Partition of reverse critical energy

The dynamical theory treats the partition of reverse critical energy in terms of the atomic motions within the molecule at the transition 

Alternatively, the essence of the theory can be expressed succinctly in mathematical terms. If the transition state reaction coordinate is defined by a 3N- dimensional vector in mass normalised space, which is projected onto the 3-dimensional mass normalised subspace of the product separation coordinate, the proportion q of the reverse critical energy appearing as relative translational energy of products is 

The dynamical theory might be thought of [251] as an adaptation for complex molecules of the classic analysis of the linear triatomic [285], which distinguishes between the cases of late downhill and early downhill [161]. There is, however, no assurance that this analysis 

The dynamical theory has satisfactorily reproduced the proportions of reverse critical energy partitioned into translation in the elimination of HF from the molecular ions of a number of fluoroalkanes and fluoro-alkenes [167], One broad conclusion was that, in the decompositions studied, late transition states tended to favour partition of reverse critical energy into translation, whereas early transition states did not, cf. late and early downhill [285] (see Sect. 8.4.2). Constraints due to conservation of angular momentum were also evident. 

The loss of ketene from the molecular ion of acetanilide is the largest system studied to date [176]. The theory predicted that almost none of the reverse critical energy should appear as translational energy release, which was what had been found experimentally. 

---

The partition of reverse critical energy in the loss of HCN from a series of ring-substituted benzaldoxime methyl esters was investigated some years ago [191]. It was found that the fraction of the total available energy [(E — E0) 4- ER ] released as translation tended to increase with the electron-donating power of para substituents. The comment was made that the relationship between the lateness of the transition state and the translational energy release might bear upon the results [191 see also 151, 305]. 

---