# Quasi-Chemical Theory for Anion Hydration and Specific Ion Effects: Cl$^-$(aq) \emph{vs.} F$^-$(aq)

## TL;DR

This paper applies quasi-chemical theory and dynamics calculations to compare hydration structures and free energies of chloride and fluoride ions, providing insights into specific ion effects relevant to biological and chemical systems.

## Contribution

It introduces a combined approach of electronic structure and dynamics to accurately model anharmonicity and competing hydration structures of Cl$^-$ and F$^-$ ions.

## Key findings

- Cl$^-$ and F$^-$ hydration structures differ significantly.
- Predicted hydration free energy difference matches experimental data.
- Cl$^-$ exhibits more flexible hydration interactions than F$^-$.

## Abstract

Anion hydration is complicated by H-bond donation between neighboring water molecules in addition to H-bond donation to the anion. This situation can lead to competing structures for chemically simple clusters like (H$_2$O)$_n$Cl$^-$ and to anharmonic vibrational motions. Quasi-chemical theory builds from electronic structure treatment of isolated ion-water clusters, partitions the hydration free energy into inner-shell and outer-shell contributions, and provides a general statistical mechanical framework to study complications of anion hydration. The present study exploits dynamics calculations on isolated (H$_2$O)$_n$Cl$^-$ clusters to account for anharmonicity, utilizing ADMP (atom-centered basis sets and density-matrix propagation) tools. Comparing singly hydrated F$^-$ and Cl$^-$ clusters, classic OH-bond donation to the anion occurs for F$^-$, while Cl$^-$ clusters exhibit more flexible but dipole-dominated interactions between ligand and ion. The predicted Cl$^-$ -- F$^-$ hydration free energy difference agrees well with experiment, a significant theoretical step for addressing issues like Hofmeister ranking and selectivity in ion channels.