VARIATIONAL PRINCIPLE FOR THE GROUND-STATE ENERGY AS A FUNCTIONAL OF THE ONE-PARTICLE DENSITY-MATRIX - BEYOND HARTREE-FOCK THEORY

In parallel with standard density-functional theory, we study the ener gy of the ground state. of a finite many-body system as a functional o f the one-particle density matrix. We show that the formulation of a v ariational principle that is valid beyond the Hartree-Fock limit requi res that two-body correlations be included not only in the ground-stat e energy but also in the constraints. As an illustration, we apply a l inear-response argument to derive formulas for first-order corrections to the Hartree-Fock density matrix. Further analysis suggests an appr oach in terms of the density matrix of an independent-particle system, which Fan be introduced by the application of an alternative variatio nal principle. This approach is reminiscent of Kohn-Sham theory, but t he effective external potential is not required to be local. This vari ational method can be implemented in a systematic fashion by means of the linked-cluster expansion. In an appendix we study a variant of the Hohenberg-Kohn theorem for nonlocal potentials.