Convergence of molecular and macroscopic continuum descriptions of ion hydration

Using computer simulations we study the boundary between explicit molecular and macroscopic continuum dielectric descriptions of ion hydration. The continuum model reasonably describes electrostatic potential fluctuation contributions to the hydration free energy, but fails to capture first-order potential contributions in the uncharged state. Once this contribution is accounted for, cationic and anionic free energies become indistinguishable with increasing size, in agreement with continuum model predictions. The ion radius at which the hydration free energies converge scales as the square root of the absolute charge (v = 0.54 +/- 0.04) and compares to the length scale ion-water dipole interactions equal the thermal energy.