Electron-propagator methods versus experimental ionization energies

Select electron-propagator (EP) methods agree as closely with experimental standards for molecular vertical ionization energies as they do with computational data of nearly full-configuration-interaction quality. Several EP methods consistently attain higher accuracy than alternatives with equal arithmetic bottlenecks expressed in terms of occupied (O) and virtual (V) orbital dimensions. The cubically scaling methods realize a mean absolute error (MAE) below 0.2 eV and are feasible whenever conventional self-consistent-field calculations are performed. O2V3-scaling EP self-energies achieve an MAE slightly above 0.1 eV and are as feasible as conventional second-order perturbative calculations of total energies. OV4 methods are more accurate (MAEs ∼0.075 eV) than ΔCCSD(T) and are more efficient than third-order total-energy calculations. An equally accurate generalization with full self-energy matrices and non-iterative O2V4 contractions produces Dyson orbitals in their most general form. Composite EP models that accurately estimate the effects of basis-set saturation drastically improve efficiency without sacrificing accuracy. No adjustable parameters are employed in the self-energy formulas or in the generation of reference-state orbitals. When Dyson-orbital probability factors indicate that Koopmans's theorem is qualitatively valid, simple perturbative corrections suffice to approach chemical accuracy.