Slow Dynamics when Computing Transport Properties

IMPLICATIONS OF SLOW DYNAMICS WHEN COMPUTING TRANSPORT PROPERTIES 

Recall that Del Popolo and Voth computed the dynamics of [C2mim] [NO3] and saw evidence of what they termed dynamic heterogeneity. This can be quantified using a so-called non-Gaussian parameter/ a t), given by 

What are the implications of these studies on the calculation of macroscopic dynamical properties of ionic liquids At the very least, they suggest that one should be careful when applying standard computational techniques used for simple liquids to ionic liquids. Most of these techniques assume ergodic behavior, but the work described above shows this may not always be the case. Due to the sluggish dynamics of ionic liquid systems, one should carry out very long simulations to ensure adequate sampling. 

Consider the simplest dynamic property one can compute, the self-diffusivity, Dj. The standard approach for computing Ds is to conduct an equilibrium MD simulation and accumulate the mean-square displacement as a function of time. The self-diffusivity is then computed using the Einstein equation  

The parameter p can be computed as a function of time using the following expression  

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