Topological enantiomers

Figure 4. The trefoil knot a closed ring with a minimum of three crossing points. The rings (a), (b) and (c) are topological stereoisomers the two knots (a) and (b) are topological enantiomers.

Whatever the beauty of the resolved systems discussed above, it should be noticed that the enantiomers obtained after resolution are not topological enantiomers but classical geometrical diastereomers. In each case, a rigid chiral function... 

To our knowledge, it is the first preparative resolution of topological enantiomers. 

To obtain the pure topological enantiomers, the chiral auxiliary was easily replaced by the hexafluorophosphate anion. 

Fig. 10. The topologically relevant step in the synthesis of the propellane 53 53a and 53b are topological enantiomers...

Liquid extraction was used to make diastereomers, exploiting the high solubility of potassium triflate in water compared with the binaphthylphosphate salts. The two diastereomers have different solubilities and the (+) isomers of knot and anion crystallise together [49, 50], while the laevorotatory knot remains soluble. Counterion exchange with hexafluorophosphate gave the pure topological enantiomers. The optical rotatory power of the copper knots is very high At the sodium D-line (589 nm), the optical rotatory power was 7.000 mol 1 L dm They are beautiful molecules with a remarkable property ... 

In Figure 3.5, regular projections of knots with crossing numbers less than seven are shown, together with their symbolic notations commonly used in knot theory. For each topologically chiral knot only one of the two topological enantiomers is shown. 

The structures XI to XIII or XIV and XV are topological stereoisomers since they have identical connectivity (homeomorphic), but no continuous deformation will allow them to interconvert (not isotopic). Furthermore, structures XII and XIII are topological enantiomers and the knots XII or XIII and the unknotted ring XI are topological diastereomers. 

Fig. 1 Constitutional isomers, topological isomers, topological diastereomer.s. and topological enantiomers. (View this art in color at www.deklcer.com.)...

Figure 3.45 (a) A trefoil knot and (b) its topological enantiomer are topological isomers of (c) a macrocycle. 

Figure 2 Topological stereoisomers (a) the trivial ring and (b and c) the TrefoU knots which are closed rings with three crossing points, b and c are topological enantiomers.

In addition, the compounds of Figure 2(b) and (c) are topological enantiomers since the mirror image of any presentation of Figure 2(b) is identical to a given presentation of Figure 2(c). 

The pure topological enantiomers were liberated from the diastereomeric salts by counterion exchange with hex-afluorophosphate. The optical rotatory power of the cop-per(I) knots is very high At the sodium D line (589 nm). 

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