Many-Body Theory of Effective Local Potentials for Electronic Excitations. I

We compare the Hartee-Fock (HF), Talman-Shadwick (TS), exact Slater (S), Slater Xα, and local-density (LD) schemes, and investigate how well the associated one-electron potentials describe electronic excitations. We discuss in some detail the role of self-interaction in the different schemes, and demonstrate that the Xα and LD schemes effectively represent ionic ( V N-1 ) potentials in the core region. In fact, for excited f electrons, the LDA is very similar to a relaxed HF average V N-1 potential with a 4 d core hole. Furthermore, we demonstrate how the self-interaction shifts of core levels arise because of incomplete local cancellation between the orbital-specific Hartree self-interaction and the average, orbital-independent exchange hole. The atomic dipole polarizability is introduced via the LS -dependent HF scheme and, in numerical applications to 4 d ionization of atomic Ba, we compare the effective HF 1 P V N-1 one-electron potential with the ionic HF av V N-1 and the neutral-atom HF V N potentials. We also compare it with the RPAE, with and without inclusion of relaxation, and demonstrate the effects of external screening by adding and removing electrons (Ba 1- - Ba 2+ ). Finally we motivate in some detail our opinion that the self-interaction in the LDA may be considered as simulating relaxation owing to a systematic partial cancellation between self-interaction and relaxation effects for outer and intermediate shells.