Performance on molecules, surfaces, and solids of the Wu-Cohen GGA exchange-correlation energy functional

We present the results of Kohn-Sham calculations on molecules, surfaces, and solids which were obtained using a recently proposed exchange-correlation energy functional [Z. Wu and R. E. Cohen, Phys. Rev. B 73, 235116 (2006)]. The Wu-Cohen (WC) functional, like the well-known PBE functional [J. P. Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)], is of the generalized gradient approximation form and was derived from the homogeneous electron gas and mathematical relations obeyed by the exact functional. The results on molecular systems show that among the functionals we tested, PBE remains superior for the energetics of covalent and noncovalent bonds. While this is not too surprising for noncovalent bonds due to the very good performance of PBE, unfortunately this holds also for covalent bonds, where PBE is a functional of rather poor quality. Calculations on transition-metal surfaces show that WC improves over local-density approximation (LDA) and PBE for the surface formation energy of $3d$ elements, while LDA is the best for heavier elements. In most cases, the lattice constant of solids as determined by the WC functional is in between the LDA and PBE results and on average closer to experiment. We show for each group of compounds which functional performs best and provide trends. In the particular case of lattice constants whose values are determined by weak interactions (e.g., the interlayer distance in graphite), the LDA functional is more accurate than the generalized gradient approximation functionals.