Reversible Excited-State Proton Geminate Recombination: Revisited.

About three decades ago, Pines and Huppert found that the excited-state proton transfer to water from a photoacid (8-hydroxy-1,3,6-pyrene trisulfonate (HPTS)) is followed by an efficient diffusion-assisted reversible geminate-recombination of the proton. To model the reaction, Pines, Huppert, and Agmon used the Debye-Smoluchowski equation with boundary conditions appropriate for reversible contact reaction kinetics. This reaction model has been used successfully to quantitatively fit the experimental data of the time-resolved fluorescence of HPTS and several commonly used photoacids. A consequence of the reversibility of this reaction is an apparent long-time tail of the photoacid fluorescence signal, obeying (after lifetime correction) a t-3/2 power law asymptotics. Recently, Lawler and Fayer reported that in bulk water the observed power-law decay of the long-time fluorescence tail of HPTS is -1.1 rather than -1.5, as expected from the spherically symmetric diffusion model. In the current study, we reaffirm our previous reports of the power-law behavior of HPTS fluorescence. We also demonstrate that molecular-level complications such as the deviation from spherical symmetry, rotational dynamics, competitive proton binding to the sulfonate moieties of HPTS, distance-dependent diffusion coefficient, and the initial starting point of the proton can affect the observed kinetics only at intermediate times, but not at asymptotically long times. Theoretically, we analyze the rebinding kinetics in terms of the number of extrema of the logarithmic derivative, showing subtle effects on the direction of approach to the asymptotic line (whether from above or below), which also appears to be corroborated experimentally.