  The inverse Kohn-Sham density-functional theory (inv-KS) for the electron
density of the Hartree-Fock (HF) wave function was revisited within the context
of the optimized effective potential (HF- OEP). First, it is proved that the
exchange potential created by the inv-KS is equivalent to the potential
obtained by the HF-OEP when the HF-OEP realizes the HF energy of the system
under consideration. Next the real-space grid (RSG) implementations of the
inv-KS and the HF-OEP are addressed. The total HF energies EHF for the wave
functions on the effective potentials optimized by the inv-KS are computed for
a set of small molecules. It is found that the mean absolute deviation (MAD) of
EHF from the HF energy is clearly smaller than the MAD of EHF, demonstrating
that the inv-KS is advantageous in constructing the detailed structure of the
exchange potential vx as compared with the HF-OEP. The inv-KS method is also
applied to an ortho-benzyne radical known as a strongly correlated polyatomic
molecule. It is revealed that the spin populations on the atomic sites computed
by the UHF calculation can be faithfully reproduced by the wave functions on
the inv-KS potential.
