  Using finite basis sets, it is shown how to construct a local Hamiltonian,
such that one of its infinitely many degenerate eigenfunctions is the ground
state full configuration interaction (FCI) wave function in that basis set.
Formally, the local potential of this Hamiltonian is the optimized effective
potential and the exact Kohn-Sham potential at the same time, because the FCI
wave function yields the exact ground-state density and energy. It is not the
aim of this paper to provide a new algorithm for obtaining FCI wave functions.
A new potential is the goal.
