Excited-state reversible geminate reaction. I. Two different lifetimes

Abstract

We obtain an accurate long-time solution for the diffusive kinetics of an excited geminate pair dissociating reversibly in solution, where the excited-state lifetimes of the bound and unbound states may be nonequal. We analyze the long-time asymptotic behavior, finding a transition between two types of behaviors. In region A, the excited bound pair decays as t−3/2 exp(−t/τ0′), where τ0′ is the lifetime of the unbound state. In region AB, the decay is a pure exponential. At the critical value of the parameters where the transition occurs, we find a t−1/2 exp(−t/τ0′) decay. These predictions are tested against an exact numerical solution of the corresponding coupled partial differential equations. For region A, we supply an experimental example involving time-resolved excited-state proton transfer from 5-cyano-2-naphthol to dimethyl sulfoxide.