  Aiming to combine density functional theory (DFT) and wavefunction theory, we
study a mapping from the many-body interacting system to an
effectively-interacting Kohn-Sham system instead of a non-interacting Kohn-Sham
system. Because a ground state of effectively-interacting systems requires
having a solution for the correlated many-body wavefunctions, this provides a
natural framework to many-body wavefunction 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, hydrogen molecule and heteronuclear diatomic
molecule -- we investigate properties of many-body wavefunctions 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
non-interacting 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.
