Selection rules for ring currents in radial π systems: trannulene substructures in hydrogenated fullerene cages

Maps of induced current density are computed with the coupled Hartree–Fock, distributed-gauge, CTOCD-DZ method for the trannulene isomers of the hydrogenated fullerenes C20H10 and C24H12. Orbital analysis identifies ‘in-plane’ ring currents in trannulenes that obey equivalent selection rules to those for conventional annulenes. Thus, in systems of either type, 4-electron diatropicity is associated with electron counts of 4n + 2, 2-electron paratropicity with 4n.