Aromaticity Index Can Predict and Explain the Stability of Polycyclic Conjugated Hydrocarbons

For deciphering the secret of the conventional Hückel ’s (4n + 2)-rule and also for extending it to polycyclic systems the aromaticity index, ΔZ, is introduced based on the graph-theoretical molecular orbital method, which has been developed by the present author. All the information either stabilizing or destabilizing the π-electronic system of a given graph G is contained in the characteristic polynomial, PG(x), obtained by expanding the secular determinant of H MO theory. Instead of this conventional procedure the present author succeeded in obtaining the general expression of PG(x) in terms of the non-adjacent number, p(G, k), for G, defined for the topological index, ZG. By extending this idea ΔZ is defined by taking into account all the contributions not only from the constituting rings but also from the possible combinations of disjoint rings in G. By using ΔZ mathematical origin of the Hückel’s rule was clarified and expanded to the “extended Hückel’s rule” for polycyclic conjugated systems. Applications to bicyclic and polycyclic networks are demonstrated. Discussion on the aromaticity of fullerenes and nanotubes is presented.