A stochastic golden-rule treatment for thermal desorption of gases from solid surfaces

The thermal desorption rate of a gas molecule from a solid surface has been derived using a stochastic time-dependent perturbation method. In this approach the solid surface is modeled by a fluctuating thermal bath which exerts a random force on the gas molecule. The rate of desorption is derived using a first order time-dependent perturbation method and an ensemble averaging over the distribution of random force. We use a generalized Langevin equation to model the stochastic process. The final operator expression of the rate constant contains two parameters pertaining to the solid surface, i.e., temperature T and the friction kernel γ(t). A simple analytical expression is given when the molecule-surface bond is approximated by a truncated-harmonic potential, and both the high temperature and low temperature limits of the rate constant are given in this approximation. Simplified expression of rate constant is also obtained in the limit of Markovian approximation.