System-Size Dependence of Electrolyte Activity Coefficients in Molecular Simulations

A systematic study of the dependence of electrolyte activity coefficients on simulation system size has been undertaken. Using implicit-solvent simulations for which calculations with low statistical uncertainty are feasible, it was found that the chemical potential for a NaCl model depends strongly on simulation system size at concentrations up to about 0.3 mol/L; system-size effects at higher concentrations are much smaller. Similar trends were confirmed in systems with an explicit solvent. System-size effects on the chemical potential, when uncorrected, can lead to systematic errors in the activity coefficient greater than 10%. The rigorous method to correct for such system-size effects is to perform multiple simulations at each concentration and extrapolate to infinite system size. Unfortunately, this becomes impractical for explicit-solvent simulations at low concentrations, because of computational limitations that lead to large statistical uncertainties in the results. Somewhat counterintuitively, we find that lower systematic errors for the Henry's law reference chemical potential are obtained by using simulations at higher concentrations, for which system-size effects are much smaller, to obtain estimates for the reference chemical potential. This is the case even though at these higher concentrations deviations from the Debye-Hückel limiting law (or its empirical extensions) are greater than those at lower concentrations.