Antiaromaticity in fluorenylidene dications. Experimental and theoretical evidence for the relationship between the HOMO/LUMO gap and antiaromaticity

The relationship between the calculated energy of the HOMO-LUMO gap, where (ε_LUMO - ε_HOMO)/2 is defined as Δ_HL, and of the longest wavelength transition in the UV-visible spectrum, ΔE, was examined for a series of aromatic and antiaromatic cations and dications. TD-DFT calculations accurately modeled the energies of a series of dications including fluorenylidene dications whose UV-visible spectra are reported, as well as the energies of a series of aromatic and antiaromatic monocations whose spectra were previously reported. There is a linear correlation of the energy of the longest wavelength transition, ΔE _calc, with Δ_HL. There is no linear relationship between ΔE_calc and the sum of the NICS values, but there is a linear relationship between ΔE_calc multiplied by the number of atoms in the conjugated system, ΔE_calc(T), and the sum of the NICS values. There is also an approximate linear relationship between the average ¹H NMR shift and the sum of the NICS values. These relationships give further support to the suggestion that the magnetic and energetic criteria of aromaticity and antiaromaticity are related. Furthermore, the data suggest that species that have ΔE_calc(T) < 20 are antiaromatic whereas those with ΔE_calc(T) > 30 are aromatic.