Role of metals in the catalytic Chemical Vapor Deposition (CVD) growth of carbon nanotubes (CNTs) or graphene was investigated using DFT. Crucial processes involved in the growth of CNTs/graphene: methane dissociation to produce C, C diffusion and nucleation kinetics were studied on the (1 1 1) surface of different transition metals, i.e., Fe, Co, Ni, and Cu. Based on the DFT calculation results, the present study explains why Ni-based catalyst is a suitable CVD substrate for growing CNTs: it has a moderate reactivity towards methane dissociation; low energy barrier for C atom surface diffusion, which makes C to diffuse easily to the metal/CNTs edges and contribute to CNTs growth; relatively high nucleation barriers, making it more resistant for deactivation caused by the cover of carbon clusters. Meanwhile, this study also shows that Cu may be an appropriate catalyst for graphene synthesis due to the particularly low diffusion and nucleation barriers of C atoms on Cu, which suggest that C atoms tend to be more uniformly distributed and nucleate easily on the Cu surface. Key limitation of Cu is the low reactivity of this metal towards methane dissociation. Since Fe and Ni are very reactive towards C-H bond breaking, Cu based alloys, e.g. Cu8Ni, were proposed as a suitable catalyst for graphene production. (C) 2014 Elsevier B.V. All rights reserved.