Angular momentum and spectral decomposition of ring currents: Aromaticity and the annulene model

By a widely accepted criterion, an aromatic (anti-aromatic) π-conjugated system is one that sustains a global diatropic (paratropic) ring current when perturbed by a perpendicular external magnetic field. Calculation of induced current densities by the specific distributed-gauge method known as the ipsocentric approach offers practical and conceptual advantages. Physically realistic distributions of current density are obtained with modest basis sets. In the ipsocentric choice, molecular orbital contributions are free of unphysical occupied - occupied mixing and so form the basis of an interpretation of current patterns in terms of frontier orbital symmetries, energies and nodal patterns. Selection rules for the sense of ring current in planar carbocycles can be formulated in terms of angular momentum: a diatropic (paratropic) current arises when a virtual excitation connects orbitals whose angular momentum quantum numbers differ by one (zero). Here we explore the extension of this reasoning to other systems based on the monocycle: to heterocycles and clamped systems, where the symmetry lowering can produce significant angular momentum mixing. It is shown that simple arguments can account for the existence and sense of current also in these systems, and hence for their aromaticity on the magnetic criterion. It is possible to understand why, for example, ab initio calculations show that clamping of a benzene (1) or cyclooctatetraene (2) cycle with cyclobutadieno-groups destroys the ring current of the free planar monocycle, but clamping with HB-BH or HN-NH units allows the current to persist, in planar geometries.