Vacondio S, Varsano D, Ruini A, Ferretti A. Numerically Precise Benchmark of Many-Body Self-Energies on Spherical Atoms.
J Chem Theory Comput 2022;
18:3703-3717. [PMID:
35561415 PMCID:
PMC9202310 DOI:
10.1021/acs.jctc.2c00048]
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Abstract
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We 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. We 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.
We also solve the linearized Sham–Schlüter equation
(LSSE) and compare the resulting xc potentials against exact data.
We 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. Our 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. We 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.
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