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 Kramers 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.
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