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It is well known that the endothermic reaction

{\rm O}_2 (^3\Sigma^-_g)\ +\ {\rm H}(^2S)\ \longrightarrow\ {\rm OH}(^2\Pi)\ +\ {\rm O}(^3P)
\end{displaymath} (3)

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 O2 consumption in a typical hydrocarbon-air flame at atmospheric pressure[1].

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 + O2 PES has a deep well (about 2.38 eV below the H + O2 asymptote), which supports many bound states and resonances, corresponding to the HO2 complex. This has prompted research into the HO2 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 O2 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 HO2 complex, one expects the substates $\Omega $ for given total angular momentum state J to be coupled (in every practical coordinate system)[34]. Consequently, $\Omega $ 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 + O2 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.

next up previous
Next: Theory Up: Time-dependent quantum mechanical calculations O Previous: Time-dependent quantum mechanical calculations O
Anthony J. H. M. Meijer