Bandgaps of Atomically Precise Graphene Nanoribbons and Occam’s Razor

Rationalization of energy gaps of atomically precise AGNRs, “bulk” (ΔEac) or “zigzag-end” (ΔEzz), could be challenging and controversial concerning their magnitude, origin, substrate influence (ΔEsb), and spin-polarization, among others. Hereby, a simple self-consistent and “economical” interpretation is presented, based on “appropriate” DFT (and 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 ΔEac, ΔEzz, and ΔEsb. Thus, an excellent agreement between experiment and theory emerges, provided some established stereotypes are reconsidered and/or abandoned. The primary source of discrepancies is the finite length of AGNRs together with inversion-symmetry conflict and topological end/edge states, which invariably mix with other “bulk” states making their unambiguous detection/distinction difficult. This can be further tested by eliminating end-states (and ΔEzz), by eliminating empty (non-aromatic) end-rings