Dynamics of reactions involving diffusive barrier crossing

We develop a first passage time description for the kinetics of reactions involving diffusive barrier crossing in a bistable (and also in a more general) potential, a situation realized, for example, in some photoisomerization processes. In case the reactant is in thermal equilibrium, the first passage times account well for the reaction dynamics as shown by comparison with exact numerical calculations. A simple integral expression for the rate constants is presented. For a case involving a reactant initially far off equilibrium, a two relaxation time description for the particle number N(t) is derived and compared with the results of an "exact" calculation. This description results from a knowledge of N(t=0), N(t=0), ∫₀^∞dt N(t), i.e., the first passage time, and ∫₀^∞dt t N(t).