Energy-Scaled Debye-Huckel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions

In this report, an energy-scaled Debye-Hu''ckel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hu''ckel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Pade polynomial is used to interpolate the electrostatic energy at finite size. The Pade polynomial is further interpreted as the electrostatic energy of an effective Debye-Hu''ckel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.