Back-of-Envelope Prediction of Aromaticity of Non-Benzenoid Conjugated Hydrocarbons

摘要

For deciphering the secret of the Hueckel's (4«+2)-rule and for extending it to polycyclic systems the aromaticity index, ΔZ, is introduced based on the graph-theoretical molecular orbital method. All the information either stabilizing or destabilizing the it-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. The present author derived the general expression of P_g(x) in terms of the non-adjacent number, p(G,k), for G, the sum of which gives the topological index, Z_G of G. By using ΔZ mathematical origin of the Hueckel's rule was clarified and expanded to the "extended Hueckel's rule" for polycyclic conjugated systems.