  The random phase approximation (RPA) for the electron correlation energy,
combined with the exact-exchange energy, represents the state-of-the-art
exchange-correlation functional within density-functional theory (DFT).
However, the standard RPA practice -- evaluating both the exact-exchange and
the RPA correlation energy using local or semilocal Kohn-Sham (KS) orbitals --
leads to a systematic underbinding of molecules and solids. Here we demonstrate
that this behavior is largely corrected by adding a "single excitation" (SE)
contribution, so far not included in the standard RPA scheme. A similar
improvement can also be achieved by replacing the non-self-consistent
exact-exchange total energy by the corresponding self-consistent Hartree-Fock
total energy, while retaining the RPA correlation energy evaluated using
Kohn-Sham orbitals. Both schemes achieve chemical accuracy for a standard
benchmark set of non-covalent intermolecular interactions.
