Electrophile affinity: quantifying reactivity for the bromination of arenes.

Electrophile affinity (Ealpha), a recently proposed theoretical construct based on computed energies of arenium ion formation, rationalizes the substrate reactivity and regioselectivity of S(E)Ar bromination of three sets of available experimental arene data where closely related conditions had been employed uniformly. The Ealpha parameters (computed at B3LYP/6-311+G(2d,2p)) correlated very well (r = 0.987) with the partial rate factors (log f) for 18 regiospecific brominations of benzene and various methyl benzenes. Analysis of the bromination reactivities of 32 mono- and polysubstituted benzenes including various polar groups gave similar results (r = 0.982). The electrophile affinity treatment also accounted satisfactorily (r = 0.957) for bromination reactivities of polybenzenoid hydrocarbons. Conversely, comparisons with NBO-based charges and the electrostatic potential at nuclei (EPN) were not generally successful. The uniform effectiveness of Ealpha treatments for the cases analyzed with regard both to relative substrate reactivity (e.g., benzene vs toluene) and to regiospecificity (e.g., the positional reactivity of toluene) supports the "limiting case" conventional interpretation of the electrophilic aromatic substitution mechanism as being governed by the energy of sigma-complex formation. Although other mechanisms are possible under different conditions, the computed energies of arene-dibromine pi-complex formation for the polysubstituted benzene set examined correlated poorly with experimental reactivity data (r = 0.714) and only varied from 1.8 (for benzene) to 3.5 kcal/mol, in contrast to the 10(12) range in reactivity measured experimentally.