Cluster-Continuum Calculations
of Hydration Free Energies
of Anions and Group 12 Divalent Cations
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Abstract
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 (Zn<sup>2+</sup>, Cd<sup>2+</sup>, and Hg<sup>2+</sup>) together with Cu<sup>2+</sup> and the anions OH<sup>–</sup>, SH<sup>–</sup>, Cl<sup>–</sup>, and F<sup>–</sup>. 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<sup>–1</sup> and MSE of 0.9
kcal mol<sup>–1</sup> between theoretical and experimental
hydration free energies, which range from −72.4 kcal mol<sup>–1</sup> for SH<sup>–</sup> to −505.9 kcal mol<sup>–1</sup> for Cu<sup>2+</sup>. Using B3PW91 with DFT-D3 dispersion
corrections (B3PW91-D) and SMD yields a STDEV of 3.3 kcal mol<sup>–1</sup> and MSE of 1.6 kcal mol<sup>–1</sup>, 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