Quantifying the Accuracy of Density Functionals on Transition Metal Bulk and Surface Properties.

Density functional theory would be exact when the exact exchange-correlation () functional would be known, but since it is regretfully not known, dozens of functionals have been developed in the past decades, with some of them better suited for describing certain systems and/or properties. For transition metals (TMs), recent systematic studies assessing bulk properties─shortest interatomic bond distance, δ, cohesive energy, , and bulk modulus, ─and surface features─surface energy, γ, work function, ϕ, and interlayer distances, δ─of 27 TM bulks and 81 TM surfaces, highlighted that generalized gradient approximation (GGA) based functionals are, overall, better suited than other types of functionals for the TMs bulk and surfaces description, such as Perdew-Burke-Ernzerhof (PBE) or Vega-Viñes (VV). Still, some basic local density approximation functionals were not assessed, such as the Hedin-Lundqvist (HL) and Perdew-Zunger (PZ), or GGAs such as the revised Perdew-Burke-Ernzerhof (revPBE) or the Armiento-Mattsson (AM05). Here, we expand the analysis by not only including them but also the recent meta-GGA strongly constrained appropriately normed (SCAN) functional, characterized by fulfilling all 17 mathematical conditions an must comply, plus the Bayesian error estimation functional (BEEF) , a functional parametrized over a large and diverse set of experimental results using machine learning. The present results reveal that none of the studied excel neither PBE nor VV, yet AM05 and SCAN performance is quite acceptable, while BEEF probably needs more shells of parametrization to reach competitive accuracy levels.