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JOURNAL OF CHEMICAL PHYSICS
VOLUME 108, NUMBER 16
22 APRIL 1998
Nonequilibrium unimolecular dissociation influenced by intramolecular vibrational energy redistribution Toshiko Kato¯ Seibo Jogakuin Jr. College, Fukakusa, Fushimi-ku, Kyoto, 612-0878, Japan
~Received 22 September 1997; accepted 21 January 1998! Unimolecular dissociation rates of energized molecules influenced by the slow intramolecular vibrational energy redistribution ~IVR! are formulated for no-barrier potentials of the reaction coordinate R. The master equation as to states projected on the reactive mode is presented and is solved by reducing the equation to an equivalent diffusion equation. An approximate solution for the steady state condition gives the generalized dissociation rate constant k D which is expressed as 21 21 21 k 21 D 5k diff 1k de 1k RRKM , where k diff , k de , and k RRKM represent the internal energy diffusion rate constant, equilibrium barrier crossing rate constant by bound-continuum transitions, and the fragmentation rate constant corresponding to the flux which crosses the critical configuration R 5R ‡ , respectively. The former two rates, which are due to IVR, are expressed by the transition kernel between states of the reactive mode, and the latter gives the RRKM rate which is valid in the rapid IVR limit. The rate limiting steps for various reactions are discussed. © 1998 American Institute of Physics. @S0021-9606~98!00816-2#
I. INTRODUCTION
into fragments’ vibrational (V), rotational (R), and interfragment (T) modes, where the reactive T mode is composed of translational (TT) and orbital (TL) modes, a scheme of reactive energy and angular momentum transfers for no-barrier association and dissociation reactions was presented. An example of the time evolution of the reactive mode energy E T and interfragment distance R of an energized reactant NO2 pair in the gas phase is shown in Fig. 1, and E T vs R curves of the association and dissociation processes of the trajectory are shown in Fig. 2. The reactive mode energy E T , which is defined as the sum of the potential and kinetic energies of interfragment motion, was found to play a key role in dissociation dynamics; a reactant pair associates when E T ,0 and the pair dissociates when E T .0. Energy transfer among T2R2V modes continues during the pair is bound, which is an energy redistribution process among vibrational degrees of freedom of the parent molecule. Dissociation into fragments was found to occur by three steps: first, energy redistribution among T2R2V modes at an inner turning point of interfragment motion, where E T changes sign from negative to positive by VT ~from V to T mode! and/or TR ~from T to R) followed by RT energy transfers, and the product vibrational distribution is determined; second, energy redistribution among TT 2TL2R modes at an outward region, where interfragment orbital angular momentum l is determined, E T becomes larger than the l dependent effective barrier V eff(R l ) which is slightly positive, and the product rotational distribution is determined; and third, separation of fragments by transferring energy from TL to TT with constant E T and l. When positive E T acquired in the first step is found to be E T 0 which reflects the separating fragments from I to R is shown by thin lines.
ible passage to products occurs by the translational energy given to the reactive mode. A phase space surface S PS defined by the reactive mode energy E T 50 must be identified as another TS which allow partial recrossing when E T
