an analytic expression for the velocity autocorrelation function, Z(t) = (l/3)(v(0).v(/)), where v(t) is the velocity of an arbitrary molecule at time t, has been of interest since the start of molecular simulation. The self-diffusion coefficient can be obtained from Z(t) using the Green-Kubo formula. 

The foundations of DPD have been considered in a number of publica-tions. The rules of dissipative particle dynamics were derived from the underlying molecular interactions by a systematic coarse graining procedure. Evans derived expressions for the self-diffusion coefficient and shear viscosity of the DPD particles in the form of the Green-Kubo time correlation functions. DPD can be used to model arbitrarily shaped objects made up of fused spheres by... 

As stated in the introduction, molecular simulations can be used as complementary tools to characterize ionic liquids from a modelling approach. The transport coefficients can be calculated through the corresponding Green-Kubo relations (Allen Tildesley, 1987 Frenkel Smit, 2002). Within this formalism, the self-diffusion coefficient (D) of each ion is calculated from its velocity autocorrelation function (vacf) through the following expression ... 

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