Re-interpretation of the 2(N+1)2 rule for polyhedral closed-shell π-systems

The 2(N+1)2 rule for cage molecules is not always associated with aromaticity. This is due primarily to the fact that this rule does not take into account the arrangement of individual circuits in a polycyclic π-system. Therefore, some polyhedral systems with 2(N+1)2 π-electrons may have negative topological resonance energies (TREs) even if they have large negative nucleus-independent chemical shift (NICS) values at the cage centers. In general, spherical systems with 2(N+1)2 π-electrons do not exhibit marked bond-length alternation even if they are not aromatic at all.