Rate constants for chemical reactions limited by electron, proton, or atom-group transfer in a large molecular system are formulated for the case where the reaction coordinate is composed not only of intramolecular or atomic vibrational motions but also of conformational fluctuations of the system itself driven by thermal motions of solvent molecules. These fluctuations are diffusive, being describable in terms of Brownian motions. Their relaxation time tau-regarded as proportional to the viscosity-eta of solvents is much longer than periods of the vibrational motions. In this situation it is shown that when reactant populations get to decay single exponentially after a time of order tau in exthothermic reactions, rate constant k(s) tends, irrespective of initial conditions, to the inverse of the first passage time for initially thermalized reactants. This k(s) can be expressed as 1/(k(e)-1 + k(f)-1), where k(e) represents the thermal equilibrium rate constant obtainable by the usual theories such as the transition-state theory, while k(f) represents a fluctuation-limited rate constant decreasing with increasing tau or eta. When k(e) is written as nu-exp (-DELTA-G*/k(B)T) with the height DELTA-G* of the transition state and the frequency factor-nu at temperature T, we show k(f) approximately tau-alpha-nu-1-alpha-exp(-gamma-DELTA-G*/k(B)T) with positive constants-alpha and gamma both smaller than unity. When k(e) << k(f) in the small-tau-nu limit, we get k(s) approximately equal to k(e), covering the result of the usual theories. When k(f) << k(e) in the large-tau-nu limit, on the other hand, we get k(s) approximately equal to k(f). This limit is consistent with recent observations that k(s) is proportional to eta-alpha in some reaction, including biochemical ones. In this limit, k(s) (proportional to nu-1-alpha) depends only weakly on nu, which measures the strength of the matrix element causing the reaction. The reactant distribution is maintained in a nonthermal equilibrium form during the reaction.
