Going Beyond the GW Approximation Using the Time-Dependent Hartree-Fock Vertex.

Area of Science:

• Atomic physics
• Quantum chemistry
• Many-body perturbation theory

Background:

• Extending time-dependent Hartree-Fock (TDHF) theory to charged excitations is crucial for accurate atomic property predictions.
• Many-body perturbation theory (MBPT) provides a framework for these extensions.

Purpose of the Study:

• To assess the performance of the TDHF vertex within MBPT for charged excitations in spherical atoms.
• To evaluate its accuracy for predicting atomic polarizabilities, ionization energies, and photoemission satellite spectra.

Main Methods:

• Recasting the TDHF vertex as a reducible vertex for a self-energy expansion in orders of the bare Coulomb interaction.
• Numerical application to spherical atoms in their neutral electronic configuration.

Main Results:

• The TDHF vertex significantly outperforms the random phase approximation for atomic polarizabilities.
• It yields more accurate ionization energies than GW and low-order self-energies for light, few-electron atoms.
• Performance for ionization energies degrades for heavier atoms due to limitations of the Coulomb interaction expansion.
• The TDHF vertex introduces relevant features in satellite spectra, though experimental spectra are not fully reproduced due to missing nonlinear effects.

Conclusions:

• The TDHF vertex offers a valuable improvement over simpler methods for certain atomic properties, particularly in lighter elements.
• Consistent treatment of vertex corrections in both self-energy and polarizability is suggested for optimal results.
• Further development is needed to account for nonlinear effects like hole relaxation for complete spectral reproduction.