Dications of fluorenylidenes. Relationship between electrochemical oxidation potentials and antiaromaticity in diphenyl-substituted fluorenyl cations

The antiaromaticity of a series of dications of p-substituted diphenylmethylidene fluorenes was explored using three criteria attributed to aromaticity/antiaromaticity. The relative stability of the dications (energetic criterion) was measured via the redox potentials obtained by electrochemical oxidation under very fast sweep rates with microelectrodes. Comparison of redox potentials with those of a model system, p-substituted tetraphenylethylenes, shows relatively small destabilization of the potentially antiaromatic fluorenylidene dication. However, the amount of destabilization is comparable with the limited electrochemical data available for other antiaromatic systems. Nucleus independent chemical shifts (NICS) were calculated for these dications (magnetic criterion) and indicated their antiaromaticity. A good linear relationship between experimental and calculated (B3LYP/6-31G(d)) H-1 and C-13 NMR shifts for the three dications, 3c, 3e, and 3f, for which NMR data has been reported, validated the accuracy of the NICS values. Bond length alternation/ elongation (structural criterion) was explored via the harmonic oscillator model of aromaticity (HOMA) using the geometries calculated with density functional theory, but there was insufficient variation to evaluate relative antiaromaticity. In addition, the presence of benzannulation appears to restrict bond length alternation to such an extent that the magnitude of the HOMA index is of little use in evaluating the antiaromaticity of many polycyclic hydrocarbons. Both NICS values and redox potentials for formation of the dication in these systems show a strong linear correlation with sigma(p)(+) values, with the more antiaromatic fluorenylidene dication possessing the more electron-withdrawing substituent. The correlation between NICS values and redox potentials is also good, as might be expected, suggesting a strong relationship between magnetic and energetic characteristics of antiaromaticity. However, magnetic characteristics appear to be a more sensitive probe than energetic characteristics evaluated through redox potentials or structural characteristics evaluated through HOMA calculations.