Non-simple pathways and networks

For convenience, a distinction is made between "simple" and "non-simple" pathways or networks. A pathway, network, or any portion of one of these is called simple if it meets both of the following criteria ... 

For reactions with non-simple pathways or networks, the formulas and procedures described so far are not valid. Any step involving two or more molecules of intermediates as reactants destroys the linearity of mathematics, and any intermediate that builds up to higher than trace concentrations makes the Bodenstein approximation inapplicable. Such non-simple reactions are quite common. Among them are some of the kinetically most interesting combustion reactions, detonations, periodic reactions, and reactions with chaotic behavior. However, a discussion of more than only the most primitive types of non-simple reactions is beyond the scope of this book. The reader interested in more than this is referred to another recent volume in this series [1], in which such problems are specifically addressed. 

If only a small minority of reaction steps are non-simple, much benefit can be had by breaking the pathway or network down into "piecewise simple" portions and then applying the methods described in the preceding sections to these [8], To this end the pathway or network is cut at the offending intermediates or steps, as will now be shown. 

All arrows represent multistep, irreversible pathways, and aldehyde and possibly aldol build up to higher than trace concentrations. The network is non-simple for that reason and also because the aldehyde, an intermediate, acts in addition as a co-reactant in the pathway to the aldol. 

If a pathway or network turns out to be non-simple, a good strategy is to try to break it up into piecewise simple portions that can be studied independently. Whether and how this can be done depends on the reaction at hand. The job is easiest if the portions are irreversible, so that none of them feeds back into a preceding one, and if the non-trace intermediates can be synthesized. 

Based on this physical view of the reaction dynamics, a very broad class of models can be constructed that yield qualitatively similar oscillations of the reaction probabilities. As shown in Fig. 40(b), a model based on Eckart barriers and constant non-adiabatic coupling to mimic H + D2, yields out-of-phase oscillations in Pr(0,0 — 0,j E) analogous to those observed in the full quantum scattering calculation. Note, however, that if the recoupling in the exit-channel is omitted (as shown in Fig. 40(b) with dashed lines) then oscillations disappear and Pr exhibits simple steps at the QBS energies. As the occurrence of the oscillation is quite insensitive to the details of the model, the interference of pathways through the network of QBS seems to provide a robust mechanism for the oscillating reaction probabilities. 

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