A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory

We revisit the connection between equation-of-motion coupled cluster (EOM-CC) and random phase approximation (RPA) explored recently by Berkelbach [J. Chem. Phys. 149, 041103 (2018)] and unify various methodological aspects of these diverse treatments of ground and excited states. The identity of RPA and EOM-CC based on the ring coupled cluster doubles is established with numerical results, which was proved previously on theoretical grounds. We then introduce new approximations in EOM-CC and RPA family of methods, assess their numerical performance, and explore a way to reap the benefits of such a connection to improve on excitation energies. Our results suggest that addition of perturbative corrections to account for double excitations and missing exchange effects could result in significantly improved estimates.