Dynamical Approaches to Unimolecular Rates

In the previous chapters theories were discussed for calculating the unimolecular rate constant as a function of energy and angular momentum. The assumption inherent in these theories is that a microcanonical ensemble is maintained during the unimolecular reaction and that every state in the energy interval E → E + dE has an equal probability of decomposing. Such theories are viewed as statistical since the unimolecular rate constant is found from a statistical counting of states in the microcanonical ensemble. A dynamical description of unimolecular decomposition is concerned with properties of individual states of the energized molecule. Of interest are the decomposition probabilities for the states as well as the rate of transitions between the states. Dynamical theories of unimolecular decomposition deal with the properties of vibrational/rotational energy levels, state preparation and intramolecular vibrational energy redistribution (IVR). Thus, the presentation in this chapter draws extensively on the previous chapters 2 and 4. Unimolecular decomposition dynamics can be treated using quantum and classical mechanics, and both perspectives are considered here. The role of nonadiabatic electronic transitions in unimolecular dynamics is also discussed. A molecule which can dissociate does not, strictly speaking, have a discrete energy spectrum. The relative motion of the product fragments is unbounded and, in this sense the motion of the unimolecular system is infinite, and hence the energy spectrum is continuous. However, it may happen that the dissociation probability of the molecule is sufficiently small that one can introduce the concept of quasi-stationary states. Such states are commonly referred to as resonances since the energy of the unimolecular fragments in the continuum is in resonance with (i.e., matches) the energy of a vibrational/rotational level of the unimolecular reactant. For unimolecular reactions there are two types of resonance states. The simplest type, a shape resonance, occurs when a molecule is temporarily trapped by a fairly high and wide potential energy barrier. The second type of resonance, called a Feshbach or compound-state resonance, occurs when energy is initially distributed between vibrational/rotational degrees of freedom of the molecule which are not strongly coupled to the fragment relative motion, so that there is a time lag for unimolecular dissociation.