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Conclusions

In the current article we presented results for calculations on the H + O2 reaction for total angular momentum J=10. We discussed the importance of the Coriolis coupling for $J\le10$. We performed our calculations in two different coordinate embeddings: one in which the intermolecular axis R is the z-axis (``R-embedding'') and one in which the O2 molecular axis ris the z-axis (``r-embedding''). We also derived a ``selection rule'' for the orbital angular momentum quantum number l for use in r-embedding calculations. This rule is analogous to the j=odd rule for use in the R-embedding calculations. In our calculations we used a parallel computer with the Coriolis coupled method of Goldfield and Gray.[69]

Our J=10 coupled channel (CC) calculations show that trends from our calculations on J=0, J=1, J=2, and J=5[43] continue for J=10. We see the resonance structure that is prevalent for J=0 and J=1further disappear. We attribute this to the fact that for J=10 the wave function has more $\Omega $ states that have to be summed over, leading to overlap of resonances in the total reaction probability and to subsequent washing out of the resonances. This explanation is corroborated by the fact that the helicity conserving calculations in the R-embedding (HC-Rcalculations), which have only one $\Omega $ state available show much more resonance structure. We also see that the increase in the reaction probability at 1.25 eV that is very clear for J=0 disappears for J=10.

Our calculations show that Coriolis coupling becomes more important with higher total angular momentum J. This becomes clear when comparing the HC calculations with the CC calculations for both embeddings. For J=1 there is not much difference between the two types of calculations in both embeddings, whereas for J=10 the difference is significant. These differences can be explained using the classical model from paper I.[43] From this analysis of the HC and CC results we conclude for J>10 that HC calculations with initial conditions as in this paper will always overestimate the CC calculations, especially at higher energies.

A consequence of the higher importance of the Coriolis coupling for higher J is that we feel that a method in which a number of $\Omega $ states would be left out to decrease the size of the calculation may result in inaccurate results compared to the complete calculation. Preliminary calculations support this hypothesis. However, more research is needed to answer this question completely.[95]

Summarizing, we see a gradual decrease of the reaction probability with increasing total angular momentum. This makes us confident that we can create an approximate model to calculate the reaction probability as a function of J based on only a few CC calculations with different J.[95] Based on our current set of calculations, we conclude that we have to go up to J=25 to get a reaction probability that is negligible. Our calculations also show that Coriolis coupling becomes more important with increasing J, making HC calculations for J>0 unreliable.

Currently, we are working on the implementation for CC calculations for J>10. To be able to perform these calculations we need to implement a ``wrapping'' method[69] to balance the load on the processors in our calculations. We will also implement a propagation method that uses only real algebra[96] to decrease the number of evaluations of $\hat{H}\Psi$ per time step, leading to shorter computation times. For this particular method we have already shown[97] that it can be used in conjunction with the flux-based analysis method used here.[29]

Partial support for this research comes from NSF grant CHE-9526658. We also acknowledge generous grants of computer time from the Argonne High Performance Computing Research Facility, the Maui High Performance Computing Center and the National Partnership for Advanced Computer Infrastructure.


next up previous
Next: Bibliography Up: Time-dependent quantum mechanical calculations O Previous: Helicity conserving calculations
Anthony J. H. M. Meijer
1998-10-14