  Density functional theory has been an essential analysis tool for both
theoretical and experimental chemists since accurate hybrid functionals were
developed. Here we propose a local hybrid method derived from the optimized
effective potential (OEP) method and compare its distinct features with
conventional nonlocal ones from the Hartree-Fock (HF) exchange operator. Both
are formally exact for ground states and thus show similar accuracy for
atomization energies and reaction barrier heights. For excited states, the
local version yields virtual orbitals with N-electron character, while those of
the nonlocal version have mixed characters between N- and (N+1)-electron
orbitals. As a result, the orbital energy gaps from the former well approximate
excitation energies with a small mean absolute error (MAE = 0.40 eV) for the
Caricato benchmark set. The correction from time-dependent density functional
theory with a simple local density approximation kernel further improves its
accuracy by incorporating multi-configurational effects, resulting in the total
MAE of 0.27 eV that outperforms conventional functionals except for MN15.
