We present a theory study of the physisorption of the series of methylbenzenes (toluene, xylene and mesitylene), as well as benzene, on graphene. This is relevant for the basic understanding of graphene used as a material for sensors and as an ideali
zed model for the carbon in active carbon filters. The molecules are studied in a number of positions and orientations relative graphene, using density functional theory with the van der Waals functional vdW-DF. We focus on the vdW-DF1 and vdW-DF-cx functionals, and find that the binding energy of the molecules on graphene grows linearly with the number of methyl groups, at the rate of 0.09 eV per added methyl group.
