▎ 摘　　要

The interaction of graphene with various metal surfaces is investigated using density functional theory and the meta-generalized gradient approximation (MGGA) M06-L functional. We demonstrate that this method is of comparable accuracy to the random-phase approximation (RPA). With M06-L we study large systems inaccessible to RPA with H adsorbed on graphene on a selected strongly (Ni) and a selected weakly (Pt) interacting substrate. Very stable graphane-like clusters, where every other C atom binds to a H atom above and every other to a metal atom below, are found on both substrates. Such graphane-like clusters have been proposed to be responsible for opening a band gap in graphene. On Ni we find that the binding energies of the H clusters are almost constant with the cluster size, whereas on Pt the binding energies increase with the cluster size. Comparing the Perdew-Burke-Ernzerhof and M06-L functionals we demonstrate the importance of accounting for dispersive interactions.