Topological chirality molecular links

The method that we have described enables us to prove the topological chirality of most topologically chiral molecular knots and links. 

We shall now apply the techniques that we described above to prove the topological chirality of some molecular knots and links. Note that if we succeed in proving that a molecular graph is topologically chiral then it will follow that the molecule that it represents is chemically chiral, since any molecular motion corresponds to a rigid or flexible deformation of the molecular graph. In particular, it is not chemically possible for one molecular bond to pass through another molecular bond. 

We can use this same approach to prove that other molecular knots and links are topologically chiral. For example, consider the molecular link illustrated in Figure 18. This catenane was synthesized by Nierengarten et al. [12]. For this molecule the set T(G) consists of many unlinks together with many copies of the (4,2)-torus link, illustrated as L in Figure 12. However we saw earlier that this unoriented link is topologically chiral. Therefore, the molecular (4,2)-torus link is topologically chiral as well. 

In a similar way we can prove that the embedded cell complex of the molecular (4,2)-torus link (see Figure 18) is topologically chiral. Also, by adding appropriate labels we can similarly prove the topological chirality of the oriented embedded cell complex of the molecular Hopf link (see Figure 19). 

Figure 3.22 Molecular graphs show that (a) two unconnected macrocycles are considered to be the topological isomer of two linked macrocycles as the two situations cannot be interconverted without breaking bonds and (b) topological chirality can be imparted by molecular species becoming entangled.

Despite the numerous molecular topologies reported to date, it is clear that very few of the intrinsic properties of these assemblies such as the topologically unconditional chirality of trefoil knots and Solomon links or the incredible kinetic inertness of Cu(I)-based [2]catenates have been exploited. A step forward for a better understanding and use of these supramolecular assemblies resides in the availability of researchers to exploit such properties. 

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