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In both molecular physics and condensed matter theory, deeper understandingof the correlation energy density epsilon_c (r) remains a high priority. Byadopting Loewdin's definition of correlation energy as the difference betweenthe exact and the Hartree-Fock values, here we propose two alternative routesto define this. One of these involves both exact and Hartree-Fock (HF)wavefunctions, while the second requires a coupling constant integration. As anexact analytical example of the first route, we treat the two-electron modelatom of Moshinsky, for which both confinement potential and interactions areharmonic. Though the correlation energy density epsilon_c (r) is knownanalytically, we also investigate numerically its relation to the exactground-state density in this example.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Proposed definitions of the correlation energy density from a  Hartree-Fock starting point: The two-electron Moshinsky model atom as an  exactly solvable model