A 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 non-relativistic 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, g0-1, representing electronic correlations is interpreted as a polarisation 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. (orig.)