The stochastic theory and its relations to the general reaction rate theory

Abstract

A short review of the recent development of the stochastic approach to chemical reactions in condensed media is made. The relations of this approach to a general formulation of chemical kinetics are discussed on the basis of a many-frequency oscillator model. It is shown that the classical transition-state theory is not a particular case of the stochastic theory neither in the case of small viscosity nor in the case of large viscosity. The recent quantum generalizations of the stochastic theory are identical to earlier results of a quantum transition-state theory that correspond to the case of large viscosity. Such generalizations based on previous results of a collision theory are made for the case of small viscosity. It is shown that these quantum generalizations of the stochastic theory are possible only in the temperature range of moderate tunneling defined in terms of a characteristic temperature.

Nonlinear coupling model for reactions in dense media

“…This is also possible making use of TST if one is satisfied with the formal expression of this theory by disregarding the physical conditions of its validity. A previous analysis [10] of this point has shown that direct transition (no recrossing) of the saddle-point region can take place only when the thermal equilibrium in that region is disturbed.…”

“…The line of minimum energy q in (1) is a curved line [8,10], which coincides with a normal mode coordinate in the initial (final) and the transition states. If V 12 in (1) is not very small, the potential V(q) along q can be approximated with a parabolic function…”

“…where χ cl ac is a well-defined transmission coefficient [8,10]. Setting χ cl ac = 1, we obtain the classical expression of transition-state (or activated complex) theory.…”