Many-Body Perturbation Theory for molecules: Physicists' approach versus Chemists' approach

First devised in the 50's, Many-Body Perturbation Theory proposes to capture the electronic correlation by performing expansions. Along with the years, physicists, mostly focused on infinite solids, and chemists, mostly interested in molecules, have developed different approximations or, in other words, have selected different Feynman diagrams. Some consider all the diagrams up to a given order [1], others select a family of diagrams and perform infinite summation on this class [2].

Today with the computer code MOLGW [3], both approaches have been implemented and can be compared directly using the same basis sets for molecules. Here we benchmark the importance of different diagrams for the ionization potential of 34 small molecules.
We study the mean-field starting point dependence and the effect of self-consistency schemes. We conclude on the remarkable robustness of the GW approximation.

[1] L.S. Cederbaum and W. Domcke, Adv. Chem. Phys. 36, 205 (1977).
[2] L. Hedin, Phys. Rev 139, A796 (1965).
[3] F. Bruneval et al., Comput. Phys. Commun. 208, 149 (2016).