Charge hydration asymmetry: the basic principle and how to use it to test and improve water models

Charge hydration asymmetry (CHA) manifests itself in the experimentally observed strong dependence of free energy of ion hydration on the sign of the ion charge. This asymmetry is not consistently accounted for by popular models of solvation; its magnitude varies greatly between the models. While it is clear that CHA is somehow related to charge distribution within a water molecule, the exact nature of this relationship is unknown. We propose a simple, yet general and rigorous criterion that relates rotational and charge inversion properties of a water molecule's charge distribution with its ability to cause CHA. We show which electric multipole components of a water molecule are key to explain its ability for asymmetric charge hydration. We then test several popular water models and explain why specific models show none, little, or strong CHA in simulations. We use the gained insight to derive an analogue of the Born equation that includes the missing physics necessary to account for CHA and does not rely on redefining the continuum dielectric boundary. The proposed formula is as simple as the original, does not contain any fitting parameters, and predicts hydration free energies and entropies of spherical cations and anions within experimental uncertainty. Our findings suggest that the gap between the practical continuum electrostatics framework and the more fundamental explicit solvent treatment may be reduced considerably by explicitly introducing CHA into the existing continuum framework.