Accounting for memory effects in calculating the rate constant of a chemical reaction

The first-escape-time method has been used in solving the problem of calculating chemical reaction rate constants on the basis of a model in which a classical particle passes from one potential well to the other, this model describing non-Markovian Brownian motion by means of a generalized Langevin equation with the correlation function of the Ornstein-Uhlenbeck process. Singular perturbation theory was used in the solution. An analytical formula was obtained for the rate constant; calculations using this formula require the solution of a cubic equation. Analysis of the results shows that within a certain interval of parameters, non-Markov character is not manifested; i.e., the rate constant of the process is very little different from the result of the Kramers model. It has been established that the result obtained by this method is the same as that obtained by calculating the rate constant on the basis of the stationary flux method.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 2, pp. 138–143, March–April, 1988.