Numerically Precise Benchmark of Many-Body Self-Energies on Spherical Atoms.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Many-Body Perturbation Theory

Background:

• Accurate prediction of electronic properties in atoms and molecules is crucial.
• Many-body perturbation theory (MBPT) methods, like the GW approximation, are essential for describing electron interactions.
• Developing computationally efficient and accurate methods beyond standard GW is an active research area.

Purpose of the Study:

• To investigate the performance of beyond-GW approaches in MBPT for atomic systems.
• To assess the accuracy of different self-energies (GW, 2B, GW+SOSEX) for calculating ionization potentials.
• To explore strategies for incorporating beyond-GW diagrams into MBPT calculations.

Main Methods:

• Numerical treatment of atoms using B-splines and spherical harmonics within the spherical approximation.
• Calculation of ionization potentials using the quasi-particle equation (QPE) with GW, second Born (2B), and GW+SOSEX self-energies.
• Solving the linearized Sham-Schlüter equation (LSSE) and comparing resulting exchange-correlation (xc) potentials.

Main Results:

• The GW+SOSEX self-energy provides a viable scheme to go beyond GW in finite systems, particularly when applied to PBE or PBE0 starting points.
• The GW approximation shows comparable performance to GW+SOSEX if a hybrid starting point (e.g., PBE0) is used.
• The second Born (2B) self-energy with a Hartree-Fock starting point also yields promising results, suggesting its potential as a beyond-GW scheme.

Conclusions:

• The GW+SOSEX approach is a practical method for improving upon GW calculations in finite atomic systems.
• The study highlights the importance of the starting point for MBPT calculations, with hybrid functionals offering advantages.
• The 2B approach with Hartree-Fock presents a promising alternative for beyond-GW calculations in finite systems.