  Thermochemistry of gas-phase ion-water clusters together with estimates of
the hydration free energy of the clusters and the water ligands are used to
calculate the hydration free energy of the ion. Often the hydration
calculations use a continuum model of the solvent. The primitive quasichemical
approximation to the quasichemical theory provides a transparent framework to
anchor such efforts. Here we evaluate the approximations inherent in the
primitive quasichemical approach and elucidate the different roles of the bulk
medium. We find that the bulk medium can stabilize configurations of the
cluster that are usually not observed in the gas phase, while also
simultaneously lowering the excess chemical potential of the ion. This effect
is more pronounced for soft ions. Since the coordination number that minimizes
the excess chemical potential of the ion is identified as the optimal or most
probable coordination number, for such soft ions, the optimum cluster size and
the hydration thermodynamics obtained without account of the bulk medium on the
ion-water clustering reaction can be different from those observed in
simulations of the aqueous ion. The ideas presented in this work are expected
to be relevant to experimental studies that translate thermochemistry of
ion-water clusters to the thermodynamics of the hydrated ion and to evolving
theoretical approaches that combine high-level calculations on clusters with
coarse-grained models of the medium.
