  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 and a dielectric continuum model of outer sphere
hydration contributions, predicts an average hydration shell occupancy of 4.0.
This underestimate is attributed to the harmonic approximation for the clusters
in conjunction with the approximate dielectric continuum model treatment of
outer sphere contributions. Finally, a maximum entropy fitting of inner sphere
occupancies that leads to insensitive composite free energy approximations
suggests a value in the neighborhood of -68 kcal/mol for the hydration free
energy of Na+ (aq) under these conditions with no contribution supplied for
packing or van der Waals interactions.
