  Range-separated methods combining a short-range density functional with
long-range random phase approximations RPAs with or without exchange response
kernel are tested on rare-gas dimers and the S22 benchmark set of weakly
interacting complexes of Jurecka et al. [Phys. Chem. Chem. Phys. 8, 1985 (2006
)] . The methods are also compared to full-range RPA approaches. Both range
separation and inclusion of the Hartree-Fock exchange kernel largely improve
the accuracy of intermolecular interaction energies. The best results are
obtained with the method called RSH+RPAx, which yields interaction energies for
the S22 set with an estimated mean absolute error of about 0.5-0.6 kcal/mol,
corresponding to a mean absolute percentage error of about 7%-9% depending on
the reference interaction energies used. In particular, the RSH+RPAx method is
found to be overall more accurate than the range-separated method based on
long-range second-order M{\o}ller-Plesset MP2 perturbation theory RSH+MP2 .
