  The ground-state correlation energy calculated in the random-phase
approximation (RPA) is known to be identical to that calculated using a subset
of terms appearing in coupled-cluster theory with double excitations. In
particular, this equivalence requires keeping only those terms that generate
time-independent ring diagrams, in the Goldstone sense. Here I show that this
equivalence extends to neutral excitation energies, for which those calculated
in the RPA are identical to those calculated using an approximation to
equation-of-motion coupled-cluster theory with double excitations (EOM-CCD).
The equivalence requires three approximations to EOM-CCD: first, the
ground-state double-excitation amplitudes are obtained from the ring-CCD
equations (the same as for the correlation energy); second, the EOM eigenvalue
problem is truncated to the single-excitation (one particle + one hole)
subspace; third, the similarity transformation of the Fock operator must be
neglected, as it corresponds to a dressing of the single-particle propagator,
which is not present in the conventional RPA.
