Collision model for activated rate processes: turnover behavior of the rate constant

A theory of reaction rates is developed on the basis of the Bhatnagar-Gross -Krook model, which assumes instantaneous Maxwellization of the particle ve locity at each collision. This model may be regarded as an alternative to t he Kramers model for reaction dynamics in the condensed phase. The main res ults are two expressions for the rate constant for single- and double-well potentials. These cover the entire range of collision frequency. These expr essions predict a turnover of the rate constant as a function of the collis ion frequency, analogous to the Kramers-Mel'nikov-Meshkov solution for the rate constant in the Kramers model. In contrast to the prediction for the K ramers model, the maximal value of the rate constant is noticeably below th e TST estimate even for so high a barrier as 30k(B)T. This is a consequence of two facts: (1) The rate constant grows slowly from zero at small collis ion frequencies. (2) In addition, the rate of growth increases weakly with the barrier height, Delta U, as ln(Delta U/k(B)T). Simulated results indica te good agreement with the theory. (C) 1999 American Institute of Physics. [S0021-9606(99)51448-7].