Vibrational Dynamics of Molecules above Dissociation.

Local mode A-B-A triatomic molecules are modelled as coupled Morse oscillators using classical and quantum techniques. Classical studies indicate large volumes of non-dissociating classical phase space, even well above the dissociation threshold. The trapped classical motion corresponds to excitation in both bond modes of the system. Quantum studies have been performed as a function of coupling constant (mass ratio) and of dissociation energy. Quantum doubly excited vibrational resonances are found with lifetimes of up to 10('6) vibrational periods. The lifetimes of the states as (H/2PI) (or dissociation energy) is varied are in accordance with the correspondence principle. Substantial deviation from the predictions of statistical theories is noted in the distributions of lifetimes, as well as in the fact that all of the resonances are only weakly coupled to the "direct" dissociation channels. Approximate quantum calculations, based on the Golden Rule are applied, successfully, to the calculation of these lifetimes. Semiclassical approximations are incorporated into the Golden Rule formalism, leading to a technique for the calculation of quantum lifetimes, which can be simply applied to arbitrary molecular potential energy surfaces.