Mean-field resonance-theoretic view of benzenoid networks

Abstract

A simple classically based "mean field" resonance-theoretic approach is described to anticipate the effects of various modes of electron pairing (as in π-bond formation) for general "alternant" benzenoid conjugated π-networks. This simplified approach avoids generation and manipulation of individual resonance structures, whence application is facilitated, even for very large systems -so large that there might be hundreds or millions or moles or even substantially greater numbers of resonance structures. Some of the predictions so facilitated for several general circumstances are conveniently manifested as explicit algebraic formulas for numbers of unpaired electrons. The simplicity (and apparent reliability) of these algebraic formulas is emphasized; they involve no more than counts of different "kinds" of π-center carbons, e.g., the numbers of π-centers of different functionalities (primary, secondary, or tertiary) which are "starred" (in an "alternant" system) as well as those which are "unstarred". The argumentation also provides some information about rough locations for the (unpaired) spin densities, and ultimately also about the presence of low-lying excited states, magnetic moments, reactivities, and more. In particular these easily used ideas, which are extensions of those already familiar in "classical" organic chemistry should then aid in nano-technological developments.