The coupled-cluster self-energy

An improved description of electronic correlation in molecules and materials can only be achieved by uncovering connections between different areas of electronic structure theory. A general unifying relationship between the many-body self-energy and coupled-cluster theory has remained hitherto unknown. Here, we present a formalism for constructing the coupled-cluster self-energy from the coupled-cluster ground state energy. Our approach illuminates the fundamental connections between the many-body self-energy and the coupled-cluster equations. As a consequence, we naturally arrive at the coupled-cluster quasiparticle and Bethe-Salpeter equations describing correlated electrons and excitons. This deep underlying structure explains the origin of the connections between RPA, $GW$-BSE and coupled-cluster theory, whilst also elucidating the relationship between vertex corrections and the amplitude equations.