Quasiparticle spectra and excitons of organic molecules deposited on substrates: G0W0-BSE approach applied to benzene on graphene and metallic substrates

We present an alternative methodology for calculating the quasi-particle energy, energy loss, and optical spectra of a molecule deposited on graphene or a metallic substrate. To test the accuracy of the method it is first applied to the isolated benzene (C6H6) molecule. The quasiparticle energy levels and especially the energies of the benzene excitons (triplet, singlet, optically active and inactive) are in very good agreement with available experimental results. It is shown that the vicinity of the various substrates (pristine/doped graphene or (jellium) metal surface) reduces the quasiparticle HOMO-LUMO gap by an amount that slightly depends on the substrate type. This is consistent with the simple image theory predictions. It is even shown that the substrate does not change the energy of the excitons in the isolated molecule. We prove (in terms of simple image theory) that energies of the excitons are indeed influenced by two mechanisms which cancel each other. We demonstrate that the benzene singlet optically active (E1u) exciton couples to real electronic excitations in the substrate. This causes it substantial decay, such as {\Gamma} = 174 meV for pristine graphene and {\Gamma} = 362 meV for metal surfaces as the substrate. However, we find that doping graphene does not influence the E1u exciton decay rate.