Linear, cyclic, and Möbius strip polyacenes: The influence of the topology on the size-dependent HOMO-LUMO energy gap

The electronic structure of finite and infinite linear, cyclic, and Möbius strip polyacenes has been investigated by adopting simple Hückel methodology without and with variable β resonance integrals and the more involved MNDO scheme. Using the Hückel approach, it turns out that the linear polyacenes and the Möbius ladder molecules exhibit HOMO-LUMO gap which monotonously decrease with chain length while their cyclic analogs have a sawtooth behavior. The originality of the approach is to combine band structure and MO approaches to get analytical forms of the energy levels. These results are corroborated at the MNDO levels where the geometry relaxation effects are taken into account. The optimized MNDO structures show that the Möbius defect is localized and extends over approximately one-third of the ladder. Accounting for geometry distortion at the MNDO level results in an increase of the gap of the Möbius strip relative to the linear and cyclic finite size structures, but the similar results for the two methods confirm that the topology is the main factor acting on HOMO-LUMO energy gaps.