Diamagnetic and paramagnetic ring currents in expanded porphyrins

Ipsocentric current density maps are computed at the coupled Hartree-Fock level in the 6-31G** basis set for the planar C(2v) B3LYP geometries of the expanded porphyrins, sapphyrin and orangarin. Both give clearly dominant global macrocyclic ring currents, but with opposite senses of circulation: in 22[small pi] sapphyrin, a diatropic current runs, with some bifurcation, around the conventional 22-centre delocalisation pathway; in 20[small pi] orangarin, a paratropic current runs around the inner 17-atom pathway. In agreement with the annulene analogy for these macrocycles, analysis of orbital contributions shows that in each case topology, energy and symmetry of the frontier orbitals together determine the macrocyclic ring current. In sapphryrin, 4-electron diamagnetism (aromaticity) arises from translationally allowed HOMO-LUMO excitations as in benzene itself; in orangarin, 2-electron paramagnetism (antiaromaticity) arises from rotationally allowed HOMO-LUMO excitations as in planarised cyclooctatetraene. The active orbitals invoked in the explanation of ring currents are those involved in the longstanding four-orbital model of porphyrin electronic spectra.