Knots chiral trefoil

The pattern of crossings in knots means that they can be chiral objects. This is particularly the case for the three-crossing knot 3i (trefoil knot). However, 4X. the four-crossing knot already discussed above, is not chiral, which could be very... 

Figure 24 Fonnation of a chiral trefoil knot using a Chiragen ligand. (Reproduced from Ref. 61. Wiley-VCH, 2004.)...

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 28. Principle of the resolution of the dicopper(I) molecular trefoil knot Cu2(K-84) +. The chiral auxiliary used is S-(+)-l,l -binaphthyl-2,2 -diyl phosphate (BNP-).

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... 

In contrast, as illustrated by the example of the Jones polynomial for the trefoil knot, the polynomial of a chiral knot is in principle, and indeed in the majority of... 

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... 

A trefoil knot is a chiral object. The above 1,3-phenylene-linked dicationic knot has been resolved via fractional crystallisation of its diastereomeric salts using the chiral anion (5)-(+)-l,r-binaphthyl-2,2 -diyl phosphate. ... 

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.

Synthetically, Sauvage s group have been able to extend this work as far as three metal centres, giving rise to the (unconditionally chiral) doubly interlocked [2]catenate 10.137. ° The synthetic procedure is similar to those employed for the trefoil knots 10.135 and singly interlocked... 

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