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To define a role for AIMD simulation on the limited time and space scales accessible to those demanding methods, this paper organizes McMillan−Mayer theory, the potential distribution approach, and quasi-chemical theory to provide theory for the thermodynamic effects associated with long-length scales. The theory treats composition fluctuations that would be accessed by larger-scale calculations, and also longer-ranged interactions that are of special interest for electrolyte solutions. The quasi-chemical organization breaks-up governing free energies into physically distinct contributions: packing, outer- shell, and chemical contributions. Here we study specifically the outer-shell contributions that express electrolyte screening. For that purpose we adopt a primitive model suggested by observation of ion-pairing in tetraethylammonium tetrafluoroborate dissolved in propylene carbonate. Gaussian statistical models are shown to be effective physical models for outer-shell contributions, and they are conclusive for the free energies within the quasi-chemical formulation. With the present data set the Gaussian physical approximation obtains more accurate mean activity coefficients than does the Bennett direct evaluation of that free energy.  Figure 1

Multi-Scale Theory in the Molecular Simulation of Electrolyte Solutions