In this paper, the authors investigate the performance of beyond-GW approaches in many-body perturbation theory by addressing atoms described within the spherical approximation via a dedicated numerical treatment based on B-splines and spherical harmonics. The authors consider the GW, second Born (2B), and GW + second order screened exchange (GW+SOSEX) self-energies and use them to obtain ionization potentials from the quasi-particle equation (QPE) solved perturbatively on top of independent-particle calculations. They also solve the linearized Sham-Schlüter equation (LSSE) and compare the resulting xc potentials against exact data. The authors find that the LSSE provides consistent starting points for the QPE but does not present any practical advantage in the present context. Still, the features of the xc potentials obtained with it shed light on possible strategies for the inclusion of beyond-GW diagrams in the many-body self-energy. Their findings show that solving the QPE with the GW+SOSEX self-energy on top of a PBE or PBE0 solution is a viable scheme to go beyond GW in finite systems, even in the atomic limit. However, GW shows a comparable performance if one agrees to use a hybrid starting point. They also obtain promising results with the 2B self-energy on top of Hartree-Fock, suggesting that the full time-dependent Hartree-Fock vertex may be another viable beyond-GW scheme for finite systems.
Vacondio, S.; Varsano, D.; Ruini, A.; Ferretti, A.. in: Journal of Chemical Theory and Computation - 18:6(2022)
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