Fourth-Order Algebraic Diagrammatic Construction for Electron Detachment and Attachment: The IP- and EA-ADC(4) Methods.

We present a non-Dyson fourth-order algebraic diagrammatic construction formulation of the electron propagator, featuring the distinct IP- and EA-ADC(4) schemes for the treatment of ionization and electron attachment processes. The algebraic expressions have been derived automatically using the intermediate state representation approach and implemented in the Q-Chem quantum-chemical program package. The performance of the novel methods is assessed with respect to high-level reference data for ionization potentials and electron affinities of closed- and open-shell systems. While only minor improvements over the corresponding third-order methods are observed for one-hole ionization and one-particle electron attachment processes from closed-shell systems (MAE = 0.27 eV and MAE = 0.05 eV), a significantly enhanced performance is found in case of open-shell reference states (MAE = 0.11 eV and MAE = 0.02 eV). A particularly appealing feature of the novel methods is their accurate treatment of satellite transitions. For closed-shell reference states, we obtain accuracies of MAE = 0.81 eV and MAE = 0.27 eV, while in case of open-shell reference states, mean absolute errors of MAE = 0.15 eV and MAE = 0.27 eV are found.