Uncovering relationships between the electronic self-energy and coupled-cluster doubles theory

We derive the coupled-cluster doubles (CCD) amplitude equations by introduction of the particle-hole-time decoupled electronic self-energy. The resulting analysis leads to an expression for the ground state correlation energy that is exactly of the form obtained in coupled-cluster doubles theory. We demonstrate the relationship to the ionization potential/electron affinity equation-of-motion coupled-cluster doubles (IP/EA-EOM-CCD) eigenvalue problem by coupling the reverse-time self-energy contributions while maintaining particle-hole separability. The formal relationships established are demonstrated by exact solution of the Hubbard dimer.