Comments on Koopmans' Theorem and Electron Relaxation with Valence Ionization

The electron relaxation energy, E_R, is a well-recognized limitation of Koopmans' approximation for ionization energies. Several characteristic aspects of ER for first ionizations of atoms are discussed. It is shown that (1) Slater's screening model gives good account of the basic trends in E_R with valence ionizations of main-group atoms but fails for d electron ionizations of transition metals, (2) the relatively large E_R for ionization of 3d electrons is association with the 3d shielding of 3s and 3p electrons (these relaxation characteristics help to clarify the filling of the 4s and 3d orbitals in the periodic table), and (3) there is more than a proportional decrease in E_R when the valence density removed from an atom is less than a complete electron (this indicates that the intraatomic portion of E_R will be less for ionization from a delocalized orbital than from a localized orbital).