The random phase approximation (RPA) is attracting renewed interest as auniversal and accurate method for first-principles total energy calculations.The RPA naturally accounts for long-range dispersive forces withoutcompromising accuracy for short range interactions making the RPA superior tosemi-local and hybrid functionals in systems dominated by weak van der Waals ormixed covalent-dispersive interactions. In this work we present planewave-based RPA calculations for a broad collection of systems with bond typesranging from strong covalent to van der Waals. Our main result is the RPApotential 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 representarchetypical examples of metal-organic interfaces. Comparison with semi-localdensity approximations and a non-local van der Waals functional show that onlythe RPA captures both the weak covalent and dispersive forces which are equallyimportant for these systems. We benchmark our implementation in the GPAWelectronic structure code by calculating cohesive energies of graphite and arange of covalently bonded solids and molecules as well as the dissociationcurves of H2 and H2+. These results show that RPA with orbitals from the localdensity approximation suffers from delocalization errors and systematicallyunderestimates covalent bond energies yielding similar or lower accuracy thanthe Perdew-Burke-Ernzerhof (PBE) functional for molecules and solids,respectively.
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