  The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit
solvation model which also captures electrolytic solvent effects. It combines
an account of the dielectric solvent response with a mean-field description of
solvated finite-sized ions. We present a general solution scheme for the MPB
equation based on a fast function-space oriented Newton method and a Green's
function preconditioned iterative linear solver. In contrast to popular
multi-grid solvers this approach allows to fully exploit specialized
integration grids and optimized integration schemes. We describe a
corresponding numerically efficient implementation for the full-potential
density-functional theory (DFT) code FHI-aims. We show that together with an
additional Stern layer correction the DFT+MPB approach can describe the mean
activity coefficient of a KCl aqueous solution over a wide range of
concentrations. The high sensitivity of the calculated activity coefficient on
the employed ionic parameters thereby suggests to use extensively tabulated
experimental activity coefficients of salt solutions for a systematic
parametrization protocol.
