  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 treatment 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.
