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 (ß0) 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 ß0 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).