Background of the Hammett equation as observed for isolated molecules: meta- and para-substituted benzoic acids

Fundamental model compounds for the Hammett equation, meta- and para-substituted benzoic acids, were investigated by the density functional theory at the B3LYP/6-311+G(d,p) level. Energies of 25 acids and of their anions were calculated in all possible conformations and from them the energies of the assumed mixture of conformers. Relative acidities correlated with the experimental gas-phase acidities almost within the experimental uncertainty, much more precisely than in the case of previous calculations at lower levels. Dissection of the substituent effects into those operating in the acid molecule and in the anion was carried out by means of isodesmic reactions starting from monosubstituted benzenes. Both effects are cooperating in the resulting effect on the acidity; those in the acid molecule are smaller but not negligible. They are also responsible for some deviations from the Hammett equation (through-resonance of para donor substituents) and for the weaker resonance in the acid molecule in meta derivatives; in the anions the inductive and resonance effects are almost equal. On the other hand, the cooperation of effects in the acid and in the anion makes the relative acidity more sensitive to electron withdrawing and is probably one of the reasons why the Hammett equation is so generally valid.