Reactive differential cross-sections

Hayes, E. F.J Walker, R. B. "Reactive differential cross sections in the rotating linear model reactions of fluorine atoms with hydrogen molecules and their isotopic variants, Zt. 

Differential and Integral Cross Sections. In Figure 7 are shown the state-to-state 1-average reactive differential cross sections for F-fH2 (degeneracy-averaged over m., summed over m and but resolved with respect to the final vibrational state v ). In each figure. 

We highlight some recent work from our laboratory on reactions of atoms and radicals with simple molecules by the crossed molecular beam scattering method with mass-spectrometric detection. Emphasis is on three-atom (Cl + H2) and four-atom (OH + H2 and OH + CO) systems for which the interplay between experiment and theory is the strongest and the most detailed. Reactive differential cross sections are presented and compared with the results of quasiclassical and quantum mechanical scattering calculations on ab initio potential energy surfaces in an effort to assess the status of theory versus experiment. 

We have carried out reactive differential cross section measurements in CMB experiments [21,22] and determined the spatial distribution and energy distribution of the products from reaction (1) and (2). The results are compared with those of quasiclassical and quantum mechanical (approximate) dynamical computations on ab initio surfaces, which have been carried out by Schatz [13,25,26] and by Clary [12,26,27] at the experimental energies. 

The determination of the reactive differential cross section IC ) from quasiclassical trajectory calculations has been reviewed by Truhlar and Muckerman. Two procedures have been used in the past to display the cross section. The first is the histogram method. One serious problem with this method is that a continuous function 1(0) is being approximated by a discontinous histogram. In addition, there are problems with choosing the locations and widths of the angular bins. The second procedure is to expand 1(0) in a series of Legendre polynomials. " However, there are also problems with this method. First, it isn t certain at what point to truncate the series to minimize the uncertainty in 1(0). In addition, there is no simple expression for the uncertainty in the differential cross section. Because of these problems only a small number of comparisons of differential cross sections for different potential energy surfaces have been made. 

Fig. 2. Reactive differential cross section for the LEPS potential based upon 10,026 reactive trajectories. The uncertainties were estimated from equations (7) and (8) as follows the uncertainty shown in the top part is 6f and that shown in the bottom part is 6f/sin 9 or 51, whichever is smaller.

Fig. 6. The total differential cross-section in A2/sr for the HF D reactive channel, (a) Shows the experimental results while (b) presents the result of the scattering calculation. Note the ridge running from large 0 (backward) at low energies to small 0 (sideways) at higher Ec s.

D. Partial Cross Sections, Product State Distributions, and Differential Cross Sections III. Reactive Scattering Theory... 

The classical theory makes especially clear the inherent ambiguity of data analysis with the optical model, and this ambiguity carries over into the quantum model. If we wish to use experimental differential cross sections to gain information about V0(r) and P(b) or T(r), we must assume a reasonable parametric form for V0(r) that determines the shape of the cross section in the absence of reaction. The value P(b) is then determined [or T(r) chosen] by what is essentially an extrapolation of this parametric form. In the classical picture a V0(r) with a less steep repulsive wall yields a lower reaction probability from the same experimental cross-section data. The pair of functions V0 r), P b) or VQ(r), T(r) is thus underdetermined. The ambiguity may be relieved somewhat (to what extent is not yet known) by fitting several sets of data at different collision energies and, especially, by fitting other types of data such as total elastic and/or reactive cross sections simultaneously. 

It is clear that the unmistakable resonance fingerprint provided by a narrow Lorentzian peak in the integral cross section (ICS) will be rare for reactive resonances in a collision experiment. However, a fully resolved scattering experiment provides a wealth of data concerning the reaction dynamics. We expect that the state-to-state differential cross sections (DCS) as functions of energy can be analyzed, using various methods, to reveal the presence of reactive resonances. In the following subsections, we discuss how various collision observables are influenced by existence of a complex intermediate. Many of the resonance detection schemes that have been proposed, such as the use of collision time delay, are purely theoretical in that the observations required are not currently feasible in the laboratory. Nevertheless, these ideas are also discussed since it is useful to have method available... 

In the case of a reactive scattering event, j3 is replaced by / (tod/tob), as we did above for the scattering angles and differential cross-sections. 

Here, the superscript R denotes reactive scattering into a specific final arrange channel q q. The total differential cross section, nR(0, cp), for reaction out state in Eq. (7.25) is given by the sum over final states at energy E as... 

The first exact quantum calculations of integral and differential cross sections on the adiabatic state were reported in 2001 by Honvault and Laimay [15,81]. They have carried out quantum reactive scattering calculations of the title reaction on the DK PES within the Time Independent Quantum Mechanical (HQM) framework using the hyperspherical close-coupling method. 

More recently we described the calculation of differential cross sections (DCSs) for the CI+H2 reaction.[35] These were used in the interpretation of ongoing crossed molecular beam studies. The rationale for this investigation is that DCSs offer, in principle, a far more detailed probe of the dynamics than the integral cross sections (ICSs). This paper [35] marked the first ever fully quantum mechanical determination of reactive DCSs for a set of coupled ab initio PESs. Because of space constraints, no details of the determination of the DCSs were reported.[35] The goal of the present article is to present, for future reference, these details. 

Clary, D.C. (1994) Four-atom reaction dynamics, J. Phys. Chem. 98, 10678-10688. Pack, R.T. and Parker, G.A. (1987) Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory, J. Chem. Phys. 87, 3888-3921. Truhlar, D.G., Mead, C.A. and Brandt, 5I.A. (1975) Time-Reversal Invariance, Representations for Scattering Wavcfunctions, Symmetry of the Scattering Matrix, and Differential Cross-Sections, Adv. Chem. Phys. 33, 295-344. 

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