Molecular knots chirality/achirality

We shall now see how to apply the theorem to the molecular trefoil knot, which was illustrated in Figure 17. We can create a molecular cell complex G by replacing each isolated benzene ring by a cell and each chain of three fused rings by a single cell. We prove by contradiction that our molecular cell complex is topologically chiral. Suppose that it is topologically achiral. Then there is a defor-... 

Let us assume that a rotaxane is formed from an axle with two different stoppers and a wheel that bears a directionality defined by the sequence of atoms in the macrocycle. Both of these subunits are achiral, both are identical to their mirror images. Nevertheless, the corresponding rotaxane exists in two enantiomeric forms, although no chiral center is present in the molecule (Fig. 4). It is the molecular topology that makes these species chiral, and consequently, this phenomenon was coined "topological chirality.. It also exists for catenanes, knots, and other mechanically bound molecules. Shown in Fig. 4 is a detailed structure of such a rotaxane. The wheel contains one sulfonamide group that provides the directionality of... 

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