π-electron currents in polycyclic conjugated hydrocarbons : Coronene and its isomers having five and seven member rings
We have outlined novel graph theoretical model for computing π-electron currents in π-electron polycyclic conjugated hydrocarbons. We start with Kekule valence structures of a polycyclic conjugated hydrocarbon and their conjugated circuits. To each 4n+2 conjugated circuits we assign counter clockwise current i and to each 4n conjugated circuit we assign clockwise current i. By adding the contributions from all conjugated circuits in a single Kekule valence structure one obtains π-electron current pattern for the particular Kekule valence structure. By adding the conjugated circuit currents in all Kekule valence structure one obtains the pattern of π-electron currents for considered molecule. We report here π-electron current patters for coronene and 17 its isomers, which have been recently considered by Balaban et al., obtained by replacing one or more pairs of peripheral benzene rings with five and seven member rings. Our results are compared with their reported π-electron current density patters computed by ab initio molecular orbital (MO) computations and satisfactory parallelism is found between two so disparate approaches.