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Conclusions

We showed how to calculate total reaction probabilities and state-resolved probabilities using flux-based methods if one has only the real part of a wave packet evolving according to the usual or a modified Schrödinger equation. We confirmed the general idea by calculating total reaction probabilities for the D + H2(J=0) reaction, obtaining good agreement with results computed using asymptotic product analysis. We also showed that asymptotic product analysis is a limiting case of the flux-based T-matrix formalism[7], and a flux-based approach to calculating total reaction probabilities[5,6] is a limiting case of both. In comparison with flux approaches based on complex wave packets, we expect considerable reductions in computing time will be gained.

The asymptotic analysis approach[3,4,12] does not require computing derivatives and manipulating cumbersome arrays corresponding to the wave packet and its derivative on a surface. Therefore, it is simpler than both flux approaches discussed here. Under suitable conditions it is the ideal choice. Suitable conditions are that the analysis be done far enough out in the product channel, and that analysis be carried out in product coordinates. It is less straightforward to use reactant coordinates for such a calculation. This is unfortunate, since sometimes a problem can be described more compactly in these coordinates. In contrast, both flux methods[5,6,7] described here do not require the analysis surface to be asymptotic, and analysis can be done in any coordinate system. [In case of the T-matrix method, one might have to transform $\psi_F({\bf x},E)$ to the coordinate system used for the propagation of $\psi ({\bf x},t)$]. Using distorted waves in the T-matrix formalism of Ref. [7] can lead to considerable reductions in computation time. In both flux methods several analysis surfaces can be used to compute branching ratios.

An interesting future application of the ideas presented here is to the calculation of the cumulative reaction probability, N(E), which upon Boltzmann averaging yields rate constants [20]. In particular, since the transition state wave packet method proposed by Zhang and Light [21] for calculating N(E)involves flux analysis of wave packets that is similar to the flux analysis considered here, the real wave packet approach should apply in a similar fashion, resulting in greater efficiency.


\begin{ack}AJHMM and EMG were supported by NSF grant CHE-9526658. SKG was suppor...
...iences, U.S.
Department of Energy, under Contract No. W-31-109-ENG-38.
\end{ack}


next up previous
Next: Bibliography Up: Flux analysis for calculating Previous: Results for D + H
Anthony J. H. M. Meijer
1998-06-19