  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.
