CLASSIFICATION OF TOPOLOGICALLY CHIRAL MOLECULES

Graphs are partitioned into six classes from the perspective of chiral ity, depending on whether they are topologically achiral, whether ther e is at least one topologically achiral embedding, whether there is at least one rigidly achiral embedding, and whether there is at least on e rigidly achiral presentation. Three of these classes are well repres ented by a variety of chemical structures: topologically chiral molecu lar graphs with no topologically achiral embeddings, topologically chi ral molecular graphs with at least one rigidly achiral embedding, and topologically achiral molecular graphs with at least one rigidly achir al presentation. Known representatives of these three classes are desc ribed. Various meanings associated with the concepts ''molecular graph '' and ''intrinsic chirality'' are critically discussed. Previous arra ngements of molecular graphs and molecules in a hierarchical order, ra nging from the most to the least chiral, are interpreted in terms of t he graph's and molecule's ''chiral persistence''.