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This study benchmarks the Dyson-algebraic diagrammatic construction (ADC) and multi-channel Dyson equation (MCDE) methods for calculating ionization potentials of small molecules, revealing significant deviations between Dyson and non-Dyson ADC approaches. The findings indicate that the non-Dyson framework may compromise accuracy, with discrepancies around 0.1 eV, thus questioning its reliability for correlated theories of the single-particle Green's function. Additionally, the screened (3,1)-MCDE method demonstrates improved performance over its unscreened version, enhancing the precision of spectral function calculations.
Non-Dyson ADC methods may introduce up to 0.1 eV errors in ionization potential calculations, challenging their reliability in correlated electron systems.
The Dyson-algebraic diagrammatic construction (ADC) and the multi-channel Dyson equation (MCDE) formalisms explicitly leverage multi-particle channels to formulate correlated theories of the single-particle Green's function that produce positive semi-definite spectral functions by construction. While the MCDE is strictly rooted in the Dyson formalism, most ADC calculations are performed in the non-Dyson (nD) framework that decouples electron attachment and detachment sectors. We benchmark the Dyson-ADC(2)-X [that is equivalent to the (3,1)-MCDE] and ADC(3) approximations on a set of 58 ionization potentials of 23 small molecules for which near-full configuration interaction reference data exist. Comparison of Dyson- to nD-ADC(3) reveals deviations of the order of 0.1 eV between both methods, calling into question the reliability of the nD approximation. We show that Dyson-ADC gives similar accuracy for first IPs as for semi-valence and semi-core transitions. Finally, we also benchmark the screened (3,1)-MCDE that screens all ladder interactions, and show that it improves over its unscreened counterpart.