  Inferring properties of macroscopic solutions from molecular simulations is
complicated by the limited size of systems that can be feasibly examined with a
computer. When long-ranged electrostatic interactions are involved, the
resulting finite size effects can be substantial and may attenuate very slowly
with increasing system size, as shown by previous work on dilute ions in bulk
aqueous solution. Here we examine corrections for such effects, with an
emphasis on solvation near interfaces. Our central assumption follows the
perspective of H\"{u}nenberger and McCammon [J. Chem. Phys. 110, 1856 (1999)]:
Long-wavelength solvent response underlying finite size effects should be well
described by reduced models like dielectric continuum theory, whose size
dependence can be calculated straightforwardly. Applied to an ion in a periodic
slab of liquid coexisting with vapor, this approach yields a finite size
correction for solvation free energies that differs in important ways from
results previously derived for bulk solution. For a model polar solvent, we
show that this new correction quantitatively accounts for the variation of
solvation free energy with volume and aspect ratio of the simulation cell.
Correcting periodic slab results for an aqueous system requires an additional
accounting for the solvent's intrinsic charge asymmetry, which shifts electric
potentials in a size-dependent manner. The accuracy of these finite size
corrections establishes a simple method for a posteriori extrapolation to the
thermodynamic limit, and also underscores the realism of dielectric continuum
theory down to the nanometer scale.
