On the basis of some principles of the theory of density functionals, we obtain a fully specified ensemble of eigenstates of an effective (one-body) Hamiltonian whose average energy is identical to the ground-state total energy of the interacting system. It is shown that within the present framework accurate approximation schemes can be devised through which the ground-state total energy is obtained by the knowledge of two quantities only, the average density of the electrons, and the external potential.