Abstract
The solvent effect on the prefactor of activated rate processes is usually described in terms of a Langevin equation or a generalized Langevin equation (GLE). The validity of such GLEs in the presence of a strong “external” potenial (activation energy barrier) has been verified only for unphysical limiting models. Starting from a microscopic description of the system, we obtain a set of conditions under which a GLE is valid. For effective particles moving along a reaction coordinate, X, this GLE is applicable to those particles which are initially at fixed position, X o, and a different GLE with a different friction, ζ 0( X 0, t), is required for particles in different initial positions. Thus, though a GLE may be suitable for describing the reactive motion over a restricted region ( piecewise validity), it is of doubtful validity when applied to the whole reaction path.
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