GW Vertex Corrected Calculations for Molecular Systems.

Hedin's scheme is solved with the inclusion of the vertex function (GWΓ) for a set of small molecules. The computational scheme allows for the consistent inclusion of the vertex both at the polarizability level and in the self-energy. A diagrammatic analysis shows that the self-energy formed with this four-point vertex does not lead to double counting of diagrams, that can be classified as direct "bubbles" and exchange diagrams. By removing the exchange diagrams from the self-energy, a simpler approximation is obtained, called GWtc-tc . Very good agreement with expensive wave function-based methods is obtained for both approximations.