We compute individual ion activity coefficients (IIACs) in aqueous NaCl, KCl, NaF, and KF solutions from explicit-water molecular dynamics simulations. Free energy changes are obtained from insertion of single ionsaccompanied by uniform neutralizing backgroundsinto solution by gradually turning on first Lennard-Jones interactions, followed by Coulombic interactions using Ewald electrostatics. Simulations are performed at multiple system sizes, and all results are extrapolated to the thermodynamic limit, thus eliminating any possible artifacts from the neutralizing backgrounds. Because of controversies associated with measurements of IIACs from electrochemical cells with ion-selective electrodes, the reported experimental data are not widely accepted; thus there remains a knowledge gap with respect to the contributions of individual ions to solution nonidealities. Our results are in good qualitative agreement with these reported measurements, though significantly larger in magnitude. In particular, the relative positioning for the activity coefficients of anions and cations matches the experimental ordering for all four systems. This work establishes a robust thermodynamic framework, without a need to invoke extra hypotheses, that sheds light on the behavior of individual ions and their contributions to nonidealities of aqueous electrolyte solutions.

We obtain activity coefficients in NaCl and KCl solutions from implicit-water molecular dynamics simulations, at 298.15 K and 1 bar, using two distinct approaches. In the first approach, we consider ions in a continuum with constant relative permittivity (ɛr) equal to that of pure water; in the other approach, we take into account the concentration-dependence of ɛr, as obtained from explicit-water simulations. Individual ion activity coefficients (IIACs) are calculated using gradual insertion of single ions with uniform neutralizing backgrounds to ensure electroneutrality. Mean ionic activity coefficients (MIACs) obtained from the corresponding IIACs in simulations with constant ɛr show reasonable agreement with experimental data for both salts. Surprisingly, large systematic negative deviations are observed for both IIACs and MIACs in simulations with concentration-dependent ɛr. Our results suggest that the absence of hydration structure in implicit-water simulations cannot be compensated by correcting for the concentration-dependence of the relative permittivity ɛr. Moreover, even in simulations with constant ɛr for which the calculated MIACs are reasonable, the relative positioning of IIACs of anions and cations is incorrect for NaCl. We conclude that there are severe inherent limitations associated with implicit-water simulations in providing accurate activities of aqueous electrolytes, a finding with direct relevance to the development of electrolyte theories and to the use and interpretation of implicit-solvent simulations.

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We obtain activity coefficients and solubilities of NaCl in water–methanol solutions at 298.15 K and 1 bar from molecular dynamics (MD) simulations with the Joung–Cheatham, SPC/E, and OPLS-AA force fields for NaCl, water, and methanol, respectively. The Lorentz–Berthelot combining rules were adopted for the unlike-pair interactions of Na+, Cl–, and the oxygen site in SPC/E water, and geometric combining rules were utilized for the remainder of the cross interactions. We found that the selection of appropriate combining rules is important in obtaining physically realistic solubilities. The solvent compositions studied range from pure water to pure methanol. Several salt concentrations were investigated at each solvent composition, from the lowest concentrations permitted by the system size used up to the experimental solubilities. We first calculated individual ion activity coefficients (IIACs) for Na+ and Cl– from the free energy change due to the gradual insertion of a single cation or anion into the solution, accompanied by a neutralizing background. We obtained the salt solubilities by comparing the chemical potentials in solution with solid NaCl chemical potentials calculated previously using the Einstein crystal method. Mean ionic activity coefficients obtained from the IIACs are in reasonable agreement with experimental data, with deviations increasing for solutions of higher methanol content. Predictions for the salt solubility are in surprisingly good agreement with experimental data, despite well-known challenges in the simultaneous calculation of activity coefficients and solubilities with classical MD simulations. The present study demonstrates that good predictions for these two important phase equilibrium properties can be obtained for mixed-solvent electrolyte solutions using existing nonpolarizable models and further suggests that the previously proposed single ion insertion technique can be extended to complex mixed-solvent solutions as well.