Opacity function

Fig. 17. The angle-dependent integrated opacity function dan(00 —> v = 0,1, f = 0 6, Eq, Jmax) versus Jmax computed for the experimental energy Eq = 1.200eV. This quantity is computed by restricting the partial wave sum in the DCS to the terms J < Jmax- The result is shown for forward and backward scattering to illustrate the J-contributions to scattering at different 0.

Quasiclassical trajectory Calculations of opacity functions and cross ... 

When potential surfaces are available, quasiclassical trajectory calculations (first introduced by Karplus, et al.496) become possible. Such calculations are the theorist s analogue of experiments and have been quite successful in simulating molecular reactive collisions.497 Opacity functions, excitation functions, and thermally averaged rate coefficients may be computed using such treatments. Since initial conditions may be varied in these calculations, state-to-state cross sections can be obtained, and problems such as vibrational specificity in the energy release of an exoergic reaction and vibrational selectivity in the energy requirement of an endo-... 

This perturbation result somewhat surprisingly corresponds exactly to the classical formulation (see text that follows) through identification of the classical opacity function P(b) with its quantal form... 

Figure 3.12 The angle-dependent integrated opacity function da (00 — = 0,1, j = 0...

Figure 4 Quasi-classical opacity function P(p), defined as the fraction of reactive trajectories for a given impact parameter, p (solid line). Also plotted is Krei, the component of the relative incident-target H atom kinetic energy parallel to the surface, following a non-reactive collision (dotted line). The results correspond to H-on-D for the flat-surface potential described in the text.

A few words on the form of P, (p) are in order. Our opacity is very different from that often encountered in textbooks of gas phase reactions, where P, is assumed to be constant up to some value of p, and zero beyond that. Similar holes (regions of low reactivity at low p) in the opacity function have been computed for the ER reactions of H(g) with Cl adsorbed onto Au( 1 1 1) [91,92] and with H physisorbed onto graphite [85]. For H atoms on a corrugated Cu(l 1 1) surface we find smaller holes than in Fig. 4, but the reactivity still becomes small near zero impact [38]. Note that the reaction cross section, defined as... 

We have also computed reaction probahilities for H2(i = O.j = 0) and. / > 0. The opacity functions P J) (total reaction probability as a function of total angular momentum J at a fixed oiiorg> ) arc plotted in figure 6 for four colfision oiiorgios (25, 56, 84 tmd 100 me ). 

The opacity function P(Et,ans,b), i.e., the reaction probability averaged over all orientations at a given impact parameter b and translational energy can be expressed as... 

Figure 4 Opacity function for the H + H20(004) —> OH + H2 reaction at various initial relative kinetic energies...

At any total scattering energy E, elements of the multichannel S matrix In the RLM are labelled by the total angular momentum Index I, and by the Initial and final vibrational quantum numbers v and v. Equations for physical observables in the BCRLM have been given previously (24-26), and we only summarize the final results here, In order to establish a common notation. The opacity function gives the Impact parameter dependence of the reaction probabilities. 

There Is also a small reduction In the Interference oscillations In the forward direction. It Is significant to note, however, that the background angular distribution Is sideways peaked, as a consequence of the generally Increasing behavior of the opacity functions of Figure 7 at low 1. 

HF(v =2)+H at E 1.807 eV. The solid curve Is the direct result of the extraction procedure discussed In the text, and the dashed curve Is a smoothed version. The dotted curve reproduces the opacity function of Figure 1 for comparison. 

Figure 9. Background angular distributions for the reaction F+H2(v=0) + HF(v = 2)+H at E - 1.807 eV. The solid curve Is based on the opacity function shown In Figure 7 as a solid curve, and the smoother, dashed curve shows the angular distribution which results from the smoothed opacity function of Figure 7.

The F-HH2 reaction on this newer potential surface demonstrates one way In which the BCRLM will produce an angular distribution at the reaction threshold which Is not smooth and backward-peaked. In this case, the absence of a significant reaction probability for low partial waves, and the appearance of a resonance feature at larger partial waves, combine to produce an opacity function which peaks at large partial waves, and hence an angular distribution which has a predominant forward distribution of reaction products. Ve have seen results similar to these (41) In the angular distribution for the reactions F+D2(v 0) DF(v 3,4)+D on this same surface. 

Figure 12. Opacity functions at several energies for the reaction F+H2(v=0) + HF(v 2)+H on surface 3 of reference 41.

A generalized opacity function P, may simply be defined by rearranging the expression for oba in terms of the S matrix, to obtain... 

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