# Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions

## TL;DR

This study uses density functional theory-based molecular dynamics to analyze the solvation free energies of charged hard spheres, revealing the importance of charge effects, cavitation, and charge hydration asymmetry, with implications for electrolyte models.

## Contribution

It introduces a DFT-MD approach to decompose ion solvation free energies and highlights the limitations of simple charged hard sphere models compared to real ions.

## Key findings

- Uncorrected Ewald summation yields unphysical solvation energies.
- Charging free energies are approximately linear for cations, with small non-linearity for anions.
- Charge hydration asymmetry for hard spheres exceeds that of real ions.

## Abstract

Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation (DFT-MD) and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry (CHA) for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.