Constrained molecular dynamics and the mean potential for an ion pair in a polar solvent

A constrained molecular dynamics (MD) method for the calculation of the potential of mean force is described, and applied to study the solvent-separated and contact ion pair equilibrium in a polar solvent. The method uses holonomic constraints on the MD to fix ion pair internuclear separation. The average force exerted on the ions by the solvent is computed as a function of ion separation, and the potential of mean force follows from an integration of the mean force. The ion pair mean potential, the reaction equilibrium constant and the solvent structure in the vicinity of the ions are examined for two model solvents with differing molecular dipole moments. The relevance of this study for the dynamics of the contact ion pair-solvent separated ion pair reaction is pointed out.