Full configuration interaction wave function as a formal solution to the optimized effective potential and Kohn-Sham models in finite basis sets

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.