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

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.