Patterns of Ring Currents in Conjugated Molecules: A Few-Electron Model Based on Orbital Contributions

Abstract

In the CTOCD-DZ (continuous transformation of origin of current density-diamagnetic zero) formulation of coupled Hartree−Fock theory for magnetic response of closed-shell systems, induced current density at each point is calculated with the gauge origin at that point. In addition to its economy and accuracy for total current maps, CTOCD-DZ is shown to yield a unique and physically motivated definition of, and symmetry criteria for, orbital contributions to current density. This leads to a few-electron interpretation of ring currents. Only the four HOMO electrons of an aromatic (4n+2)-electron monocycle contribute significantly to the ring current, and in general only a small subset of the high-lying π electrons dominate the more complex patterns of current in polycyclic π systems. Benzene, naphthalene, hexacene, pyracylene, coronene, and corannulene are treated as examples.