Comparison of semiclassical, quasiclassical, and exact quantum transition probabilities for the collinear H + H2 exchange reaction

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Abstract
Using the classical (CSC), primitive (PSC), and uniform (USC) semiclassical expressions for transition probabilities given by Miller and co‐workers, we have calculated the reactive and nonreactive 0 → 0 and 0 → 1 transition probabilities for the collinear H + H2 exchange reaction. Comparison with previously calculated exact quantum and quasiclassical results for the reactive and nonreactive 0 → 0 transitions reveals that the semiclassical approximations are not very good, especially the CSC and PSC ones. All three semiclassical probabilities for the reactive 0 → 0 transition exceed unity in the collision energy range from 0.0 to 0.2 eV above the quasiclassical reaction threshold. This feature coupled with the failure of any of the semiclassical approximations to produce the marked quantum effects present in this transition causes these results to be less accurate than the corresponding quasiclassical ones. For the reactive and nonreactive 0 → 1 transitions the USC results are in qualitative agreement with the exact quantum ones and are better than the standard quasiclassical results. However, the reverse quasiclassical results are almost as good as the USC ones for these transitions. A probable reason for the inability of the USC expression to produce the strong oscillations observed in the exact quantum results is that the latter are due to interference between direct and resonant (i.e., compound state) processes whereas the present formulation of the semiclassical method does not encompass such phenomena. A comparison of the total reaction probabilities obtained by the USC and quasiclassical methods with the exact quantum one indicates that the USC result is more accurate than the quasiclassical one, except at collision energies less than 0.50 eV. This improved accuracy is due to a partial cancellation of errors in the contributing 0 → 0 and 0 → 1 USC reactive transition probabilities.