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A density-matrix formalism is developed based on the one-particledensity-matrix of a single-determinantal reference-state. The v-representableproblem does not appear in the proposed method, nor the need to introducefunctionals defined by a constrained search. The correlation-energy functionalsare not universal; they depend on the external potential. Nevertheless, modelsystems can still be used to derive universal energy-functionals. In addition,the correlation-energy functionals can be partitioned into individual termsthat are -- to a varying degree -- universal; yielding, for example, anelectron gas approximation. Variational and non-variational energy functionalsare introduced that yield the target-state energy when the reference state --or its corresponding one-particle density matrix -- is constructed fromBrueckner orbitals. Using many-body perturbation theory, diagrammaticexpansions are given for the non-variational energy-functionals, where theindividual diagrams explicitly depend on the one-particle density-matrix.Non-variational energy-functionals yield generalized Hartree--Fock equationsinvolving a non-local correlation-potential and the Hartree--Fock exchange;these equations are obtained by imposing the Brillouin--Brueckner condition.The same equations -- for the most part -- are obtained from variationalenergy-functionals using functional minimizations, yielding the (kernel of)correlation potential as the functional derivative of correlation-energyfunctionals. Approximations for the correlation-energy functions areintroduced, including a one-particle-density-matrix variant of thelocal-density approximation (LDA) and a variant of the Lee--Yang--Parr (LYP)functional.Comment: 68 Page, 0 Figures, RevTeX 4, Submitted to Phys.Rev.A (on April 28  2003

Reference-state one-particle density-matrix theory