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Charge transfer energies of benzene physisorbed on a graphene sheet from constrained density functional theory

Constrained density functional theory (CDFT) is used to evaluate the energy level alignment of a benzene molecule as it approaches a graphene sheet. Within CDFT the problem is conveniently mapped onto evaluating total energy differences between different charge-separated states, and it does not consist in determining a quasi-particle spectrum. We demonstrate that the simple local density approximation provides a good description of the level aligmnent along the entire binding curve, with excellent agreement to experiments at an infinite separation and to GW calculations close to the bonding distance. The method also allows us to explore the effects due to the presence of graphene structural defects and of multiple molecules. In general all our results can be reproduced by a classical image charge model taking into account the finite dielectric constant of graphene.