物理化学学报 >> 2011, Vol. 27 >> Issue (05): 1000-1004.doi: 10.3866/PKU.WHXB20110518

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Möbius环并苯的分子对称性

邢生凯, 李云, 赵学庄, 蔡遵生, 尚贞锋, 王贵昌   

  1. 南开大学化学学院,天津 300071
  • 收稿日期:2010-12-15 修回日期:2011-03-18 发布日期:2011-04-28
  • 通讯作者: 赵学庄, 王贵昌 E-mail:zhaoxzh@nankai.edu.cn; wangguichang@nankai.edu.cn

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 E-mail:zhaoxzh@nankai.edu.cn; wangguichang@nankai.edu.cn

摘要:

一般来说, 点群理论认为Möbius带环分子最高的对称性只能是C2. 本文讨论了由18个苯环组成的环并苯的异构体分子, 包括柱面的Hückel型分子(HC-[18])和扭转180°的Möbius带环分子(MC-[18]). 结果表明除了点对称性外, Möbius带环分子还存在一种可称为环面螺旋旋转(TSR)变换的对称性, 为此还引用了环面正交曲线坐标系. 此外, 还讨论了这些分子关于TSR对称性匹配的原子集和原子轨道(AO)集. 根据TSR对称性的循环群特征, 可以建立此类群的不可约表示及有关特征标. 这类分子的分子轨道(MO)关于TSR群的不可约表示是纯的, 然而所含的相应的原子轨道对称性匹配的线性组合(SALC-AO)成分可以是多种的.

关键词: Möbius环并苯, 分子对称性, 环并苯, 环面螺旋旋转变换, 环面正交曲线坐标系, 环面群

Abstract:

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

MSC2000: 

  • O641