Acta Phys. -Chim. Sin. ›› 2011, Vol. 27 ›› Issue (05): 1000-1004.doi: 10.3866/PKU.WHXB20110518

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Molecular Symmetry of Möbius Cyclacenes

XING Sheng-Kai, LI Yun, ZHAO Xue-Zhuang, CAI Zun-Sheng, SHANG Zhen-Feng, WANG Gui-Chang   

  1. College of Chemistry, Nankai University, Tianjin 300071, P. R. China
  • Received:2010-12-15 Revised:2011-03-18 Published:2011-04-28
  • Contact: ZHAO Xue-Zhuang, WANG Gui-Chang;


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 orthogonal 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.

Key words: Möbius cyclacene, Molecular symmetry, Cyclacene, Torus screw rotation transformation, Torus orthogonal curvilinear coordinates, Torus group


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