  Carbon nanostructures are ideal substrates for functionalization with
molecules, since they consist of a single atomic layer giving rise to an
extraordinary sensitivity to changes in their surrounding. The
functionalization opens a new research field of hybrid nanostructures with
tailored properties. Here, we present a microscopic view on the
substrate-molecule interaction in the exemplary hybrid material consisting of
graphene functionalized with perylene molecules. First experiments on similar
systems have been recently realized illustrating an extremely efficient
transfer of excitation energy from adsorbed molecules to the carbon substrate -
a process with a large application potential for high-efficiency photovoltaic
devices and biomedical imaging and sensing. So far, there has been no
microscopically founded explanation for the observed energy transfer. Based on
first-principle calculations, we have explicitly investigated the different
transfer mechanisms revealing the crucial importance of F\"orster coupling. Due
to the efficient Coulomb interaction in graphene, we obtain strong F\"orster
rates in the range of 1/fs. We investigate its dependence on the
substrate-molecule distance R and describe the impact of the momentum transfer
q for an efficient energy transfer. Furthermore, we find that the Dexter
transfer mechanism is negligibly small due to the vanishing overlap between the
involved strongly localized orbital functions. The gained insights are
applicable to a variety of carbon-based hybrid nanostructures.
