  Using Green-function many-body theory, we present the details of a formally
exact adiabatic-connection fluctuation-dissipation density-functional theory
based on range separation, which was sketched in Toulouse, Gerber, Jansen,
Savin and Angyan, Phys. Rev. Lett. 102, 096404 (2009). Range-separated
density-functional theory approaches combining short-range density functional
approximations with long-range random phase approximations (RPA) are then
obtained as well-identified approximations on the long-range Green-function
self-energy. Range-separated RPA-type schemes with or without long-range
Hartree-Fock exchange response kernel are assessed on rare-gas and
alkaline-earth dimers, and compared to range-separated second-order
perturbation theory and range-separated coupled-cluster theory.
