The hydration number of Na+ in liquid water

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Abstract
An `ab initio' molecular dynamics simulation of a Na+ ion in aqueous solution is presented and discussed. The calculation treats a Na+ ion and 32 water molecules with periodic boundary conditions on a cubic volume determined by an estimate of zero partial molar volume for this solute in water at normal density and at a temperature of 344 +/- 24 K. Analysis of the last half of the 12 ps trajectory shows 4.6 water molecules occupying the inner hydration shell of the Na+ ion on average, with 5 being the most probable occupancy. The self-diffusion coefficient observed for the Na+ is 1.0 x 10$^{-5}$ cm$^2$/s. The quasi-chemical theory of solutions provides the framework for two more calculations. First a complementary calculation, based on electronic structure results for ion-water clusters hydrated by a dielectric continuum model of the solution, predicts an average hydration shell occupancy of 4.0. This underestimate can be attributed to the harmonic approximation of interactions within the clusters and to the approximate treatment with the dielectric continuum model of extra-cluster contributions to the free energy of solvation. Finally, an information theory fit of the simulation data leads to an an absolute hydration free energy estimate of -80 kcal/mol.

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