Accuracy of exchange-correlation functionals and effect of solvation on the surface energy of copper

Surface energies are important for predicting the shapes of nanocrystals and describing the faceting and roughening of surfaces. Copper surfaces are of particular interest in recent years since they are the preferred surfaces for growing graphene using chemical vapor deposition. In this study we calculate the surface energies of copper for the three low-index facets (111), (100), and (110) and one high-index facet, (210), using density-functional theory with both the local-density approximation and various parametrizations of the generalized-gradient approximation to the exchange-correlation functional. To assess the accuracy of the different functionals, we obtain the average surface energies of an isotropic crystal using a broken-bond model. We use this method, which can be generalized to other crystal structures, to compare calculated surface energies to experimental surface energies for fcc crystals. We find that the recent exchange-correlation functionals AM05 and PBEsol are the most accurate functionals for calculating the surface energies of copper. To determine how solvents affect the surface energies of copper, we perform calculations using a continuum solvation model. We find that aqueous solvation changes the overall magnitude of the surface energies only slightly but leads to more isotropic surface energies.