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 + H_{2}(*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
to the coordinate system used
for the propagation of
]. 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.