▎ 摘　　要

We present a comparative van der Waals density-functional (vdW-DF) study of graphene adsorbed on (111) surfaces of Ni, Cu, Pd, Ag, Au, and Pt, using the second version of vdW-DF (vdW-DF2) of Lee et al. [Phys. Rev. B 82, 081101 (R) (2010)] and the exchange functional (C09) developed by Cooper [Phys. Rev. B 81, 161104(R) (2010)]. We show that the use of the vdW-DF2 correlation together with the C09 exchange yields the most satisfactory results: Adsorption geometries of graphene are in good agreement with available experiment data, and the electronic structure of graphene varies depending on the nature of the substrate. Band-gap opening at the K point observed on the Ni (111) surface is reproduced reasonably well.