Elementary finite order perturbation theory for vertical ionization energies

Abstract

The analysis of ionization energies in Rayleigh–Schrödinger perturbation theory and in propagator theory, previously known separately through third order in electron interaction, are compared in detail using elementary algebraic methods and their equivalence is explicitly shown. Relaxation terms are identified as the ΔESCF contributions and appropriate rules are described for their construction from the electron propagator diagrams of arbitrary order. Correlation terms are obtained separately. The transition operator method is analyzed and found to differ from ΔESCF in third order, contrary to earlier claims.