Model studies of mode specificity in unimolecular reaction dynamics

Essentially exact quantum mechanical calculations are carried out to determine the energies and lifetimes of the quasibound states for a system of two (nonlinearly) coupled oscillators (one of which is harmonic, the other being able to dissociate). For weak coupling the system displays mode specificity, i.e., the unimolecular rate constants are not a monotonic function of the total energy, but increased coupling and frequency degeneracy tends to destroy mode specificity. A somewhat surprising result is that for a given coupling the degree of mode specificity is roughly independent of the energy, in marked contrast to the fact that there is an energetic threshold for the onset of ''stochastic trajectories'' of the corresponding classical system: i.e., there seems to be no relation between statistical/mode-specific behavior of the unimolecular rate constants and stochastic/regular classical trajectories. In order to be able to treat more physically relevant models; i.e., those with more than two degrees of freedom, a semiclassical model is constructed and seen to be able to reproduce the accurate quantum mechanical rates reasonably well