Reaction probability opacity function

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... 

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. 

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 4 shows the dependence on final rotational state of the Cl+H2(v=0, j =0)—> HCl(v=OjO DCSs at two different collision energies. We observe that the DCSs all have a very similar shape. Likely, this implies that the overall shape of the DCS is determined by the reactive probability (opacity) as a function of impact parameter and by an overall deflection function b), while the product final state distribution is governed by the shape of the PES in the exit region of the arrangement channels. We remark also that the determination of fully final-state resolved DCS does not present any particular difficulty for our time-independent method, but would not be feasible with some of the time-dependent methods which have been applied recently to the X+H2 reactions. [7, 16]... 

This is a fundamental parameter to characterize a chemical reaction. It is represented by the symbol ctr, and can be defined as follows. First, we realize that, in a binary collision, not all collisions are expected to be reactive, i.e. it must hold that reaction probability. Typically, one uses the so-caUed opacity function P(b), which is the fraction of collisions with impact parameter b that are reactive. Hence, 0 > P(b) > 1, and one can write... 

With known Bp(Yc.b) the cross section Cq measured for preparation Ap and the steric properties of the reaction can now oe correlated. For this purpose we use the angip. dependent opacity function P(b,Tt) introduced by Levine and Bernstein [28] which describes the probability that a reaction occurs if a collision with impact parameter b leads to a reaction angle Yc- t toss section is then given by... 

From the properties of the open part of the scattering matrix we can derive related properties of the cross section, reaction probabilities, and opacity functions. From its unitarity we obtain ... 

Figure 3.9 Opacity functions P b), where P is the reaction probability for a collision at given b (for a specified total energy E). (a) The simplest step function, Eq. (3.31) with a constant sterio factor p. (b) Computed for the H + H2 exchange reaction at E= 11 kcal mol [adaped from M. Karplus, R. N. Porter, and R. D. Sharma, J. Chem. Phys. 43, 3259 (1965)]. This shows that the steric factor p is not necessarily independent of the impact parameter as assumed in case (a) and in Eq. (3.31).

In the former case, only 10 % of vinyl groups took part in the interaction after 100 h but in the latter, 25 % reaction was obtained during 24 h. The first result is probably due to the opacity of the polymer, excluding the UV from the centre of the particles. Another observation suggests that fraction of the functional groups may be inaccessible to voluminous reactants. 

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