van der Waals exchange-correlation functionals over bulk and surface properties of transition metals

The correct description of van der Waals (vdW) interaction forces is required for accurately describing dispersion bonded systems. Several approaches have been proposed to include London dispersion in density functional theory exchange-correlation functionals, where the family of so-called van der Waals (vdW-DF) exchange-correlation functionals have shown a better performance than local or semi local exchange-correlation functionals for describing molecular adsorption on metals. Despite the numerous benchmarks performed with these functionals, their performance in predicting bulk properties of transition metals has hitherto not been investigated in detail. We have therefore tested five vdW-DF exchange-correlation functionals, vdW-DF2, optPBE-vdW, BEEF-vdW, optB88-vdW and C09(x)-vdW to assess their performance in the prediction of lattice constants, bulk moduli, cohesive energies and surface energies of bulk Ni, Cu, Rh, Pd, Ag, Ir, Pt and Au (in fcc crystal structure). These transition metals are commonly used for benchmarking density functionals because they are important for applications in catalysis. The results are compared with experimental data and the PBE exchange-correlation functional. We found that both the optB88-vdW and the C09(x)-vdW exchange-correlation functionals estimate all properties with high accuracy, in better agreement with experimental data than PBE and other considered vdW functionals. The C09(x)-vdW functional clearly outperforms all other exchange-correlation functionals for surface energies for the (1 1 1) termination of different metals. We have also evaluated the interatomic electron density emerging from different functionals, and concluded that the observed differences are a result of the predicted lattice parameter, rather than a direct consequence of the functional form. Plane-wave and real-space grid-based expansions of the electron density are also compared, revealing good agreement between the two approaches for lattice parameters, cohesive energies, and surface energies, but more severe differences in bulk moduli. On the basis of our results, we recommend using the CO9(x)-vdW for studying bulk properties and surface energies of transition metals.