From How to Why. Graph-Theoretical Verification of Quantum-Mechanical Aspects of (pi)-Electron Behaviors in Conjugated Systems

A number of empirically known rules of the (pi)-electronic stability of conjugated hydrocarbon molecules caused by their topological structure were analyzed for the first time systematically with the graph-theoretical molecular orbital theory developed by the author’s group. The main tool in this analysis is the topological index (or Z index) proposed by the present author for characterizing the topological nature of the structural formula of a hydrocarbon molecule, coupled with the perturbation theory of the Huckel molecular orbital method proposed by Coulson and Longuet-Higgins. A mathematical foundation was given to the global quantum-mechanical aspects of (pi)-electron behaviors in conjugated systems and also to the diagrammatic recipe of the classical organic electron theory proposed by Robinson and Ingold. Through this analysis the specific "How" obtained by quantum chemical calculations is now explained by mathematically reasonable "Why".