The Kramers model of chemical relaxation in the presence of a radiation field

The combined use of the ‘reduced’ model theory, adiabatic elimination of the fast variables and continued fraction procedure is shown to make it possible to study chemical relaxation in the presence of radiative excitation. This requires that the reaction coordinate be assumed to be slow compared to the velocity. The latter variable, in turn, has to be assumed to be slow compared to the high-frequency ‘thermal bath’ dynamics. The strong diffusional assumption (the variation of reaction coordinate being very slow compared to the velocity) is shown to result in a simple analytical expression for the rate of escape from a potential well. For low-frequency radiation fields not even the higher-order contributions of the adiabatic expansion can produce significant corrections to these analytical formulae. These results are insensitive to whether the additive stochastic force is really white or the velocity autocorrelation function can exhibit a damped oscillatory behaviour. On the contrary (in the latter case, which is especially relevant to the field of molecular dynamics at liquid state) high-frequency fields are shown to excite the high-frequency modes of the ‘thermal bath’, thereby leading to significant changes in the short-time dynamics of the reacting system. Our approach permits information to be transmitted from this short-time regime to the long-time one concerning the escape from the reactant well.