Inverse optically-induced ring currents in ring-shaped molecules

Permanent electronic ring currents can be supported within a manifold of $\Gamma_E$ degenerate excited electronic states as $E_{\pm} = E_x \pm i E_y$ excitations. This requires at least a 3-fold-symmetry rotational axis or higher, and includes the subclass of ring-shaped molecules. In [Phys. Rev. Res. {\bf 3}, L042003 (2021)] we showed the existence of inverse-current manifolds, where the direction of the electronic ring-current in each degenerate state $E_\pm$ is opposite to the circular polarization of the generating light-fields. This phenomenon can be traced back to vibronic effects, namely the exchange of orbital angular momentum between the circulating electrons and vibrational modes with the required symmetry. Here we consider the case of fixed nuclei and find that ring-shaped molecular systems can posses inverse-current manifolds on a purely electronic-structure basis, i.e. without intervention of vibronic coupling. The effect is illustrated and explained first on a simple tight-binding model with cyclic symmetry, and then considering the {\it{ab initio}} electronic structure of benzene and sym-triazine. A framework for discriminating regular- and inverse-current $\Gamma_E$ manifolds in molecules using quantum chemistry calculations is provided.