Aiming to combine density functional theory (DFT) and wave-function theory, we study a mapping from the many-body interacting system to an effectively interacting Kohn-Sham system instead of a noninteracting Kohn-Sham system. Because a ground state of effectively interacting systems requires having a solution for the correlated many-body wave functions, this provides a natural framework to many-body wave-function theories such as the configuration interaction and the coupled-cluster method in the formal theoretical framework of DFT. Employing simple one-dimensional two-electron systems—namely, the one-dimensional helium atom, the hydrogen molecule, and the heteronuclear diatomic molecule—we investigate properties of many-body wave functions and exact exchange-correlation potentials of effectively interacting Kohn-Sham systems. As a result, we find that the asymptotic behavior of the exact exchange-correlation potential can be controlled by optimizing that of the effective interaction. Furthermore, the typical features of the exact noninteracting Kohn-Sham system, namely, a spiky feature and a step feature in the exchange-correlation potential for the molecular dissociation limit, can be suppressed by a proper choice of the effective interaction. These findings open a possibility to construct numerically robust and efficient exchange-correlation potentials and functionals based on the effectively interacting Kohn-Sham scheme.

• Received 29 June 2019

DOI:https://doi.org/10.1103/PhysRevA.101.012510