Connections between many-body perturbation and coupled-cluster theories

6 pagesHere, we build on the works of Scuseria (et al.) this http URL and Berkelbach this https URL to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method introduced by Nooijen are also put forward. The present work allows to easily transfer key developments and general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks