Aromaticity in spin-polarized systems: can rings be simultaneously alpha aromatic and beta antiaromatic?

The partition of the multicenter electron delocalization indices and the nucleus independent chemical shift indices into alpha and beta contributions in open-shell systems has been performed. In general it is shown that a full understanding of aromaticity in these systems cannot be achieved by restricting the calculations to the global properties but by dissecting these properties into alpha and beta terms. The 4n+2- and 4n-aromaticity rules for singlet and triplet annulenes, respectively, reduce to a general aromaticity rule when the alpha and beta terms are studied separately. This new rule allows us to extend the concept of conflicting aromaticities to radical systems that are simultaneously alpha-aromatic and beta-antiaromatic or vice versa. The existence of such systems is demonstrated here by means of multicenter electron delocalization indices and nucleus independent chemical shifts. Finally, the global aromatic/antiaromatic character of these radical systems is estimated by means of aromatic stabilization energy, which is shown to be either slightly positive or slightly negative, thus reflecting the small aromatic/antiaromatic character of these radicals and reinforcing the conclusions obtained with aromaticity indices.