  Adsorbates on graphene can create resonances that lead to efficient electron
scattering and strongly affect the electronic conductivity. Therefore a proper
description of these resonances is important to get a good insight of their
effect on conductivity. The characteristics of the resonance and in particular
its T-matrix depend on the adsorbate itself but also on the electronic
structure of graphene. Here we show that a proper tight-binding model of
graphene which includes hopping beyond the nearest-neighbor lead to sizable
modifications of the scattering properties with respect to the mostly used
nearest neighbor hopping model. We compare results obtained with hopping beyond
the nearest-neighbor to those of our recent work Phys. Rev. Lett. 113, 146601
(2013). We conclude that the universal properties discussed in our recent work
are unchanged but that a detailed comparison with experiments require a
sufficiently precise tight-binding model of the graphene layer.
