It is evident from these equations that trajectory calculations give microscopic, or state-to-state, information for a reaction. Finally, the thermal rate coefficient for the elementary reaction can be obtained by summing the k(v, J) over each weighted level [Pg.82]

In Table II we compare rate coefficients calculated [20] for the He + HCt reaction using three different theories - the ACCSA, the statistical adiabatic channel model (SACM) of Troe [14] and classical trajectory calculations [16]. The trajectory calculations have been parameterized to give the simple formula [Pg.8]

These calculations show that classical trajectory techniques as usually applied to chemical reactions are a useful tool for the study of cluster dynamics. We have made direct calculations of microscopic rate coefficients for some of the elementary steps of the early stages of nucleation. We have focused our attention on the formation and dissociation of quasibound clusters, however, this same approach would provide useful, fundamental information if applied to other mechanistic steps, particularly the stabliziation step, equation (2). [Pg.237]

The development of the collision dynamics approach to bimolecular reactions has for the most part departed from models that seek analytical expressions for rate coefficients, and has centered on trajectory calculations, a method made possible by the development of high speed computers. [Pg.80]

In Ref. Esposito, Capitelli, Kustova Nagnibeda (2000), the dissociation rate coefficients diss calculated within the framework of the Treanor-Marrone model are compared with those obtained from trajectory calculations Esposito, Capitelli Gorse (2000), some recommendations for the optimum choice for the parameter U for the specific reactions are given. Eigure 1 presents the temperature dependence of the state-dependent dissociation rate coefficients in an (N2, N) mixture. The coefficients are calculated for different [Pg.129]

Let us consider first the in vacuo cases. Dynamical aspects of the reaction in vacuo may be recovered by resorting to calculations of semiclassical trajectories. A cluster of independent representative points, with accurately selected classical initial conditions, are allowed to perform trajectories according to classical mechanics. The reaction path, which is a static semiclassical concept (the best path for a representative point with infinitely slow motion), is replaced by descriptions of the density of trajectories. A widely employed approach to obtain dynamical information (reaction rate coefficients) is based on modern versions of the Transition State Theory (TST) whose original formulation dates back to 1935. Much work has been done to extend and refine the original TST. [Pg.24]

We can calculate the thermal rate constants at low temperatures with the cross-sections for the HD and OH rotationally excited states, using Eqs. (34) and (35), and with the assumption that simultaneous OH and HD rotational excitation does not have a strong correlated effect on the dynamics as found in the previous quantum and classical trajectory calculations for the OH + H2 reaction on the WDSE PES.69,78 In Fig. 13, we compare the theoretical thermal rate coefficient with the experimental values from 248 to 418 K of Ravishankara et al.7A On average, the theoretical result [Pg.442]

Theoretical analyses of the reaction have been performed by Bettens et al. [39] and by Klippenstein et al. [ 15]. The former used classical trajectories on a calculated potential energy surface. Klippenstein et al. used high level electronic structure methods to calculate the potential energy surface, coupled with the analytical solutions outlined above [36], detailed transition state theory and trajectory calculations. Their paper contains a great deal of insight into the mechanism and the temperarnre dependence of the overall rate coefficient. [Pg.83]

Recent advances have resulted from the development of more powerful experimental methods and because the classical collision dynamics can now be calculated fully using high-speed computers. By applying Monte Carlo techniques to the selection of starting conditions for trajectory calculations, a reaction can be simulated with a sample very much smaller than the number of reactive encounters that must necessarily occur in any kinetic experiment, and models for reaction can therefore be tested. The remainder of this introduction is devoted to a simple explanation of the classical dynamics of collisions, a description of the parameters needed to define them, and the relationship between these and the rate coefficient for a reaction [9]. [Pg.5]

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