Dressed ion theory for bulk symmetric electrolytes in the restricted primitive model

The correlation functions of bulk symmetric electrolytes in the restricted primitive model are analyzed using the formalism of the dressed ion theory of Kjellander and Mitchell [Chem. Phys. Lett. 200, 76 (1992), J. Chem. Phys. 101, 603 (1994)]. An important result of this analysis is that the exact theory for the pair correlation functions can be cast in a form that is virtually identical to that of the Debye–Hückel theory provided one uses the renormalized charges of the ions—‘‘dressed ions’’—instead of bare ion charges. In the current work the (state dependent) charges of these dressed ions are investigated using the HNC approximation. The asymptotic decay of the pair correlation functions are analyzed in terms of the effective point charges of the ions and the effective permittivity of the electrolyte solution, concepts which are given rigorous and physically transparent definitions in the dressed ion theory. Several transitions between regimes with different qualitative behavior of the pair correlation functions are demonstrated, in addition to the well-known transition between monotonic and oscillatory damped decay. By means of an analysis of the singularities of the correlation functions in complex Fourier space, dressed ion theory provides a general method to determine these transitions from numerical pair correlation data and in this paper results are given for symmetric electrolytes with monovalent and divalent ions.