Improving the Born equation: Origin of the Born radius and introducing dielectric saturation effects

The Born equation is a seminal model to study the solvation process of ions in solution, devised originally for ions at infinite dilution. Diverse modifications have been proposed in literature since the publication of the original work by Max Born in 1920, with varying degrees of success. In this work, we analyze and discuss various modifications to the Born equation. We verify their performance for Gibbs Free Energy, Enthalpy, and Entropy of solvation using data from a comprehensive database of 143 ions with charges from −4 to ＋4 in 26 different solvents. We show how the Born radius is a natural consequence of introducing the dielectric saturation effect in an approximate form, and therefore most of the proposed models are special cases of considering a continuous radial dependence for the dielectric constant. Finally, we propose a new analytical modification to the Born equation, which encloses the previous theoretical modifications and has a better performance than previous modifications.