Stochastic classical trajectory approach to relaxation phenomena. I. Vibrational relaxation of impurity molecules in solid matrices

We present a theory of impurity vibrational relaxation in condensed media based on computer simulation of the classical equations of motion of the impurity molecule and a small number of neighboring host atoms. The host atoms are in communication with the remainder of the lattice through the presence of stochastic forces and damping terms that are constructed from knowledge of the phonon spectrum of the solid. Temperature is introduced via the fluctuation-dissipation theorem. The method is applied here to a Cl₂ impurity molecule imbedded in an argon matrix. The dependence of energy relaxation and dephasing times on interaction parameters is monitored, and comparison is made with recent spectroscopic measurements on this system.