a b s t r a c tGraphene, a single atomic layer of graphite, has been the focus of recent intensive studies due to its novel electronic and structural properties. Metals grown on graphene also have been of interest because of their potential use as metal contacts in graphene devices, for spintronics applications, and for catalysis. All of these applications require good understanding and control of the metal growth morphology, which in part reflects the strength of the metal-graphene bond. Also of importance is whether the interaction between graphene and metal is sufficiently strong to modify the electronic structure of graphene. In this review, we will discuss recent experimental and computational studies related to deposition of metals on graphene supported on various substrates (SiC, SiO 2 , and hexagonal close-packed metal surfaces). Of specific interest are the metal-graphene interactions (adsorption energies and diffusion barriers of metal adatoms), and the crystal structures and thermal stability of the metal nanoclusters.

Wave functions obtained from plane-wave density-functional theory ͑DFT͒ calculations using normconserving pseudopotential, ultrasoft pseudopotential, or projector augmented-wave method are efficiently and robustly transformed into a set of spatially localized nonorthogonal quasiatomic orbitals ͑QOs͒ with pseudoangular momentum quantum numbers. We demonstrate that these minimal-basis orbitals can exactly reproduce all the electronic structure information below an energy threshold represented in the form of environmentdependent tight-binding Hamiltonian and overlap matrices. Band structure, density of states, and the Fermi surface are calculated from this real-space tight-binding representation for various extended systems ͑Si, SiC, Fe, and Mo͒ and compared with plane-wave DFT results. The Mulliken charge and bond order analyses are performed under QO basis set, which satisfy sum rules. The present work validates the general applicability of Slater and Koster's scheme of linear combinations of atomic orbitals and points to future ab initio tight-binding parametrizations and linear-scaling DFT development.