  We performed a systematic density functional study of the adsorption of
copper, silver, and gold adatoms on graphene, especially accounting for van der
Waals interactions by the vdW-DF and the PBE+D2 methods. In particular, we
analyze the preferred adsorption site (among top, bridge, and hollow positions)
together with the corresponding distortion of the graphene sheet and identify
diffusion paths. Both vdW schemes show that the coinage metal atoms do bind to
the graphene sheet and that in some cases the buckling of the graphene can be
significant. The results for silver are at variance with those obtained with
GGA, which gives no binding in this case. However, we observe some quantitative
differences between the vdW-DF and the PBE+D2 methods. For instance the
adsorption energies calculated with the PBE+D2 method are systematically higher
than the ones obtained with vdW-DF. Moreover, the equilibrium distances
computed with PBE+D2 are shorter than those calculated with the vdW-DF method.
