Bandgaps of Atomically Precise Graphene Nanoribbons and Occam’s Razor

Rationalization of the “bulk” (ΔΕac) or “zigzag-end” (ΔΕzz) energy gaps of atomically precise AGNRs, which are directly related to fundamental applications in nanoelectronics, could be challenging and largely controversial with respect to their magnitude, origin, substrate influence (ΔΕsb), and spin-polarization, among others. Hereby a simple self-consistent, “economical” and highly successful interpretation is presented based on “appropriate” DFT (TDDFT) calculations, general symmetry principles, and plausibility arguments, which is fully consistent with current experimental measurements for 5-, 7-, and 9-AGNRs within less than 1%, although at variance with some prevailing views or interpretations for ΔΕac, ΔΕzz, and ΔΕsb. The excellent agreement with experiment and the new insight gained is achieved by invoking the approximate equivalence of Coulomb correlation energy with the staggered sublattice potential. Breaking established stereotypes, we suggest that the measured STS gaps are virtually independent of the substrate, essentially equal to their free-standing values, and that the “true” lowest energy state is closed singlet with no conventional magnetism. The primary source of discrepancies is the finite length of AGNRs together with inversion/reflexion symmetry conflict and the resulting topological end/edge states. Such states invariably mix with other “bulk” states making their unambiguous detection/distinction difficult. This can be further tested by eliminating end-states (and ΔΕzz), by eliminating “empty” zigzag rings.