Combining the Δ-Self-Consistent-Field and GW Methods for Predicting Core Electron Binding Energies in Periodic Solids

Area of Science:

• Solid-state physics
• Computational materials science
• Quantum chemistry

Background:

• Core electron binding energies are crucial for understanding material properties.
• Two main computational approaches exist: Δ-Self-Consistent-Field (Δ-SCF) using density functional theory (DFT) and the GW method.
• A formal link between these methods has been lacking.

Purpose of the Study:

• To establish a formal relationship between DFT-based Δ-SCF and GW methods for core electron binding energy calculations.
• To introduce a new formalism that clarifies the implicit dependence on electronic structure in DFT calculations.
• To investigate the impact of quasiparticle corrections from GW theory on DFT core electron binding energy predictions.

Main Methods:

• Analysis of the formal relationship between DFT total energy differences and highest occupied state eigenvalues.
• Development of a new theoretical formalism connecting Δ-SCF and GW methods.
• Application of GW quasiparticle corrections, including vertex corrections, to DFT core electron binding energy calculations.

Main Results:

• A formal equivalence is established between DFT's total energy difference and highest occupied state eigenvalue in the infinite supercell limit.
• DFT core electron binding energy accuracy is shown to implicitly depend on the valence band maximum or Fermi level eigenvalue accuracy.
• Incorporating GW quasiparticle corrections, particularly with vertex corrections, significantly improves agreement with experimental core electron binding energies.

Conclusions:

• The accuracy of DFT core electron binding energies is intrinsically linked to the accuracy of the highest occupied electronic state eigenvalue.
• GW quasiparticle corrections offer a pathway to enhance the predictive power of DFT for core electron binding energies.
• Vertex corrections in the GW framework are essential for achieving quantitative accuracy in computational predictions of core electron binding energies.