Aromaticity index can predict and explain the stability of polycyclic conjugated hydrocarbons

For deciphering the secret of the conventional Mickel's (4n + 2)-rule and also for extending it to polycyclic systems the aromaticity index, Delta Z, 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 pi-electronic system of a given graph G is contained in the characteristic polynomial, P-G(x), obtained by expanding the secular determinant of HMO theory. Instead of this conventional procedure the present author succeeded in obtaining the general expression of P-G(x) in terms of the non-adjacent number, p(G, k), for G, defined for the topological index, Z(G). By extending this idea Delta Z 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 Delta Z mathematical origin of the Mickel's rule was clarified and expanded to the "extended Mickel's rule" for polycyclic conjugated systems. Applications to bicyclic and polycyclic networks are demonstrated. Discussion on the aromaticity of fullerenes and nanotubes is presented.