A Topological Hierarchy of Molecular Chirality and other Tidbits in Topological Stereochemistry

Chemists have long been intrigued by the molecular basis of isomerism. Indeed, much of the powerful paradigm of structure based upon the molecular graph was first invented to explain isomerism, including the classifications used in modern stereochemistry. Thus, constitutional isomers describe pairs of isomeric molecular structures possessing non-homeomorphic molecular graphs, while the classical stereoisomers (enantiomers and diastereomers) possess molecular graphs which are homeomorphic and also homeotopic (interconvertable by continuous deformation in 3space). This means that classical stereoisomerism is derived from the Euclidean properties of molecular graphs, being a manifestation of some kind of molecular rigidity. Wasserman in his classic papers entitled "Chemical Topology" first focused the attention of chemists on the relevance of low dimensional topology in chemistry by proposing a possible approach to the synthesis of a molecular trefoil knot in addition to providing the foundation for the Biochemistry sub-discipline dealing with isomerism in circular DNAs. The trefoil, recently realized in a small molecule structure for the first time by Dietrich-Buchecker and Sauvage, serves as an example of a third type of isomerism which we first defined as topological stereoisomerism, as shown in Figure 1.