Correlation Energy Functionals of One-Matrices and Hartree-Fock Densities

Abstract

It is shown that only a small piece of the exact universal variational functional of the one matrix is actually unknown. The unknown piece, EC[γ], is identified and several rigorous properties of EC[γ] are derived. Based upon the derived properties, approximate forms of EC[γ] are displayed for the purpose of actual calculations, Existence theorems are then proved which allow the “single-shot” determination of exact correlation energies directly from Hartree-Fock and exchange-only densities. In fact, all ground-state and excited-state properties of the system are determined by these densities. The existence theorems do not generally apply, however, a, to finite basis sets. EC [γ] is then compared with \({\tilde E_c}\left[ \rho \right]\) which is the “single-shot” universal correlation energy functional of the Hartree- Fock density which is put forth as the correction to the Hartree-Fock energy.