  We have studied two interchange layer systems, (i) free standing partly
hydrogenated graphene (graphone), and (ii) graphone on the Nickel (111)
surface, to assess various density functional theory based computational
schemes incorporating van der Waals forces. The various van der Waals methods
have been employed ranging from the semiempirical force-field-like correction
of Grimme, through non-local van der Waals density functionals, up to the
functionals involving exact exchange and the random phase approximation for the
correlation. Generally, all computational schemes lead to a similar qualitative
picture of hydrogen layer physisorption and chemisorption to graphene. The
largest discrepancies between the approaches emerge for the energetics of the
investigated systems. Our studies shed light on the physical mechanisms of
graphene hydrogenation both in vacuum and in the proximity of metallic surface.
In particular, it is revealed that the adsorption of hydrogen atoms affects the
nature of the bonding between graphene and the Ni(111) surface, from the weak
to strong semi-covalent bonding. On the other hand, it turns out that the
adsorption of hydrogen layer to graphene is stronger in the presence of the
metallic surface.
