Topological chirality definitions

By definition, topologically chiral molecules are those whose enantiomers cannot be interconverted by continuous deformation and therefore racemization is totally excluded as long as no bond in their organic backbone is broken. In addition, the combination of this latter topological property with the high thermodynamic stability of copper(I) 2,9-diphenylphenanthroline complexes provides us with potential catalysts for enantioselective processes. 

In summary, failure to detect a rigidly achiral presentation does not mean that such a presentation cannot be found among the infinitely many presentations of a knot failure to interconvert enantiomorphous presentations by ambient isotopy does not exclude the possibility that an interconversion pathway can be found among the infinitely many pathways that are available and a palindromic knot polynomial does not necessarily mean that the knot is amphicheiral. Consequently, it may be impossible in certain cases to determine with complete certainty whether a knot is topologically chiral or not. The fundamental task of the theory of knots was stated over a hundred years ago by its foremost pioneer Given the number of its double points, to find all the essentially different forms which a closed curve can assume. 15 Yet to find invariants that will definitively determine whether or not a knot is chiral remains an unsolved problem to this day.63a Vassiliev invariants have been conjectured to be such perfect invariants.63b... 

In the present article, we will try to go beyond the above intuitive view and treat in a more rigorous fashion the concept of chirality, starting with the classical definitions and going further by discussing in detail the more recent notion of topological chirality. 

We have encountered a number of different definitions of chirality. In the spirit of making everything as simple as possible, but not simpler, 126 we suggest a concise and at the same time general definition for a chiroid (and hence of chirality) whose very simplicity makes it broadly applicable in geometry and topology, as well as in the natural sciences ... 

The two protons at C(l) are topologically nonequivalent, since substitution of one produces a product that is stereoisomerically distinct from that produced by substitution of the other. Ligands of this type are termed heterotopic, and, because the products of substitution are enantiomers, the definition can be made more precise.Ligands that on substitution produce enantiomers are enantiotopic. If a chiral assembly is generated when a point ligand is replaced by a new point ligand, the original assembly is prochiral Both C(l) and C(3) of 1,3-propanediol are prochiral centers. 

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