Ring Currents in Open-Shell Condensed Benzenoid Homologues of Some Extended Clar's Goblets

Mishra et al. have recently synthesized a "π-extended Clar's goblet". This is a "concealed" non-Kekuléan condensed benzenoid hydrocarbon formed by (a) adding to Clar's goblet some extra layers of benzenoid rings and (b) simultaneously changing the size of the moiety at the center of the structure from one hexagon to two hexagons─thereby changing that moiety from "benzenoid" to "naphthalenic". This idea is generalized and the "topological" ring-currents in Clar's goblet, and several of its homologues and oxidation states, are compared with those arising from these new structures. Quantitative calculations of topological ring-currents in these open-shell systems necessarily incorporate the technique of "Configurational State Averaging". Their predictions are compared with those from pictorial current maps generated by more sophisticated ab initio and pseudo-π calculations. It is found that (a) adding or removing electrons from frontier nonbonding orbital shells makes no difference to the ring current; (b) the number of unpaired electrons in a given goblet depends on the number of layers in it, but not on its girth; (c) as the goblet becomes "fatter", the current within the central moiety increases and the central rings become "less empty"; there is, therefore, a greater mixing of current between the upper and lower triangles within each goblet as their girths become larger; and (d) the Hückel-London "topological" calculations predict that the direction of the current around the periphery of any goblet will be counterclockwise (diamagnetic)─a conclusion that is invariably confirmed by calculations at the ipso-centric pseudo-π level.