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High level ab initio and density functional theory computations have been used to assess the aromaticity and antiaromaticity of the cations and anions derived from cyclopentadiene (C5H6), indene (C9H8), and fluorene (C13H10). On the basis of the IGLO calculated magnetic susceptibility exaltations (Λtot) and the GIAO computed nucleus independent chemical shifts (NICS), the cyclopentadienyl (C5H5-), indenyl (C9H7-), and fluorenyl (C13H9-) anions are, as expected, highly aromatic as compared with benzene, naphthalene, and anthracene. The aromaticity or antiaromaticity of the individual rings has been characterized by using the nucleus independent chemical shifts (NICS) based on the magnetic shieldings calculated at the ring centers. In addition to NICS, the computed Li+ NMR chemical shifts, another useful aromaticity probe, provide data for the individual rings. The singlet cyclopentadienyl (C5H5+) and indenyl (C9H7+) cations are as antiaromatic as cyclobutadiene and benzocyclobutadiene. However, the fluorenyl cation (C13H9+) is non-aromatic by the calculated magnetic susceptibility exaltation, due to the essentially complete compensation of the diamagnetic and the paramagnetic character. Such compensation effects are shown directly by the geometric, energetic, and magnetic differences between the delocalized and localized systems computed by means of the orbital deletion procedure (ODP), in which the critical carbocation p orbital is “deactivated”. This shows the delocalization energies of aromatic cations to be much larger than those of the antiaromatic cations, and the former are stabilized and the latter are destabilized relative to non-aromatic systems. In contrast to the cyclopentadienyl cation, which has a triplet ground state, the triplet indenyl and fluorenyl cations are higher in energy than their singlet states by 9.2. and 14.9 kcal/mol, respectively.
Jiao et al. (Tue,) studied this question.