A general quantum mechanical theory is considered for the diverse dissociation processes of polyatomic molecules. The theory emphasizes the use of the proper normal vibrational coordinates for both the initial state of the polyatomic molecule and the final state of the dissociation fragments. The present theory provides a significant advance over all previous ones that invoke the quasidiatomic hypothesis, wherein the reaction coordinate is taken to be an initial normal mode, the remaining fragment normal modes are assumed to be identical to initial state normal modes, and the dissociation into vibrationally excited fragments is assumed to arise from the final state interactions occurring during the recoil of the fragments. Our more general theory of the vibrational and translational energy distributions in the fragments leads to a generalized Franckndash;Condon description of dissociation processes in terms of multidimensional boundhyphen;continuum matrix elements which can be reduced to onehyphen;dimensional ones that are amenable to analytic approximation. The Franckndash;Condon theory leads to simple criteria for the occurrence of fragment vibrational population inversions. These criteria are dependent on known spectroscopic constants for both the initial molecule and fragments and the repulsive potential between the receding fragments. The effects of final state interactions on the product vibrational distribution are incorporated by the use of a semiclassical model which demonstrates that the Franckndash;Condon rearrangement type process is dominant for a large number of systems. The theory is explicitly used to evaluate the vibrational distributions for photodissociation of HCN and ICN. The theory may also be applied to predissociation, unimolecular decomposition, and collisional induced dissociation.
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