Inductive-resonance energy transfer in hybrid carbon nanostructures

Based on the first principles, we have shown that the decisive role in energy transfer from the fluorophore molecule to the carbon substrate (graphene) is played by the Förster-type inductive-resonance energy transfer mechanism. The Förster energy transfer rate can be calculated analytically via Fermi’s golden rule with the momentum-dependent initial final states of the graphene substrates and the HOMO (the highest occupied molecular orbital) and LUMO (the lowest unoccupied molecular orbital) states of the dye molecule. Combining first-principle calculations characterizing the hybrid carbon nanomaterials with tight-binding-based consideration of graphene wave functions allows us to obtain an analytical expression for the Förster energy transfer rate. We constructed graphical dependences of the Förster energy transfer rate at the distance R between substrate (graphene) and dye molecule for several materials. The results obtained can be applied to various hybrids based on carbon nanostructures and in general to the description of energy transfer processes in molecular functionalized nanostructures, once the molecular dipole moment and the substrate - molecule separation are known.