  We compute ionic free energy adsorption profiles at aqueous graphene
interface by developing a self-consistent approach. To do so, we design a
microscopic model for water and put the liquid on an equal footing with the
graphene described by its electronic band structure. By evaluating
progressively the electronic/dipolar coupled electrostatic interactions, we
show that the coupling level including mutual graphene/water screening permits
to recover remarkably the precision of extensive quantum simulations. We
further derive the potential of mean force evolution of several alkali cations.
