Ion Pair Potentials-of-mean-force in Water

Motivated by the surprising dielectric model predictions of alkali-halide ion pair potentials-of-mean-force in water due to Rashin, we reanalyze the theoretical bases of that comparison. We discuss recent, pertinent molecular simulation and integral equation results that have appeared for these systems. We implement di-electric model calculations to check the basic features of Rashin's calculations. We confirm that the characteristic structure of contact and solvent-separated minima does appear in the dielectric model results for the pair potentials-of-mean-force for oppositely charged ions in water under physiological thermodynamic conditions. Comparison of the dielectric model results with the most current molecular level information indicates that the dielectric model does not, however, provide an accurate description of these potentials-of-mean-force. Since literature results indicate that dielectric models can be helpfully accurate on a coarse, or chemical energy scale, we consider how they might be based more firmly on molecular theory. The objective is a parameterization better controlled by molecular principles and thus better adapted to the prediction of quantities of physical interest. Such a result might be expected to describe better the thermal-level energy changes associated with simple molecular rearrangements, i.e., ion pair potentials-of-mean-force. We note that linear dielectric models correspond to modelistic implementations of second-order thermodynamic perturbation theory for the excess chemical potential of a distinguished solute molecule. Therefore, the molecular theory corresponding to the dielectric models is second-order thermodynamic perturbation theory for that excess chemical potential. Examination of the required formulae indicate that this corresponding molecular theory should be quite amenable to computational implementation. The second-order, or fluctuation, term raises a technical computational issue of treatment of long-ranged interactions similar to the one which arises in calculation of the dielectric constant of the solvent. Satisfactory calculation of that term will require additional theoretical consideration of those issues. It is contended that the most important step for further development of dielectric models would be a separate assessment of the first-order perturbative term (equivalently the potential at zero charge) which vanishes in the dielectric models but is generally nonzero. Parameterization of radii and molecular volumes should then be based of the second-order perturbative term alone. Illustrative initial calculations are presented and discussed.