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Introduction

The reaction


$\displaystyle \rm H(^2S) + O_2 (^3\Sigma_g^-) \longrightarrow OH (^2\Pi) +
O (^3P)$      

is a rate determining step in the combustion of hydrogen and hydrocarbons. Furthermore, it accounts for approximately 80 % of the O2 consumption in a typical hydrocarbon-air flame at atmospheric pressure.[1] Given its importance for combustion chemistry, it is not surprising that this reaction has been studied extensively, both experimentally[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] and theoretically.[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43] (Note that this list of references is not exhaustive. For more references, see e.g., Refs. [30,43,44,45]).

Dynamical studies on this reaction have mainly used three different potential energy surfaces (PESs), the Melius-Blint surface[46], the DMBE IV surface of Pastrana et al,[47] and the Diatomics-in-Molecules (DIM) surface of Kendrick and Pack.[48] At first, only quasi-classical calculations were possible.[17,18,19,20,21,22,23,24,25,26,27] Only in the last five years have full quantum mechanical calculations become possible with most calculations performed for total angular momentum J=0.[28,29,30,31,32,33,34,35,36,37,38] Whenever J>0 was studied, it was done using an approximate method.[39,40,41,42] The first rigorous quantum mechanical study for J>0 (J=1, J=2, and J=5), as far as we know, was published only recently by us.[43] This paper is referred to as paper I from now on.

Quantum mechanical calculations on the H + O2( $^3\Sigma_{\rm g}^-$) reaction are quite difficult. There are two reasons for this. First, the O + OH exit channel has a long-range R-4 character, where R is the H to center-of-mass O2 distance. This ensures that one needs large grids for the calculation and in case of an iterative method also long propagation times. Second, the PES has a deep well (2.38 eV below the H + O2 asymptote), which can support many metastable states of the intermediate HO2 complex. Consequently, a large number of studies have been devoted to the HO2 complex as well,[49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67] including one that treats J>0 rigorously.[55]

There is evidence that two different reaction mechanisms play a role in the H + O2( $^3\Sigma_{\rm g}^-$) reaction.[12,13,14,15] At low collision energies, the reaction goes through a long-lived reaction complex. This is evidenced by the sharp resonance structure seen in the theoretical J=0 reaction probability as a function of energy.[28,29,30,31,43] Moreover, the experimental differential cross sections show no preference for forward or backward scattering at these energies.[14] At higher energies, a second ``direct'' mechanism becomes more important. The experimental differential cross sections at these energies show a definite preference for forward scattering, consistent with a direct mechanism.[11,14] The theoretical J=0 reaction probability shows a sharp increase at higher energies and the resonance structure becomes less pronounced.[28,29,30,31,43] In calculations for J>0 (J=1, J=2, and J=5) evidence for the existence of the two reaction mechanisms is also found.[43]

The intermediate HO$_2^\ast$ complex is a very floppy species.[68] This means that the substates $\Omega $ of the wave function for total angular momentum quantum number J are probably heavily coupled,[30] so that the Coriolis coupling between the states cannot be ignored. Our calculations for J=1, J=2, and J=5 in paper I show that, if the H - O2 distance R is taken to be the z-axis of the coordinate system, the $\Omega $ substates are indeed heavily coupled. However, our choice for the z-axis in paper I is not the only choice possible. In fact, previous (approximate) calculations for H + O2 (J>0) have used the O2 bond as the z-axis.[40,41,42] Based on the mass difference between H and O2, one would expect this choice for the z-axis to result in a calculation in which the Coriolis coupling is less important.[42] However, given the floppiness of the HO2 complex, this is by no means certain.[30]

The heavy coupling between the $\Omega $ substates for a wave function with total angular momentum quantum number J means that the H + O2 reaction is well suited to be studied with the Coriolis coupled method of Goldfield and Gray.[69,70,71] In this method the different $\Omega $ substates are distributed over the processors of a parallel computer, resulting in a highly parallel calculation with almost no communication overhead.

In this paper we examine the importance of Coriolis coupling in the theoretical description of the H + O2 ( $^3\Sigma_{\rm g}^-$) reaction. To this end we have performed (rigorous) coupled channel (CC) calculations[72] and (approximate) helicity (Jz) conserving (HC) calculations[73] for J=1, J=2, J=5, and J=10 with both choices for the z-axis. In the HC calculations the Coriolis coupling between the $\Omega $ states is neglected. The CC calculations for J=10 have not been published before. We discuss these result separately in Sec. IIIA. The CC calculations with R as z-axis for J=1, J=2, and J=5 were taken from paper I.

The organization of the paper is as follows. In Sec. II we discuss the theory needed for the CC and HC calculations, we present the transformations between the two choices for the z-axis that we use and some computational details. In Sec. IIIA we discuss the results for the J=10 CC calculations. In Sec. IIIB we compare the HC calculations to the CC calculations. Finally, in Sec. IV we give our conclusions.


next up previous
Next: Theory and Computational details Up: Time-dependent quantum mechanical calculations O Previous: Time-dependent quantum mechanical calculations O
Anthony J. H. M. Meijer
1998-10-14