We plot the total reaction probability as a function of the total energy in Fig. 1. As is clear from the figure, after propagating the wave packet for 30 000 a.u. the basic envelope of the reaction probability is resolved in the calculation. Between T=30 000 a.u. and T=150 000 a.u. only the resonances get further resolved. At T=30 000 a.u. about 97 % of the wave packet has left the grid. Pr (E) + Pnr (E) for the region between 0.85 eV and 1.8 eV never deviates more than 10-3 from 1. Between 0.8 eV and 0.85 eV the deviation is less than 10-2 from 1. The remaining 3 % of the wave packet will for the largest part contain energies that lie part outside the window of 0.8-1.8 eV that we are investigating. For the remainder it contains energies at the low energy end of the reaction probability. However, this will only make a small difference to the value of Pr (E) + Pnr(E).
It is immediately clear from Fig. 1 is that one can distinguish between two different regions in the reaction probability. The border between the two lies around E=1.25 eV. At energies lower than E=1.25 eV the average reaction probability is low, but there are many sharp resonances. At energies higher than 1.25 eV the reaction probability increases rapidly. However, the resonances are less sharp than in the former case.
An obvious explanation for this phenomenon is that at 1.25 eV one sees the onset of the exit channel. The energy needed to excite OH from the vibrational ground state to the first vibrationally excited state is 0.443 eV, whereas the difference between 1.25 eV and the onset of the reaction at 0.8 eV is 0.45 eV. In this picture, the growth then reflects the opening of the OH() channel with its rotational states. The larger number of open channels leads to more resonance states. These resonance states likely overlap, leading to the broader resonance features at higher energies. Unfortunately, detailed state-to-state reaction probabilities[32,34] show that the situation is not as straightforward as this. They show the OH() channel is minor and does not get more important at higher energies. In fact, the increase of the total reaction probability at higher energies is mainly due to an increase in the OH() reaction probability, resulting in highly rotationally excited molecules. The conclusions of those calculations[32,34] are corroborated by the experiments of Bronikowski et al. who find an OH()/OH() ratio of at 1.6 eV (this energy is outside the scope of Refs.  and , so a direct comparison is not possible).
We think that the form of the reaction probability in Fig. 1 is caused by the fact that there are two different reaction mechanisms. Evidence for the existence of two competing reaction mechanisms has been reported in the literature[16,25,26,27]. At low energies the reactants form an intermediate (long-living) HO2 complex that eventually dissociates to products. This long-lived complex gives rise to the resonance features seen below 1.25 eV in Fig. 1. At higher energies than 1.25 eV a ``direct'' reaction path opens up, in which no complex is formed. The opening of this reaction path results in an increase in the reaction probability. We attribute the broader and lower resonance features at higher energies to a superposition of resonances from the complex forming reaction onto the reaction probability for the direct reaction. Why the resonances are broader and less sharp cannot be concluded from our research. Possibly, the number of accessible states for reactants that go through an intermediate complex is larger than at lower energies, resulting in overlapping and subsequent broadening. Another possibility is that the shapes of the resonances are distorted, due to interaction between the resonances and the states that are involved in a direct reaction. Lastly, a possibility could be that the resonances are broader due to a shorter lifetime of the complexes. However, this last point seems contradictory to the life-time matrix results of Pack et al., who find that the extrema of the eigenvalues of the life-time matrix have no clear dependence on the total energy. Clearly, further research is needed to resolve the question of the reaction mechanisms for this reaction.
Until this study only a small number of rigorous quantum mechanical studies of H + O2 have appeared in the literature, all for J=0. We compared our results with two of those studies, a set of time-independent calculations by Pack, Butcher, and Parker[34,35] and a time-dependent calculation by Zhang and Zhang. We get excellent agreement with respect to the overall shape and magnitude of the reaction probability. The agreement with respect to the position and height of some of the individual resonances is not as good. This is not very surprising, since, as already noted by Pack et al., the resonance positions and widths are highly dependent on nearly every detail of the calculation (e.g., basis set size, grid size, cut-off energy).
Concluding, one can say, that definitely the overall structure of the reaction probability is reproduced correctly in our calculations. On the other hand, conclusions with respect to the individual resonances probably have to be drawn more carefully.