  The random phase approximation (RPA) is attracting renewed interest as a
universal and accurate method for first-principles total energy calculations.
The RPA naturally accounts for long-range dispersive forces without
compromising accuracy for short range interactions making the RPA superior to
semi-local and hybrid functionals in systems dominated by weak van der Waals or
mixed covalent-dispersive interactions. In this work we present plane
wave-based RPA calculations for a broad collection of systems with bond types
ranging from strong covalent to van der Waals. Our main result is the RPA
potential energy surfaces of graphene on the Cu(111), Ni(111), Co(0001),
Pd(111), Pt(111), Ag(111), Au(111), and Al(111) metal surfaces, which represent
archetypical examples of metal-organic interfaces. Comparison with semi-local
density approximations and a non-local van der Waals functional show that only
the RPA captures both the weak covalent and dispersive forces which are equally
important for these systems. We benchmark our implementation in the GPAW
electronic structure code by calculating cohesive energies of graphite and a
range of covalently bonded solids and molecules as well as the dissociation
curves of H2 and H2+. These results show that RPA with orbitals from the local
density approximation suffers from delocalization errors and systematically
underestimates covalent bond energies yielding similar or lower accuracy than
the Perdew-Burke-Ernzerhof (PBE) functional for molecules and solids,
respectively.
