Vibrational predissociation of triatomic van der Waals molecules

Abstract

In this paper we advance a quantum mechanical colinear model for vibrational predissociation on a single electronic potential surface of a linear triatomic van der Waals molecule X⋅⋅⋅BC, where BC is a conventional diatomic, while X represents a rare-gas atom. The zero-order states of the system are represented as products of an eigenfunction of the vibrating BC bond and a function describing the (bound or unbound) motion of X relative to the center of mass of BC bond which is frozen at its equilibrium configuration. The residual interaction representing the deviation between the interaction potential of X with the vibrating BC molecule, and the interaction of X with the frozen diatomic, induces discrete–continuum and continuum–continuum coupling. On the basis of the analysis of these coupling terms we assert that the zero-order basis provides a reasonable description of the initial and final states. We have also demonstrated that the zero-order resonance widths are small relative to their spacings and, furthermore, we have shown that continuum–continuum couplings prevail essentially only between adjacent continua. The dynamics of vibrational predissociation were reduced to the problem of the decay of a single resonance into a manifold of adjacently coupled continua. Closed analytical expressions for the rate of vibrational predissociation and for the vibrational distribution of the products were derived incorporating the effects of discrete–continuum and continuum–continuum coupling. We have explored the dependence of the rate of vibrational predissociation on the frequency of the BC molecule establishing a new energy gap law for this process. We have also investigated the dependence of the rate on the potential parameter of van der Waals bond and on the mass of the rare-gas atom. Finally, a study of the nature of the final vibrational distribution of the diatomic fragment resulting from the vibrational predissociation process was provided.