1 - Stereochemical Topology

Summary

Stereochemistry is the study of the three-dimensional structure of molecules, and topology is the study of those properties of geometric objects that are invariant under continuous transformations. It is not obvious that these two fields have anything in common. In fact, not long ago there was little communication between researchers in these two areas. Prior to forty years ago, analyzing the topological properties of existing molecular structures was not very difficult, because as topological objects, the graphs of all the molecular structures known at the time could be deformed into a plane. Thus, understanding the stereochemistry of a molecule only required the evaluation of its geometry and not its topology. Recently, knots and links and other molecules have been synthesized whose structures and properties come from their topology as well as their geometry. The chemical motivation for the synthesis of such topologically interesting structures is the desire to synthesize new types of molecules that might have truly unusual properties, as well as the hope that in trying to create such unique molecules, new methods of synthesis will be developed along the way. These new types of molecules are often large enough that they no longer have the rigidity that is characteristic of small molecules, so understanding their deformations is an important part of understanding their structure. In addition to purely synthetic molecules, Liang and Mislow (1994b, 1995) have discovered that knots and links and other nonplanar graphs can occur naturally in proteins.