Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (110), and (100) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. Many of these metallic surfaces have technological or catalytic applications. We compare experimental reference values to those of the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), the PBEsol (PBE for solids) GGA, the SCAN meta-GGA, and SCAN+rVV10 (SCAN with a long-range van der Waals or vdW correction). The closest agreement with uncertain experimental values is achieved by the simplest density functional (LDA) and by the most sophisticated general-purpose one (SCAN+rVV10). The long-range vdW interaction increases the surface energies by about 10%, and the work functions by about 1%. LDA works for metal surfaces through a stronger-than-usual error cancellation. PBE yields the most-underestimated and presumably least accurate surface energies and work functions. Surface energies within the random phase approximation (RPA) are also reported. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment.