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Koopmans’ theorem implies that the Hartree-Fock quasiparticle gap in a closed-shell system is equal to its single-particle energy gap. In this work, the theorem is generalized to optical transitions in the Hubbard model of graphene nanodots. Based on systematic configuration interaction calculations, it is proposed that the optical gap of a closed-shell graphene system within the Hubbard model is equal to its tight-binding single-particle energy gap in the absence of electron correlation. In these systems, the quasiparticle energy gap and exciton binding energy are found to be dominated by the long-range Coulomb interaction, and thus, both become small when only on-site Hubbard interactions are present. Moreover, the contributions of the quasiparticle and excitonic effects to the optical gap are revealed to nearly cancel each other, which results in an unexpected overlap of the optical and single-particle gaps of the graphene systems.


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