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The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicitsolvation model which also captures electrolytic solvent effects. It combinesan account of the dielectric solvent response with a mean-field description ofsolvated finite-sized ions. We present a general solution scheme for the MPBequation based on a fast function-space oriented Newton method and a Green'sfunction preconditioned iterative linear solver. In contrast to popularmulti-grid solvers this approach allows to fully exploit specializedintegration grids and optimized integration schemes. We describe acorresponding numerically efficient implementation for the full-potentialdensity-functional theory (DFT) code FHI-aims. We show that together with anadditional Stern layer correction the DFT+MPB approach can describe the meanactivity coefficient of a KCl aqueous solution over a wide range ofconcentrations. The high sensitivity of the calculated activity coefficient onthe employed ionic parameters thereby suggests to use extensively tabulatedexperimental activity coefficients of salt solutions for a systematicparametrization protocol.

Function-Space Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT