Hückel theory applied to large linear and cyclic conjugated π-systems

By use of rotational symmetry (C_n-symmetry) a lower limit to the frontier orbital (HOMO-LUMO) gap in large molecules with linear and cyclic conjugated π-systems containing simple repetitive units has been calculated within the Hückel approxmation. The frontier orbitals are shown to be the same in series of cyclic oligomers and liner polymers containing the same repetitive units. The orbital gap is calculated from the repetitive units closed on themselves to give a ring of Hückel or, alternatively, Möbius topology depending on the number of conjugated π-electrons in a liner array between the ends of the repetitive unit. For 4n (4n+2) systems the small ring of Hückel (Möbius) topology will give the frontier orbitals.