The well‐known phenomenon of proton dissociation from excited‐state hydroxy‐arenes is analyzed by the Debye–Smoluchowski equation which is solved numerically with boundary conditions which account for the reversibility of the reaction. The numerical solution is then compared with the measured dissociation profiles which were obtained by picosecond time‐resolved fluorescence spectroscopy. The intrinsic rate constants thus determined are used to predict steady‐state rates, yields, and pK values, in agreement with experiment.

Intramolecular reactions inside macromolecules (e.g., binding of ligands to iron inside heme proteins) may often be coupled to slow random fluctuations in the reaction center geometry. This motion is ‘‘perpendicular’’ to the reaction coordinate. It can be described as bounded diffusion in the presence of a binding potential field and an intramolecular rate constant which depends on the perpendicular degree of freedom. The diffusion equation is solved under the appropriate reflective boundary conditions. The transient decay of the total population is multiexponential (power law) for small diffusivity, changing to monoexponential kinetics for large diffusivity. For large times or large diffusivity, direct integration is very tedious, but an eigenvalue expansion converges rapidly. It also allows the calculation of the ‘‘average survival time’’ (an extension of the ‘‘first passage time’’) a natural candidate for replacing the reciprocal rate constant in multiexponential kinetics. An example is given for electron transfer between two loosely bound sites in a macromolecule. The average survival time shows a non-Kramers dependence on diffusivity, of the type found in the binding kinetics in heme proteins.

A unified theory of reversible diffusion‐influenced geminate and pseudo‐ first‐order reactions is developed. Explicit results are presented for the time dependence of the fraction of molecules that are dissociated at time t for a variety of initial conditions. To introduce the basic ideas of our approach, an elementary and rather complete treatment of the irreversible reaction between a pair of interacting, spherically symmetric particles is presented. The focus is on deriving relations among survival probabilities and bimolecular time‐dependent rate coefficients for the radiation and absorbing boundary conditions and the asymptotic behavior of these quantities. These relations are then generalized to reversible geminate reactions. For example, it is shown that the separation probability for an initially bound pair satisfies a simple convolution relation involving the survival probability of an irreversibly reacting geminate pair initially at contact. An analytic expression is obtained for this separation probability that is exact for free diffusion and is an accurate approximation for interacting particles. Finally, the Smoluchowski approach to irreversible pseudo‐first‐order reactions is extended to reversible reactions. The analysis is based on the generalization of the convolution relations that are rigorously valid for isolated pairs.