The exact orbital-dependent exchange (EXX) energy formalism within the line
ar-combination-of-atomic-orbital Kohn-Sham density functional theory for po
lyatomic molecules is presented and implemented. The exchange energies and
occupied orbital; energies obtained from EXX are very close to the correspo
nding Hartree-Fock (HF) values, whereas the EXX unoccupied orbital energies
are significantly lower than the HF values. We demonstrate that the curren
t approximate correlation functionals deteriorate the orbital energies when
combined with EXX.