Recent progress in electron-propagator, extended-Koopmans-theorem and self-consistent-field approaches to the interpretation and prediction of electron binding energies

Abstract

Advances in three methodologies for the prediction and interpretation of molecular electron binding energies are reviewed. Electron-propagator self-energies in the diagonal, or quasiparticle, approximation have been widely used to interpret photo-electron spectra. A new generation of diagonal approximations with superior accuracy and computational efficiency has been developed and tested vs a data base whose quality approaches full-configuration-interaction calculations on vertical ionization energies of representative closed-shell molecules. The extended-Koopmans-theorem (EKT) method often has been employed in the calculation of the lowest electron detachment energy where the initial state is represented by a correlated wavefunction or reduced-density matrices. The newly introduced complete-active-space EKT method produces electron detachment energies that approach exact results for a given active orbital space with the introduction basis functions that make much greater contributions to initial, uncharged states than to final, cationic states. Differences in self-consistent field total energies optimized for each state of interest define the ΔSCF method. Two recent theorems on the eigenvalue spectrum of the difference of two idempotent matrices have revealed how corresponding orbitals derived from SCF wavefunctions determine Dyson orbitals, probability factors, natural ionization orbitals with paired occupation numbers that describe relaxation effects and Fukui functions.