Classical diffusion model of vibrational predissociation of van der Waals complexes: truncated mean first passage time approximation

A classical diffusion theory of the vibrational predissociation for a triat omic van der Waals (vdW) complex A-BC is presented under the condition that the mean square energy transferred to the low-frequency oscillator per one "encounter'' with the repulsive part of the A-BC potential is small compar ed with the square of its dissociation energy. Unlike the case of a thermal dissociation of diatomic molecules in a heat bath, or from the case of fis sion of a strong bond in an isolated polyatomic molecule when the dissociat ion rate is given by the inverse of the mean first passage time, in the con sidered case of vibrational predissociation the dissociation energy is lowe r than the "thermal'' energy of the heat bath. For the present situation, a truncated first mean time approximation is developed and tested against nu merical solutions of the respective diffusion equation. It is shown that th e truncated first mean time approximation provides a reasonable approximati on to the predissociation rate, provided that the relevant diffusion coeffi cient depends comparatively strongly on the energy of the vdW oscillator. T his approach allows one to relate directly the mean square energy transferr ed to the vdW bond per one encounter in the initial energy state of the vdW oscillator to the rate of predissociation from this state.