Multi-scale theory in the molecular simulation of electrolyte solutions

This paper organizes McMillan-Mayer theory, the potential distribution approach, and quasi-chemical theory to provide theory for the thermodynamic effects associated with longer spatial scales involving longer time scales, thus helping to define a role for AIMD simulation directly on the time and space scales typical of those demanding methods. The theory treats composition fluctuations which 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 tetra-ethylammonium tetra-fluoroborate 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.