  We study the dynamics of a Brownian particle in Morse potential under thermal
fluctuations, modeled by Gaussian white noise whose amplitude depends on
absolute temperature. Dynamics of such a particle is investigated by
numerically integrating the corresponding Langevin equation. From the mean
first passage time (escape time), we study the dependence of Kramer's rate on
temperature and viscosity of the medium. An approximate expression for the
reaction rate is found by solving differential equation for the mean first
passage time. The expression shows a temperature dependent pre-factor for the
Arrhenius equation. Our numerical simulations are in agreement with analytical
approximations.
