Structures and electro-optical properties of Möbius [n]Cyclacenes[13-18]: a theoretical study

Due to the unusual properties of the Möbius cyclacenes (MC) such as π electrons, MC has drawn the extensive attention of scientists. In the present work, six [n]MC (n  = 13-18, n is the number of benzenoid rings) were systematically investigated to explore the size-dependent effects on structures, electro-optical properties, and frontier molecule orbits (FMO). According to the dihedral angles (C-C-C-C), the un-twisted area and twisted area are defined, respectively. The twisted area mainly distributes on seven or eight benzenoid rings for [n]MC (n  = 13-18). Further, the polarizability (α₀) and first hyperpolarizability (β₀) of [n]MC (n  = 13-18) were calculated with three density functional methods (BHandHLYP, Cam-B3LYP, and M06-2X). Results show that the α₀ values increase linearly with increasing the number (n) of benzenoid rings. Significantly, the β₀ values are increased to zigzag with increasing the number (n) of benzenoid rings. Interestingly, when n is even (14, 16, and 18), the electron transfer is from the twisted area to the un-twisted area, but the electron transfer is from the un-twisted area to the twisted area when n is odd (13, 15, and 17).