Topology of bonding in pi-electron systems

Delocalization in conjugated pi-electron systems is shown to be closely related to the topological concept of connectivity. A topological bond order is defined as a quantitative measure of the extent to which the subspace of a pair of adjacent atoms approximates a disconnected component of the molecular topological space. The agreement between this measure and molecular-orbital bond orders in the ordering of bond strengths within molecules is near perfect. There is also excellent quantitative agreement between these two measures of bond strength. Bond orders appear to be primarily determined by molecular topology. A new type of intramolecular equivalence relation between bonds, called "coresiduality," emerges from the topological analysis. Two bonds are coresidual if the residues remaining when each pair of adjacent atoms is excised from the molecule are isomorphic. Coresidual bonds have equal bond orders. Coresiduality includes, but is more general than, equivalence due to symmetry.