CAJ | 학술논문

一般来说,点群理论认为M(o)bius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M(o)bius带环分子(MC-[18]).结果表明除了点对称性外,M(o)bius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.
일반래설,점군이론인위M(o)bius대배분자최고적대칭성지능시C2.본문토론료유18개분배조성적배병분적이구체분자,포괄주면적Hückel형분자(HC-[18])화뉴전180°적M(o)bius대배분자(MC-[18]).결과표명제료점대칭성외,M(o)bius대배분자환존재일충가칭위배면라선선전(TSR)변환적대칭성,위차환인용료배면정교곡선좌표계.차외,환토론료저사분자관우TSR대칭성필배적원자집화원자궤도(AO)집.근거TSR대칭성적순배군특정,가이건립차류군적불가약표시급유관특정표.저류분자적분자궤도(MO)관우TSR군적불가약표시시순적,연이소함적상응적원자궤도대칭성필배적선성조합(SALC-AO)성분가이시다충적.
Generally speaking, the highest symmetry of a Mobius 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 Huckel [18]-cyclacene (HC-[18]) and a Mobius strip-like Mobius [18]-cyclacene (MC-[18]). We found that in addition to being described by C2 point group transformation, the molecular symmetry of Mobius 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.