The methane-graphene interaction is studied using density functional theory complemented with a semiempirical dispersion correction scheme (DFT-D), an ab initio van der Waals density functional (vdW-DF) ansatz as well as using Møller Plesset perturbation theory (MP2). The adsorption energy of 0.17 eV and the molecular distance of 3.28 Å obtained from the MP2 calculations are close to the experimental data, while the vdW-DF scheme results either in a realistic adsorption energy or a realistic adsorption geometry, depending on the underlying exchange-correlation functional. The present implementation of DFT-D overbinds about as much as bare DFT calculations underbind, but yields a meaningful adsorption height
