Helicity conserving calculations

We performed HC calculations in the *R*-embedding and in the *r*-embedding
for *J*=1, *J*=2, *J*=5, and *J*=10. Together with the CC results (for which
the *R*-embedding and the *r*-embedding give identical results) they are
plotted in Fig. 4a-d. For *J*=1 in Fig. 4a we see that
there is good agreement between the CC results (solid line) and the
HC-*r* results (dotted line).

The HC-

This trend continues for

[htb]

In Fig. 4d we see that for

In Figs. 5a-c we plot the HC-*R* reaction probabilities, the HC-*r*reaction probabilities, and the CC reaction probabilities as a function of
initial
state for *J*=10.

From comparing these results we can learn why the HC calculations give different results from the CC calculations.

In Figs. 5a-c we see for all three HC-*R* results a large number of
resonances at low energies, which is indicative of a long-lived reaction
complex. For high energies we see that only for
the reaction
probability significantly increases and the resonance structure almost
disappears. This last feature for the
calculations is
indicative of a ``direct'' reaction mechanism. The idea of two different
reaction mechanisms for the H + O_{2} (
)
has been brought up in
the literature
before.[11,12,13,14,23,24,43]
We used it in combination with a classical model in paper I to explain the CC
results for *J*=1. The same classical model can be used here to explain the
HC-*R* results. If a calculation is started in the
state (and
for a HC-*R* calculation it stays in this state), the reaction geometry can
be called ``planar''. This means that the molecule is rotating in the plane
of the three atoms. In this case it is possible for the H atom to collide
with one of the O atoms directly, leading possibly to reaction if the total
energy is sufficient. At lower energies a reaction complex will be formed.
Assuming also that the direct reaction has a higher reaction probability than
the complex forming reaction, we get a curve with a small reaction
probability and a large number of resonances at low energies and with a high
reaction probability and a smaller number of resonances at higher energies,
as in Fig. 5a. For calculations starting in the
or
states, the direct reaction path is less likely, because
initially the molecule is not rotating in the plane of the 3 atoms, making it
harder for the atom to hit one of the O atoms directly. Thus, the complex
forming reaction is favored. This results in a curve with a low reaction
probability and a large number of resonances throughout, as can be seen in
Figs. 5b and 5c. The resonance structure at low energies
in Figs. 5a-c also suggests that our explanation for the
disappearance of the resonance structure at low energies in Fig. 1
for *J*=10 in the CC-*R* calculations is correct. Since the HC-*R*calculations use only one
state, there cannot be any overlap between
different
states. Consequently, the resonance structure does not get
washed out.

The reaction model used above and the difference in reactivity between the
two reaction geometries are corroborated by experimental results. The
difference in reactivity between the two reaction geometries has been found
experimentally by Bronikowski *et al*,[13] who studied the
relative populations of the
doublet states of the ground state of
OH(), which correlate to the two different reaction geometries in the
interaction region. The reaction model used above is consistent with measurements
of differential cross sections (DCSs) by Fei *et al.*[14] At
low energies they find an almost isotropic DCS, indicative of a reaction
complex. At higher energies, they find a DCS with a large maximum in the
forward scattering region and a smaller maximum in the backward scattering
region. Both of these maxima are consistent with a direct mechanism.

From Figs. 5a-c we can also see that the main cause for the
differences between the HC-*R* and the CC results for *J*=10 lies in the
HC-*R* results for *J*=10,
at high energies
(Fig. 5a). We can also use our reaction model to explain this.
Both calculations start in the same initial state,
,
which
corresponds to a planar reaction geometry. For the HC-*R* calculation
is conserved, meaning that in this case also the reaction geometry
is conserved. In the CC calculation the
selection is lost through
Coriolis coupling, allowing the wave packet to sample other (less reactive)
reaction geometries as well. This results in a lower reaction probability,
especially at higher energies.

If we compare the HC-*r* results to the HC-*R* results in
Figs. 5a-c, we that the largest differences occur for the *J*=10,
calculation in Fig. 5a. Notable are the absence of
sharp resonances at low energies and the lower reaction probabilities at
higher energies for the HC-*r* calculation. This can be explained in the
following way. Initially, the wave packet in the HC-*r* calculation is in the
state through a coherent superposition of *K* states.
Although there is no Coriolis coupling between the *K* states, this coherence
is nevertheless lost during the calculation. The wave packet evolves
differently in each *K* state, because each *K* state has a different
Hamiltonian. This decoherence of the wave packet means that other reaction
geometries (components of other
states) become accessible to the
wave packet during the propagation, resulting in a lower reaction probability
at higher energies. The decoherence is not fast enough, however. The HC-*r*reaction probability still overestimates the correct (CC) reaction
probability. The fact that each *K* state evolves with its own Hamiltonian
also means that the reaction probability for each *K* state has a
different dependence on energy. This results in overlapping and subsequent
washing out of resonances at low energies as in the CC calculations.

We conclude from the HC calculations that neither
nor *K* are good
quantum numbers. Therefore, we think that neither the *R*-embedding nor the
*r*-embedding are optimal coordinate embeddings for this reaction. This
corroborates the observation from Ref. [30] that no
optimal frame for this reaction will be found, because of the floppiness of
the HO_{2} complex.