Variation of ion polarizability from vacuum to hydration: Insights from Hirshfeld partitioning

The results of iterative Hirshfeld partitioning on the polarizability of monovalent anions (F^-, Cl^-, and Br^-) and Na⁺in water clusters ranging from n = 0 to n = 25 are presented. In each case, the ions reach a limiting intrinsic polarizability in the fully hydrated state. For F^-, Cl^-, and Br^- using B3LYP/aug-cc-pVDZ, the intrinsic polarizabilities in the condensed-phase limit are 47.2 ± 0.7%, 47.2 ± 0.3%, and 54.2 ± 0.4% of their gasphase value at the corresponding level of theory. The extent of this scaling depends on the basis set (we also consider B3LYP/aug-cc-pVTZ), but intrinsic polarizabilities are generally within 35-55% of the gas-phase value. The sodium cation is the least polarizable in the condensed-phase limit. The average intrinsic polarizability of water in these clusters decreases with the size of the cluster, which is consistent with earlier Hirshfeld analysis of intrinsic polarizabilities of pure water (Krishtal, A.; Senet, P.; Yang, M.; van Alsenoy, C. J. Chem. Phys. 2006, 125, 034312). Further analysis demonstrates that water molecules near ions in sufficiently large clusters (n = 25) have intrinsic polarizabilities similar to those of water molecules fully coordinated in a pure aqueous cluster. The observed binodal distribution of the water intrinsic polarizability within the cluster is attributed to polarizability differences between interior and exterior water molecules. This observation is in qualitative agreement with arguments based on Pauli's exclusion principle that suggest a reduced polarizability for condensed-phase water relative to the vacuum value.