Hidden duality and accidental degeneracy in cycloacene and Möbius cycloacene

The accidental degeneracy appearing in cycloacenes as triplets and quadruplets is explained with the concept of segmentation, introduced here aim describing effective disconnection ? orbitals on these organic compounds. For periodic systems time reversal symmetry, emergent nodal domains are shown to divide atomic chains into simpler carbon structures analog benzene rings, diallyl chains, anthracene (triacene) tetramethyl-naphthalene skeletal forms. common electronic levels segments identified members degenerate multiplets global system. peculiar Möbius cycloacene also by segmentation. In last part, it that multiplicity energies for can be foreseen studying continuous limit tight-binding model; conditions put terms Chebyshev polynomials. results obtained this work have important consequences physics transport wires, together their artificial realizations.