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With the aim of understanding recent experimental data concerning noncovalent n/p-doping effects in graphene samples, we have investigated the interactions between two prototypical donor and acceptor molecules and graphene mono- and bilayer systems, by means of density functional theory calculations. We report and rationalize the structural, thermodynamical aspects, as well as charge transfers and the induced electronic structure modifications of the graphenic substrates in interaction with tetrathiafulvalene (TTF), an organic donor molecule, and tetracyanoethylene (TCNE), a typical acceptor. If the results show that p-doping of a graphene monolayer due to TCNE molecules can occur even at low concentration, n-doping of graphene requires either larger concentrations or cooperative adsorption of TTF molecules. In both cases, noncovalent doping only implies shifts of the Fermi level, and keeps the linear …