Dyson-orbital concepts for description of electrons in molecules

Dyson orbitals, their electron-binding energies, and probability factors provide descriptions of electrons in molecules that are experimentally verifiable and that generalize qualitatively useful concepts of uncorrelated, molecular-orbital theory to the exact limit of Schrödinger's time-independent equation. Dyson orbitals are defined as overlaps between initial, N-electron states and final states with N ± 1 electrons and therefore are useful in the prediction and interpretation of many kinds of spectroscopic and scattering experiments. They also are characteristic of N-electron initial states and may be used to construct electron densities, one-electron properties, and total energies with correlated Aufbau procedures that include probability factors between zero and unity. Relationships with natural orbitals, Kohn-Sham orbitals, and Hartree-Fock orbitals facilitate insights into the descriptive capabilities of Dyson orbitals. Electron-propagator approximations that employ the Dyson quasiparticle equation or super-operator secular equations enable direct determination of Dyson orbitals and obviate the need for many-electron wavefunctions of initial or final states. Numerical comparisons of the amplitudes and probability factors of Dyson orbitals calculated with several self-energy approximations reveal the effects of electron correlation on these uniquely defined, one-electron wavefunctions.