  We have performed a density functional study of graphene adsorbed on Au(111)
surface using both a local density approximation and a semiempirical van der
Waals approach proposed by Grimme, known as the DFT-D2 method. Graphene
physisorbed on metal has the linear dispersion preserved in the band-structure,
but the Fermi level of the system is shifted with respect to the conical points
which results in a doping effect. We show that the type and amount of doping
depends not only on the choice of the exchange-correlation functional used in
the calculations, but also on the supercell geometry that models the physical
system. We analyzed how the factors such as the in-plane cell parameter and
interlayer spacing in gold influence the Fermi level shift and we found that
even a small variation in these parameters may cause a transition from p-type
to n-type doping. We have selected a reasonable set of model parameters and
obtained that graphene is either undoped or at most slightly p-type doped on
the clean Au(111) surface, which seems to be in line with experimental
findings. On the other hand, modifications of the substrate lattice may induce
larger doping up to 0.30-0.40 eV depending on the graphene-metal adsorption
distance. The sensitivity of the graphene-gold interface to the structural
parameters may allow to tune doping across the samples which could lead to
possible applications in graphene-based electronic devices. We believe that the
present remarks can be also useful for other studies based on the periodic DFT.
