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

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

2008-03-18

arxiv.org/abs/0803.2594v1

Phys. Rev. A 77 (2008) 042504

Physics

Condensed Matter

Other Condensed Matter

To appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.77.042504

In both molecular physics and condensed matter theory, deeper understanding of the correlation energy density epsilon_c (r) remains a high priority. By adopting Loewdin's definition of correlation energy as the difference between the exact and the Hartree-Fock values, here we propose two alternative routes to define this. One of these involves both exact and Hartree-Fock (HF) wavefunctions, while the second requires a coupling constant integration. As an exact analytical example of the first route, we treat the two-electron model atom of Moshinsky, for which both confinement potential and interactions are harmonic. Though the correlation energy density epsilon_c (r) is known analytically, we also investigate numerically its relation to the exact ground-state density in this example.

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