Excited-state reversible geminate reaction. II. Contact geminate quenching

A realistic description of the kinetics of excited-state proton transfer to solvent ~PTTS! involves several simultaneous processes. Perhaps most well-studied is the reversibility of this diffusion-influenced reaction, leading to the t asymptotic decay of the initially bound state. This shows that the solvated geminate proton may recombine with the base adiabatically, in the excited electronic state. At the same time, the acid and base forms decay to their ground electronic state. To simplify the problem, it has mostly been assumed that their excited-state lifetimes are equal. In reality, the base has a longer lifetime, particularly in nonprotic solvents. The effect of the different lifetimes has been treated in Part I of this work, revealing an interesting transition in the long-time asymptotic behavior. In addition to reversible binding, there appears to be a strong proton-induced excited-state quenching under certain conditions. Already the steady-state work of Harris and Selinger showed strong quenching of 1-naphthol by homogeneous protons. The quenching effect has been attributed to a nonadiabatic proton attack on a ring site. However, low pH medium is not a prerequisite for promoting this reaction. Pines and Fleming demonstrated that the geminate proton itself may quench the 1-naphthol. The excited acid then decays according to the t law, whereas the excited base approaches its limiting behavior with the t law characteristic of irreversible binding reactions. The assumption of Pines and Fleming, that at asymptotically long times the two reaction channels available to the geminate proton are independent, has never been rigorously proven. This is shown by Eq. ~3.18! below, which provides the long-time asymptotics for the acid and base forms in the presence of both quenching and different lifetimes. In addition, an extended long-time solution is obtained which is seen to be a useful approximation over a wide time range. This is demonstrated in comparison with experimental data, involving both the quenching and the two-lifetime effects. Thus a realistic description of geminate PTTS reactions in the excited state is finally achieved. Mathematically, the present work bears heavily on the exposition of Part I. The addition of quenching is a seemingly minor modification to the partial differential Smoluchowski-type equation. Nevertheless, it leads unavoid-