{To the Editors of the Journal of Chemical Physics}
\opening{Dear Editors,}
\justifying
Please find enclosed our manuscript entitled \textit{``Connections between many-body perturbation and coupled-cluster theories''}, which we would like you to consider as a Communication in the \textit{Journal of Chemical Physics}.
This contribution has never been submitted in total nor in parts to any other journal, and has been seen and approved by all authors.
In the present contribution, following the works of Scuseria \textit{et al.} [\href{http://dx.doi.org/10.1063/1.3043729}{J.~Chem.~Phys.~\textbf{129}, 231101 (2008)}] and Berkelbach [\href{https://doi.org/10.1063/1.5032314}{J.~Chem.~Phys.~\textbf{149}, 041103 (2018)}], we prove exact equivalences 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.
More specifically, we show how to recast $GW$ and BSE as non-linear CC-like equations that can be solved with the usual CC machinery with the same computational cost.
The present work provides a clear path for the computation of ground- and excited-state properties (such as nuclear gradients) within the BSE@$GW$ framework that has been shown to be highly successful to compute low-lying excited states in molecular systems with a very attractive accuracy/cost ratio.
It also broaden the applicability of Green's function methods in the electronic structure community and beyond.
Because of the novelty of this work and its potential impact in quantum chemistry and condensed matter physics, we expect it to be of interest to a wide audience within the chemistry and physics communities.
