Effect of medium relaxation on the acidity constants of electronically excited states obtained by the Fِrster cycle method

The theoretical basis for the calculation of acid dissociation constants in the lowest excited singlet or triplet state of organic compounds has been reexamined in light of a recent study on solvatochromism. A mathematical analysis based on the Onsager cavity model reveals that the absorption or emission frequency of an acid and its conjugate base, as they appear in the Förster equation, should be replaced with the averages of absorption and emission frequencies corresponding to the 0–0 transition of acid and base, respectively, in order to account for Franck–Condon effects on the free energy balance. The free energy of spontaneous medium relaxation is found to be the same for absorption and emission, and proportional to one-half of the Stokes shift. in premise of the proposed method, besides the obvious requirement that both the acid and its conjugate base should fluoresce or phosphoresce, is that each excited state exists long enough for equilibrium with the medium to be established prior to emission.