We present a model calculation for barrier crossing rates of a light particle such as hydrogen, lithium, or a light interstitial in a symmetric doublehyphen;well potential. At higher temperatures migration takes place through thermally activated processes, while the dynamics are dominated by tunneling at lower temperatures. We construct a model twohyphen;dimensional system that consists of a symmetric doublehyphen;well potential for the high frequency, light particle mode and a harmonic oscillator for the lower frequency mode coupled closely to the reactive mode. This model system is, in turn, immersed in a classical bath. The reaction rate is calculated without assuming thermal equilibrium either for the light particle mode or for the nonreactive mode. Two distinct symmetries of coupling are considered for tunneling. The energy relaxation rate within each well is shown to have a significant effect on the rate in the high temperature limit. The temperature dependence of low temperature tunnelinghyphen;dominated rates is determined by the type of coupling and by a parameter that describes the displacement of the nonreactive mode.
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