  We present the theory and implementation of a Poisson-Boltzmann implicit
solvation model for electrolyte solutions. This model can be combined with
arbitrary electronic structure methods that provide an accurate charge density
of the solute. A hierarchy of approximations for this model includes a linear
approximation for weak electrostatic potentials, finite size of the mobile
electrolyte ions and a Stern-layer correction. Recasting the Poisson-Boltzmann
equations into Euler-Lagrange equations then significantly simplifies the
derivation of the free energy of solvation for these approximate models. The
parameters of the model are then either fit directly to experimental
observables, e.g. the finite ion size, or optimized for agreement with
experimental results. Experimental data for this optimization is available in
the form of Sechenov coefficients that describe the linear dependence of the
salting-out effect of solutes with respect to the electrolyte concentration. In
the final part we rationalize the qualitative disagreement of the finite ion
size modification to the Poisson-Boltzmann model with experimental observations
by taking into account the electrolyte concentration dependence of the Stern
layer. A route towards a revised model that captures the experimental
observations while including the finite ion size effects is then outlined. This
implementation paves the way for the study of electrochemical and
electrocatalytic processes of molecules and cluster models with accurate
electronic structure methods.
