The deposition of graphene layers on transition metals is particularly interesting for electrical, electronic and mechanical properties. We apply a first-principle approach based on Density-Functional theory to calculate the electronic structure of both chemisorbed and physisorbed graphene and analyze how the peculiarities of the electronic states of isolated graphene near the conical points are modified by the presence of the substrate. The strength of the interaction changes the density of states at the Fermi energy, the work function of the system  and consequently the electrical and transport properties. Graphene has been recently proposed as a new emerging lubricant [2, 3]. Its lubricating properties on iron have been explained as a passivating effect: the metal surfaces coated by graphene become almost inert and present very low adhesion and shear strength when mated in a sliding contact [4,5]. By comparing the electronic structures and the surface energies of graphene both on metals with partially filled d-shell, such as Fe, and metals with s-p electron states at the Fermi level, such as Cu or Au, we discuss the effects of the electronic properties on the passivating effect of graphene.
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