Understanding surface energies of transition metals with density-functional theory

Determining index-specific surface energies of metals is, to date, still a non-trivial task, both experimentally and theoretically. Density-functional theory (DFT) calculations within the local-density approximation (LDA) for exchange-correlation (XC) have provided understanding of qualitative trends. Yet, absolute surface energies, in particular of $d$-metals still exhibit significant uncertainties related to the description of XC: gradient-corrected functionals (GGA) which improve over the LDA for other properties often predict less accurate surface energies. This calls for a careful analysis of XC effects on surface energies, including non-local exchange and/or correlation. Here we analyze the surface energies of $4d$-metals with modern GGA functionals (PBEsol, AM05, developed to better describe bulk solids and (jellium) surfaces than the LDA and previous GGAs), using the all-electron FHI-aims code [1]. Relating the bulk cohesive energy and surface energy via a bond-cutting model we find modern GGAs can indeed correct the poorer results of the usual PBE-GGA but worsen the bulk cohesive energies of $4d$-metals. In addition, we consider hybrid XC functionals, using a cluster correction scheme [2], and discuss the effects of including exact exchange on the calculated surface energies.\\[0pt] [1] \textit{http://www.fhi-berlin.mpg.de/aims/};\\[0pt] [2] Q.-M. Hu \textit{et al.}, Phys. Rev. Lett. \textbf{98}, 176103 (2007); \textbf{99}, 169903(E).