Trefoil knots, topological chirality

To make a knot is a task easily accomplished by a child playing with a rope, or even by a careless adult with shoelaces. For a chemist playing with molecules this is an intrinsically difficult problem and so far only a few of these topologically interesting compounds have been synthesized. A strategy that finally led to success is based on the self-assembly of double-helical copper phenanthroline complexes. The helix represents the core structure from which the trefoil knot 30 in Fig. 15 is obtained in a final cyclization step. It is important to note that a trefoil knot is chiral. The resolution of the two enantiomers was recently accomplished by fractional crystallization of the diastereoisomers obtained with a chiral counterion. 

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-... 

Figure 10.54 Topological isomerism, diastereoisomerism and chirality as related to a [2] catenane, a trefoil knot and a doubly interlocked [2] catenane.

Trefoil knots are the classic examples of topologically chiral structures. The rational synthesis of molecular trefoil knots, suggested as long ago as 1953,81 was finally achieved in 1989, by Christiane Dietrich-Buchecker and Jean-Pierre Sauvage82 (Figure 18) the enantiomers of this knot were subsequently resolved.83... 

To our knowledge, topologically chiral molecules have not yet been resolved into enantiomers. However, we may anticipate that their energy barrier to racemization will be extremely high, compared to Euclidean chiral molecules. Therefore they are expected to be useful in enantioselective interactions or reactions. For example, it has been shown that tetrahedral copper(I) bis-2,9-diphenyl-l,10-phenanthroline complexes (which form the catenate subunits) are good reductants in the excited state [97] therefore the chiral Cu(I) catenates could be used for enantioselective electron-transfer reactions. Alternatively, the resolution of topologically chiral molecules would allow to answer fundamental questions, such as what are the chiroptical properties of molecular trefoil knots ... 

Experimental data about the properties of Mobius strip-like structures as the ladder 129a or knots like 127 are rather scarce. However, a theoretical analysis of the peculiarities of these constructions (see refs. 18a-d, 21b, 21c and literature cited therein) led to some conclusions of general importance. Thus it was established that a new phenomenon of topological chirality should be observed for compounds having the shape of trefoil knots or Mobius strips. Normally, chemists deal with chiral objects which can be (in principle) transformed into their mirror image by a continuous deformation. For... 

FIGURE 13 Enantiomorphs of topologically chiral constructions. Top Trefoil knot. Center Four-crossing two-component link. Bottom Oriented two-crossing link. 

Figure 3.3 The simplest chiral knots, the left-handed and right-handed trefoil knots T. and T+ no motion of the rope can convert a chiral knot into its mirror image. An orientation is specified along the rope of the two trefoil knots. Also shown are the topologically achiral figure eight knot "8", the simple link L, and the unknot U.

Demetallation of the dicopper knotted complex 5.72 occurs by treatment with KCN to give the trefoil 5.73 which acquires a topological chirality. The CD curve of this species was recorded and shows a pronounced signal in the range 280-340 nm. Unfortunately no X-ray strucmres could be determined for any of three compounds 5.71-5.73. 

Figure 22 Topologically chiral forms of a trefoil knot.

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. 

Perret-Aebi, L.E., Von Zelewsky, A., Dietrich-Buchecker, C., and Sauvage, J.P. (2004) Stereoselective synthesis of a topologically chiral molecule The trefoil knot. Angewandte Chemie - International Edition, 43,4482—4485. 

Topological chirality [8,45] implies that there is no other way for the molecule to racemize than breaking a chemical bond. Knots represent beautiful examples of such systems. In addition to their fascinating topological properties related to chirality, they may also serve as interesting chiral systems for enantioselective interactions and processes (electron transfer interaction with other molecules, in particular, DNA incorporation of knots into the structure of molecular catalysts etc...). Consequently, and as a first step, it is particularly challenging to separate the left- and right-handed forms of our synthetic trefoil knot. 

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