Using large-scale DFT calculations (up to 1,476 atoms and 18,432 orbitals), we present the first detailed analysis on the unusual electronic properties of recently synthesized porphyrin nanotubes. We surprisingly observe extremely large oscillations in the bandgap of these nanostructures as a function of size, in contradiction to typical quantum confinement effects (i.e., the bandgap increases with size in several of these nanotubes). In particular, we find that these intriguing electronic oscillations arise from a size-dependent alternation of aromatic/non-aromatic characteristics in these porphyrin nanotubes. Our analyses of band structures and orbital diagrams indicate that the electronic transitions in these nanostructures are direct-bandgap, optically active bright states that can be readily observed in photoelectron spectroscopic experiments. Most importantly due to their unusual bandgap oscillations, we find that both type I and type II donor-acceptor p-n heterojunctions are possible in these template-directed, bottom-up synthesized porphyrin nanotubes - a unique property that is not present in conventional carbon nanotubes.
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