Theoretical basis of the empirical reaction field approximations through continuum model

We derive from exact integral equations of classical electrostatics some approximate expressions of the interaction energy of a point charge distribution with a dielectric medium. We show how they can be used for computing the wave functions of solvated species imbedded in cavities formed by interlocking spheres in a polarizable continuum. We discuss the relation between these formulae and the ones proposed earlier on empirical basis and we especially emphasize the improvement that they bring out.