The kinetics of internal energy randomisation in thermal unimolecular reactions

Abstract

Huw OWEN PRITCHARD. Can. I. Chem. 58,2236Chem. 58, (1980. The aim of this paper is to present a minimal theory of thermal unimolecular reactions, including explicitly the kinetics of intramolecular randomisation processes. A quasi-diatomic model is formulated and, within the framework of the model, both firstand second-order randomisation processes among reactant and product states are examined.It is concluded that a vital mechanism for the intramolecular energy randomisation in thermal unimolecular reactions is a collisional one. On this assumption, a straightforward derivation of the Polanyi-Wigner specific rate function, as we have reinterpreted it, becomes possible.At the same time, anomalies in the fall-off curves for the thermal isomerisations of methyl isocyanide and ethyl isocyanide can be accounted for very simply: in the former case, values for both the first-and second-order randomisation rate constants can be derived, but in the latter case it is only possible to establish a lower limit for the second-order randomisation rate constant.Huw OWEN PRITCHARD. Can. I. Chem. 58.2236Chem. 58. (1980. . , Cet article a pour but de pr6senter une theorie minimale des riactions unimoleculaires thermiques incluant explicitement la cinktique du mode de distribution au hasard intramol6culaire. On formule un modtle quasi-diatomique et on examine B I'intCrieur du squelette de ce modtle le mode de distribution au hasard d'ordre 1 et d'ordre 2 entre les r6actifs et les produits.On conclut que le mtchanisme essentiel de I'tnergie intramoltculaire de la distribution au hasard dans des reactions thermiques unimoleculaires est un m6canisme de collision. Sur cette base, il devient possible de dtriver directement la fonction de vitesse I specifique de Polanyi-Wigner telle que nous I'avons rkinterpretk. En m6me temps, on peut simplement tenir compte des anomalies dans l'abaissement des courbes des isom6risations thermiques des isocyanures de mkthyle et d'6thyle: dans le premier cas, les valeurs des constantes de vitesse d'ordre un et d'ordre deux de la i distribution au hasard peuvent 6tre dCriv6es mais dans le second cas on peut seulement 6tablir une limite infkrieure pour laconstante de vitesse d'ordre deux de la distribution au hasard.[Traduit par le journal]

Improved formulae for thermal unimolecular reaction rates with randomisation failure

“…This solution followed fairly closely the lines of a previous approximate treatment of the problem, in which it was assumed that the relaxations with rates p and p, were separable, leading to the calculation of an effective rate constant d, [ -k ( E ) ] with I which the population of each grain would decay for the given randomisation rate p, ( 2 ) . This approach to the coupled p , p, I problem led to formulae which were not always easy to use numerically because of cancellation; now, we develop a much more direct derivation of the rate constant (yo) for the coupled problem, resulting in a final expression which is relatively impervious to cancellation difficulties.…”

Some analytic properties of the master equation for unimolecular reaction

“…The strong-collision result noted above has another important consequence: it facilitates a simple derivation of the quantum reformulation of the Polanyi-Wigner &(Z£)-function, and provides a simple mechanism through which the explicit kinetics of internal energy randomization can be introduced into unimolecular calculations (Pritchard 1980).…”

Defective modelling of chaotic motions on empirical potential energy surfaces

“…A second cornerstone is that states depleted by reaction are replaced on a time scale much faster than the decay processes; in the case of a single molecule, or at the low-pressure limit, this randomisation process must be first-order, although it may have a second-order component at higher pressures. 1,2 The mechanism of this process may be envisaged as follows: we start from a ground-state molecule, for which the internal motions are regular and vibrational spectra can be observed, but as the energy rises, due to anharmonicities, a pair of spectral lines will merge, i.e. have the same energy, and the wave function becomes indeterminate.…”