Dynamical treatment of unimolecular decomposition reactions. II. Short-range interfragment coupling and incomplete randomization

We investigate the dynamics of an isolated polyatomic molecule undergoing unimolecular dissociation. The intramolecular vibrational energy transfer step is treated by applying a theory of vibrational relaxation previously developed for permanently bound molecules. In contrast to an earlier study, the decomposition step is treated here subject to the assumption that, when sufficient energy is concentrated in the reaction coordinate, transitions between internal states of the molecule occur only while the incipient fragments are near their minimum classically allowed separation. Under such circumstances, it is generally not possible to divide configuration space cleanly into a randomized and a nonrandomized region, as required by the RRKM theory of unimolecular reactions. In spite of this, it is shown that, under certain conditions, the RRKM specific rate constant expression may remain valid. More generally, it is shown that the accurate specific rate constant assumes a form predicted by the transition state treatment of unimolecular reactions. The explicit rate expression derived here reveals factors which determine the accuracy of the transition state approximation for unimolecular reactions-the basic, simplifying assumption that a transition state exists which coincides with a "configuration of no return" for both decomposition and association reactions. Estimates based on our rate formulas suggest that the transition state approximation may often be sufficiently accurate to justify use of the RRKM rate expression. As part of our analysis of randomization and decomposition dynamics, we examine the time-dependent behavior of a molecule which has fragment-fragment interactions as described above but which is constrained to remain bound by the presence of an artificial "wall" which prevents the fragments from separating completely. It is found that statistical equilibrium may be achieved in this system-a significant result because the system violates some rather stringent assumptions previously invoked to prove randomization in bound molecules. This motivates a future search for a more general theory of intramolecular relaxation.