Relationship of Kohn–Sham eigenvalues to excitation energies

In Kohn–Sham density functional theory, only the highest occupied eigenvalue has a rigorous physical meaning, viz., it is the negative of the lowest ionization energy. Here, we demonstrate that for finite systems, the unoccupied true Kohn–Sham eigenvalues (as opposed to the those obtained from the commonly used approximate density functionals) are also meaningful in that good approximations to excitation energies can be obtained from them. We argue that the explanation for this observed behavior is that, at large distances, the Kohn–Sham orbitals and the quasiparticle amplitudes satisfy the same equation to order 1/r4.