Exact exchange treatment for molecules in finite-basis-set Kohn-Sham theory

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