On the assumption of external bath equilibrium, a set of simultaneous linear generalized Langevin equations (GLE) for a microscopic Hamiltonian is derived, whose potential function includes cubic (i.e., nonlinear) coupling terms, which are linear in internal coordinates but quadratic in external bath coordinates. Furthermore, on the linear GLE treatment, a closed expression of time-dependent friction coefficient and a rate constant in the Grote-Hynes theory (GHT) are derived microscopically, reflecting the reactant and solvent structures; By comparing the rate constant of GHT with that of the multidimensional transition-state theory (TST) for the whole solution system, we conclude that these rate expressions are different from each other and the deviation is due to the dynamic effect via the nonlinear coupling among the reaction, internal, and external normal coordinates. Moreover, the friction coefficient depends on temperature and the deviation becomes larger with temperature increasing. By the second-order perturbation theory, we have estimated the deviation which is approximately equal to a transmission coefficient kappa, for a real cluster reaction system : the formic acid-water-water system. We have obtained kappa of 0.92, which is smaller than unity. A mode analysis shows that two hindered translational motions of the solvent with low frequencies prevent the reaction from proceeding. Besides, we have investigated the isotope effect of a medium water molecule and found that the dynamic isotope effect for the reaction is quite large, i.e., kappa for heavy water is much smaller than that for light water. Not the change of the reactive frequency on the free energy surface but that of the frictional effect in the deuterium substitution mainly contributes to the isotope effect. Further, the temperature dependence of kappa for the reaction has been estimated and it is found that kappa becomes smaller with temperature increasing and the change of the frictional effect in temperature contributes to the temperature dependence of kappa more largely than that of the reactive frequency on the free energy surface.