ON THE ROLE OF THE ENERGY-LOSS IN TURNOVER THEORIES OF ACTIVATED RATE-PROCESSES

The diffusion theory of chemical reactions established by Kramers mode ls a chemical reaction as the escape of a Brownian particle from a pot ential well. Kramers studied the dependence of the escape rate of the particle on the frictional damping in two limits, namely, when the dam ping is weak so that the rate limiting step is the transfer of energy from the bath to the particle, and in the spatial diffusion regime whe n the transfer of energy is fast enough to maintain thermal equilibriu m of escaping particles. Mel'nikov and Meshkov extended the Kramers th eory to the full damping range by using the Wiener-Hopf method. The sy stematic solution of the non-Markovian turnover problem was given by P ollak, Grabert and Hanggi who proposed a theory that combines the norm al mode technique, as well as the approach by Mel'nikov and Meshkov. T he key quantity appearing in both turnover theories is the loss of ene rgy of the particle per oscillation. The theories, however, are asympt otic in the energy loss in the sense that their approximations for thi s quantity are correct only in the weak damping limit. In this paper, we present an alternative to the existing approximations for the energ y loss, which approaches the correct limiting behavior for both weak a nd strong friction. The basic idea is to employ a properly defined ene rgy loss of the deterministic particle dynamics. Its use in the overal l rate expression is shown to considerably improve the agreement betwe en analytical calculations and exact numerical results for the escape rate. (C) 1998 Elsevier Science B.V. All rights reserved.