Functional representation of correlations in inhomogeneous many-electron systems

We discuss the Legendre conjugate of the Hohenberg-Kohn energy-density functional, i.e., the total energy of an inhomogeneous many-electron system, considered as a functional of the external Coulomb potential (the nuclear Coulomb skeleton of a molecule, for instance) as the starting point of an alternative formulation of a theory of electronic correlations. We then relate this functional to the nonrelativistic or relativistic microscopic many-body theory. The essential bridge between the two theories is many-body perturbation theory perturbing around a mean field. We then point out that a particular choice for the latter, the g-Hartree mean field, leads to a transparent physical picture: The relevant functional of the external field, $g_0$-1, representing electronic correlations, is interpreted as a polarization charge density induced by the latter. This picture, in turn, leads to a Clausius-Mosotti type of equation for this correlation functional. Applications to atomic- and molecular-structure calculations are discussed.