Introduction

It is well known that the endothermic reaction

is a very important reaction in combustion chemistry. In fact, it is the rate determining step in the combustion of hydrogen and hydrocarbons and it determines flame propagation rates. Furthermore, Reaction (1) accounts for 80 % of the O

Given its importance to combustion chemistry, this reaction has been studied very extensively, both experimentally[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] and theoretically[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. It is not our intention to give a full review of the literature, for that the reader is referred to e.g., Refs. [1,34,37,38,39]. However, we will highlight a few aspects here.

Experimentally, a large number of studies have been devoted to determining the temperature dependence of the reaction rate for Reaction (1)[2,3,4,5,6,7]. Other experimental studies have been devoted to the branching ratio between the fine-structure components of the product O-atoms[8], the total cross sections for the reaction[9,10] and the dynamics of the reaction[11,12,13,14,15,16].

Theoretical research has been done using classical mechanics or statistical theories[17,18,19,20,21,22,23,24,25,26,27] on one of two Potential Energy Surfaces (PESs), the Melius-Blint surface[40] or the DMBE IV surface[41]. A number of conclusions can be drawn from these calculations. First, there is evidence that Reaction (1) has two different pathways. At low energies the reactants are expected to form a complex, which lives for a long time and then dissociates to products. At higher energies, the reaction is expected to follow a more direct pathway as well[16,25,26,27]. Second, the reaction is very stereospecific, which means that the maximum impact parameter is very small (between 1 and 2 a.u. depending on energy)[25,26,27].

Rigorous quantum mechanical calculations have become possible only
recently, albeit all for total angular momentum
*J*=0[28,29,30,31,32,33,34,35,36].
Total angular momentum *J* > 0 is only treated by approximate
methods[36]. The quantum mechanical calculations are made
difficult by two factors. First, the H + O_{2} PES has a deep well
(about 2.38 eV below the H + O_{2} asymptote), which supports many bound
states and resonances, corresponding to the HO_{2} complex. This has
prompted research into the HO_{2} complex
itself[42,43,44,45,46,47,48].
Second, the OH + O exit channel has a *R*^{-4} long range character
with *R* being the H to center-of-mass O_{2} distance. This ensures that
large grids and consequently large propagation times (in case of an
iterative method) are needed to converge the calculations.

Because of the floppiness of the HO_{2} complex, one expects the substates
for given total angular momentum state *J* to be coupled (in every
practical coordinate system)[34]. Consequently,
is
not expected to be a good quantum number. This means, that the coupled
states approximation or other decoupling schemes are likely to break down and
that exact treatment of total angular momentum may be
necessary[34]. Therefore, we think that this is an excellent
system on which to employ the Coriolis coupled method[49] for
total angular momentum *J*>0, since in this method the quantum dynamics
calculations are performed without any approximations. The Coriolis coupled
method has been used previously for studies on the effect of total angular
momentum on vibrational predissociation of van der Waals
complexes[49,50,51]. In this method the
sparsity of the Coriolis coupling matrix is exploited to distribute the
calculation over a number of processors of a parallel computer. We use this
technique in conjunction with a time-dependent wave packet
method[52,53,54] on the DMBE IV
PES[41].

We studied the H + O_{2} system for *J*=0, 1, 2, and 5. In this article
we focus on the dependence on total angular momentum of the global
shape of the reaction probability and of the mechanisms governing this
reaction. For this work we are not interested in the details of the
individual resonances.

The paper is organized as follows. In section II we describe
the theoretical framework for the calculation. In section III we
give some computational details and describe a method for decreasing
the size of the calculation. In section IV we
present and discuss our results and show how the dynamics change when
going from a *J*=0 system to a *J*>0 system. Lastly, section
V will present our conclusions.