Feature of Exact Exchange Kohn–Sham Orbitals with Krieger–Li–Iafrate Approximation#

Abstract

We report feature of Kohn–Sham (KS) molecular orbitals computed with the Krieger–Li–Iafrate (KLI) approximation for exact exchange through the comparison to the results of Hartree–Fock (HF) and other KS methods such as local density approximation (LDA) and generalized gradient approximation (GGA). KLI occupied orbitals have similar energies and shapes with those of HF. KLI virtual orbitals are likely to form bound states with negative eigenvalues due to the correct −1/r asymptotic behavior of KLI potentials, whereas HF virtual orbitals are mostly unbound. As a result, HF orbitals tend to be diffuse because of their plane‐wave‐like nature, and their energies are highly sensitive to the size of basis set. The energies of LDA/GGA orbitals appear to be upshifted by a constant factor from the KLI results, but they also produce unbound virtual orbitals like HF. The energy gaps between KLI occupied and virtual orbitals are very close to the corresponding experimental excitation energies compared to the other methods. We also show that Brillouin's theorem can be applied to a Slater determinant made of KLI orbitals as a corollary of the KLI approximation.