Cluster-Continuum Calculations of Hydration Free Energies of Anions and Group 12 Divalent Cations

Understanding aqueous phase processes involving group 12 metal cations is relevant to both environmental and biological sciences. Here, quantum chemical methods and polarizable continuum models are used to compute the hydration free energies of a series of divalent group 12 metal cations (Zn²⁺, Cd²⁺, and Hg²⁺) together with Cu²⁺ and the anions OH^–, SH^–, Cl^–, and F^–. A cluster-continuum method is employed, in which gas-phase clusters of the ion and explicit solvent molecules are immersed in a dielectric continuum. Two approaches to define the size of the solute–water cluster are compared, in which the number of explicit waters used is either held constant or determined variationally as that of the most favorable hydration free energy. Results obtained with various polarizable continuum models are also presented. Each leg of the relevant thermodynamic cycle is analyzed in detail to determine how different terms contribute to the observed mean signed error (MSE) and the standard deviation of the error (STDEV) between theory and experiment. The use of a constant number of water molecules for each set of ions is found to lead to predicted relative trends that benefit from error cancellation. Overall, the best results are obtained with MP2 and the Solvent Model D polarizable continuum model (SMD), with eight explicit water molecules for anions and 10 for the metal cations, yielding a STDEV of 2.3 kcal mol^–1 and MSE of 0.9 kcal mol^–1 between theoretical and experimental hydration free energies, which range from −72.4 kcal mol^–1 for SH^– to −505.9 kcal mol^–1 for Cu²⁺. Using B3PW91 with DFT-D3 dispersion corrections (B3PW91-D) and SMD yields a STDEV of 3.3 kcal mol^–1 and MSE of 1.6 kcal mol^–1, to which adding MP2 corrections from smaller divalent metal cation water molecule clusters yields very good agreement with the full MP2 results. Using B3PW91-D and SMD, with two explicit water molecules for anions and six for divalent metal cations, also yields reasonable agreement with experimental values, due in part to fortuitous error cancellation associated with the metal cations. Overall, the results indicate that the careful application of quantum chemical cluster-continuum methods provides valuable insight into aqueous ionic processes that depend on both local and long-range electrostatic interactions with the solvent