Electron-propagator methods versus experimental ionization energies.

This article focuses on the evaluation and comparison of electron-propagator (EP) methods for calculating molecular vertical ionization energies (VIEs) against both high-level computational benchmarks and experimental standards. EP methods are categorized by their treatment of self-energy operators, with computational scaling ranging from cubic (O³) to quintic (O⁵) in terms of occupied (O) and virtual (V) orbitals, and include diagonal and non-diagonal approximations. Among these, opposite-spin diagonal second-order methods (os-D2 and os-nD-D2) offer efficient calculations with mean absolute errors (MAEs) below 0.2 eV, while higher-order methods such as Q3+, L3+B, RL3, and their non-Dyson variants achieve improved accuracy with MAEs near or below 0.1 eV. Composite EP models combining basis-set extrapolations and post-second-order corrections further enhance accuracy and efficiency, reaching MAEs as low as 0.08 eV compared to experimental VIEs from a comprehensive Cambridge University dataset. The study concludes that these parameter-free EP methods provide reliable, computationally feasible alternatives to more demanding coupled-cluster approaches for predicting VIEs of closed-shell molecules, with recommendations tailored to balance accuracy, computational cost, and the need for Dyson orbitals in their general form.