GW Vertex Corrected Calculations for Molecular Systems.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Accurate prediction of molecular properties is crucial in chemistry and materials science.
• Existing computational methods often face challenges with accuracy or computational cost.
• Hedin's GW method is a powerful tool, but its full implementation, including the vertex function, has been computationally demanding.

Purpose of the Study:

• To implement and evaluate Hedin's GW scheme including the vertex function (GWΓ) for small molecules.
• To investigate the impact of including the vertex function at both the polarizability and self-energy levels.
• To develop and test a simplified approximation (GWtc-tc) by excluding exchange diagrams from the self-energy.

Main Methods:

• Solving Hedin's equations with the inclusion of the four-point vertex function (GWΓ).
• Performing diagrammatic analysis to ensure consistency and avoid double counting.
• Comparing results with established, computationally expensive wave function-based methods.

Main Results:

• The GWΓ scheme consistently includes the vertex function at both polarizability and self-energy levels.
• Diagrammatic analysis confirms no double counting of direct 'bubble' and exchange diagrams.
• A simplified GWtc-tc approximation was derived by removing exchange diagrams.
• Both GWΓ and GWtc-tc approximations show very good agreement with high-level wave function methods.

Conclusions:

• The GWΓ method provides a consistent and accurate approach for electronic structure calculations.
• The simplified GWtc-tc approximation offers a computationally efficient alternative with high accuracy.
• These methods advance the capability for reliable prediction of molecular properties.