Analytical approach to molecular liquids. III: The Born solvation free energy of two fixed ions in a dipolar solvent

The Born solvation free energy (BSFE) of two ions at a fixed distance from one another in a model polar solvent is obtained via two approaches. In the interaction-site approach, the two ions are modeled as a rigid extended dipolar dumbbell. Analytical expressions for the BSFE for such a dumbbell model in a dipolar dumbbell and a dipolar hard-sphere solvent are obtained under a mean spherical approximation (MSA). In the second approach, a thermodynamic cycle is established such that the BSFE for two ions a fixed distance apart can be expressed in terms of the solvent-averaged potential between the two ions and other known quantities. The results obtained via these two approaches are reasonably consistent, with the thermodynamic-cycle BSFE as a function of distance exhibiting more of the structure one expects to find in a molecular solvent. Both BSFE functions are substantially different from the corresponding continuum-solvent result. When the distance between two ions goes to infinity, our results reduce to earlier results for the single-ion BSFE obtained by us for a dipolar dumbbell solvent and by Chan et al. for a dipolar hard-sphere solvent. The BSFE of two ions in an ionic solution with a dielectric-continuum solvent is also obtained; it is found that the contribution of other ionic particles to the total BSFE is usually negligible if the dielectric constant of the solution is assumed to be unchanged.