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一般来说,点群理论认为Mbius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Mbius带环分子(MC-[18]).结果表明除了点对称性外,Mbius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.
In general, point-group theory considers that the highest symmetry of the Mbius band-ring molecule can only be C2. In this paper, we discuss the isomers of cyclohexene, consisting of 18 benzene rings, including the cylindrical Hückel- HC- [18]) and Mbius band-ring molecules (MC- [18]) with a 180 ° twist.The results show that in addition to the point symmetry, there exists a kind of Mbius band-ring molecule which can be called a toroidal spiral rotation (TSR) transformations, for which reference is also made to the toroidal orthogonal curvilinear coordinate system.In addition, the atomic and atomic orbitals (AO) sets of these molecules for TSR symmetry matching are also discussed. According to the cycle of TSR symmetry Group characteristics, we can establish the irreducible representations of these groups and the related signatures. The molecular orbital (MO) of these kinds of molecules is pure with respect to the irreducible representation of the TSR group, however, the linear combination of corresponding atomic orbital symmetry matches (SALC-AO) The composition can be various.