Electrical properties of polarizable ionic solutions. I. Theoretical aspects

We generalize previous work [J. Chem. Phys. 85, 6645 (1986)] on the relation between the frequency-dependent dielectric constant and conductivity and time correlation functions of electrical current and polarization in electrolyte solutions by allowing the ions and solvent molecules to be polarizable. Detailed results are given for the infinite system (no boundary), spherical system embedded in a continuum and periodic boundary conditions. The Stillinger–Lovett (SL) sum rules are derived for these geometries. It is shown, in particular, that they provide a means of calculating the high frequency dielectric constant in a molecular dynamics simulation. A test of the phenomenological coefficient-susceptibility relations and the SL conditions is presented in part II by performing molecular dynamics simulations on a model electrolyte solution with different boundary conditions.