Citation: XING Sheng-Kai, LI Yun, ZHAO Xue-Zhuang, CAI Zun-Sheng, SHANG Zhen-Feng, WANG Gui-Chang. Molecular Symmetry of Möbius Cyclacenes[J]. Acta Physico-Chimica Sinica, ;2011, 27(05): 1000-1004. doi: 10.3866/PKU.WHXB20110518 shu

Molecular Symmetry of Möbius Cyclacenes

1.
College of Chemistry, Nankai University, Tianjin 300071, P. R. China

Received Date: 15 December 2010
Available Online: 2 April 2011

Generally speaking, the highest symmetry of a Möbius cyclacene molecule is C₂ group based on the point group theory. We here investigated two isomers of cyclacene that were composed of 18 benzene units, i.e., a hoop-like Hückel [18]-cyclacene (HC-[18]) and a Möbius strip-like Möbius[18]- cyclacene (MC-[18]). We found that in addition to being described by C₂ point group transformation, the molecular symmetry of Möbius cyclacene may also be characterized by the so-called torus screw rotation (TSR) symmetrical transformation, which is a symmetry operation of the torus group introduced here. The torus ortho nal curvilinear coordinates were also introduced to express the TSR transformation. Furthermore, both the symmetry adapted atom set and the atomic orbital set that refers to the TSR transformation are discussed. Because the TSR symmetry has cyclic group characteristics, we can establish the irreducible representations and related characteristics for this cyclic group. In addition, for these cyclacenes the irreducible representation of their molecular orbitals (MOs) may be pure while their corresponding symmetry adaptive linear combination of atomic orbital (SALC-AO) components can be numerous.
- Möbius cyclacene,
- Molecular symmetry,
- Cyclacene,
- Torus screw rotation transformation,
- Torus ortho nal curvilinear coordinates,
- Torus group
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