Green Functions and Self-Consistency: Insights From the Spherium Model

Area of Science:

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

Background:

• The spherium model, with two electrons on a sphere interacting via a Coulomb operator, offers a simplified yet rich system for studying electronic correlation.
• Understanding electronic correlation is crucial for accurately predicting molecular properties and electronic behavior across different regimes.
• Green function methods are powerful tools for electronic structure calculations, but their performance can vary depending on the approximation and self-consistency treatment.

Purpose of the Study:

• To comprehensively evaluate the performance of various Green function methods for the spherium model.
• To compare perturbative GW, partially self-consistent GW, and Green function second-order (GF2) methods.
• To investigate the impact of self-consistency and corrections like second-order screened exchange (SOSEX) on calculated properties.

Main Methods:

• Application of perturbative GW, partially self-consistent GW, and GF2 methods to the spherium model.
• Computation of ionization potentials, electron affinities, energy gaps, correlation energies, and neutral excitations.
• Solution of the Bethe-Salpeter equation (BSE) for excitation calculations.
• Analysis of self-screening effects and the role of SOSEX corrections.

Main Results:

• Perturbative Green function methods, particularly with a Hartree-Fock starting point, generally yield more accurate results than self-consistent GW approaches.
• Self-consistency in GW calculations can sometimes deteriorate the accuracy of computed electronic properties.
• Partial self-consistency in GW methods can lead to artificial discontinuities in the self-energy, especially in weakly correlated systems due to satellite resonances.

Conclusions:

• The spherium model serves as an excellent testbed for Green function methods, spanning weak to strong correlation regimes.
• Perturbative Green function approaches are often preferred over self-consistent ones for reliable electronic structure calculations in this model.
• Care must be taken when implementing partial self-consistency in Green function methods to avoid artifacts in the electronic self-energy.