Can we do any better than GW with diagram expansions?

F. Bruneval [1], M. Rodriguez-Mayorga [1,2], H. Denawi [1], M. Torrent [3], N. Dattani [4], M. van Setten [5], M. Dvorak [6], P. Rinke [6]

[1] Université Paris-Saclay, CEA, SRMP, 91191 Gif-sur-Yvette, France
[2] Department of Theoretical Chemistry, VU University Amsterdam, The Netherlands
[3] Université Paris-Saclay, CEA, DAM, DIF, 91297 Arpajon, France
[4] High Performance Computing, HPQC Labs, Waterloo, Ontario, Canada
[5] IMEC, Leuven, Belgium
[6] Aalto University, Finland


The GW approximation is mostly famous for predicting the accurate band gaps of solids.
But recently the GW approximation has also become a useful tools for obtaining reliable ionization potentials in molecules.
The molecules offer us a new playground in which the implementation of new approximations are faster and in which reference values are available.

Using the GW100 benchmark set, consisting of 100 molecules selected for their diversity, we explore the possibilities to improve over the vanilla GW approximation
by incorporating additional Feynman diagrams.
Focusing on the ionization potential, we show that most corrections beyond GW are detrimental to the accuracy (and to the computational time).

Among the list of tested diagrams, only the GW reduced-density-matrix diagrams that arise from looping once the self-consistent Green's function are interesting:
they attenuate the starting point dependence and they provide a new expression for the GW total energy.

In the rest of the talk, we will explore the performance of the GW reduced-density-matrix total energies for molecules and for crystalline systems.