The Anthracene Problem: Closed-Form Conjugated-Circuit Models of Ring Currents in Linear Polyacenes

Conjugated-circuit models for induced pi ring currents differ in the types of circuit that they include and the weights attached to them. Choice of circuits for general pi systems can be expressed compactly in terms of matchings of the circuit-deleted molecular graph. Variants of the conjugated-circuit model for induced pi currents are shown to have simple closed-form solutions for linear polyacenes. Despite differing assumptions about the effect of cycle area, all the models predict the most intense perimeter current in the central rings, in general agreement with ab initio current density maps. All tend to overestimate the rate of increase with N of the central ring current for the [N]polyacene, in comparison with molecular-orbital treatments using ipsocentric ab initio, pseudo-pi, and Husckel-London approaches.