三梯级和四梯级圆筒和Mbius分子的拓扑特性研究

A Study of the Topological Properties on the Molecular Cylinder and Mbius Strip with Three-Rung and Four-Rung Ladder

Walba等以其卓越的工作,合成了三-THYME(C_(42)H_(72)O_(18))和四-THYME(C_(56)H_(96)O_(24))圆筒及其Mbius扭曲环带分子,被誉为拓扑学进入有机化学领域的奇迹,成为迄今为止拓扑立体化学研究的重要内容,但从拓扑学的观点探索分子图拓扑结构特性尚缺乏深入研究,本文作者考虑到一般性,曾将扭曲数T为偶数(0,2,4)的定义为Hckel型。

The novel topology of the molecular cylinder and Mobius strip with three-rung and four-rung ladder is discussed. Some novel results in the low dimensional topology deriving from consideration of topological symmetry of the molecular graphs defined by the subject compounds are also discussed. The Hiickel-type molecules with the even number of twists and the Mobius-type molecule with the odd number of twists are defined. It is shown that for the Hiickel-type and Mobius-type molecules with vertices and edges of constitutionally equivalent or nonequiva-lent, the topological symmetry is topological invarants(homeomorphic), while T of the number of twist are not isotopic variable. The topological chirality of these molecules, which is an interesting problem, has been solved with the invention of the topological symmetry concept applied to molecular structures. In order to completely characterize a molecule it is useful to understand the symmetries of its molecular graph in 3-space. For this purpose the topological equivalent graph and topological symmetry are said to be rigid.