Determination of Topological Equivalence Classes of Atoms and Bonds in C₂₀−C₆₀ Fullerenes Using a New Prolog Coding Program

A new general molecular coding Prolog program is used in theoretical studies of the properties of fullerene isomers and derivatives to identify the topological equivalence classes of atoms and bonds in C20−C60 fullerenes. The symmetry perception algorithm is based on an exhaustive search of a minimal code. During this search all canonical labeled mapping trees are generated, allowing construction of equivalence classes of atoms and bonds. Although the present algorithm makes a complete search of canonical labelings in the molecular graph, computational time is maintained within reasonable limits even for large regular graphs such as fullerenes. In the case of fullerenes, topological equivalence classes of atoms allow an easy generation of heterofullerene isomers, while the bond classes allow for the generation of addition or cycloaddition isomers. Also, the number of atom classes and the number of atoms in each class gives important information on the number of 13C NMR signals and intensity patterns in fullerenes.