On the cycle-dependence of topological resonance energy

The topological resonance energy (TRE) was conceived in the 1970s. From the very beginning, it was known that TRE is equal to the collective energy-effect of all cycles present in a conjugated molecule. Also in the 1970s a theory of cyclic conjugation was elaborated, by means of which it was possible to compute the energy-effect ef(Z) of each individual cycle Z present in a conjugated molecule. Yet, the connection between TRE and the ef(Z)-values was, until now, not studied. We now show that TRE and the sum of the ef(Z)-values are closely correlated but that a certain correction needs to be made by taking into account the energy-effects of pairs, triplets, quartets, etc. of cycles.