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.