Comparison of optimized effective potential with inverse Kohn-Sham method for Hartree-Fock exchange energy

The inverse Kohn-Sham (inv-KS) density-functional theory for the electron density of the Hartree-Fock (HF) wave function was revisited within the context of the optimized effective potential (HF-OEP). First, we clarify the relationship between the inv-KS and the HF-OEP within the framework of the potential-functional theory. The similarities and the differences of the approaches are then discussed on the basis of their methodological details, which motivates comparisons of the wave function provided by each method. Next, the real-space grid implementations of the inv-KS and the HF-OEP are addressed for the comparisons. The total HF energies EHF[{φiinv-KS}] for the wave functions φiinv-KS 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[{φiinv-KS}] from the HF energy is clearly smaller than the MAD of EHF[{φiOEP}], demonstrating that the inv-KS is advantageous in constructing the detailed structure of the exchange potential υx 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.