  We explore different variants of the random phase approximation (RPA) to the
correlation energy derived from closed-shell ring-diagram approximations to
coupled cluster doubles theory. We implement these variants in range-separated
density-functional theory, i.e. by combining the long-range random phase
approximations with short-range density-functional approximations. We perform
tests on the rare-gas dimers He_2, Ne_2, and Ar_2, and on the weakly
interacting molecular complexes of the S22 set of Jurecka et al. [Phys. Chem.
Chem. Phys. 8, 1985 (2006)]. The two best variants correspond to the ones
originally proposed by Szabo and Ostlund [J. Chem. Phys. 67, 4351 (1977)]. With
range separation, they reach mean absolute errors on the equilibrium
interaction energies of the S22 set of about 0.4 kcal/mol, corresponding to
mean absolute percentage errors of about 4 %, with the aug-cc-pVDZ basis set.
