Free Energies of Hydrated Halide Anions: High throughput Computations on Clusters to Treat Rough Energy-Landscapes

With a longer-term goal of addressing the comparative behavior of the aqueous halides F$^-$, Cl$^-$, Br$^-$, and I$^-$ on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal $(\mathrm{H_2O})_n\mathrm{X}$ clusters, with X = Cl$^-$, Br$^-$, and I$^-$, exhibit \emph{surface} hydration structures. Computed free energies based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (\emph{ab initio} molecular dynamics) simulation stream. This \emph{rough-landscape} procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect corrected. Nevertheless, this procedure can break down when $n \gtrsim 4$, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of $(\mathrm{H_2O})_n\mathrm{X}$ clusters, including ramified structures natural in \emph{physical cluster theories.} With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.