Collinear reactive scattering

J.M. Launay, M. Le Dourneuf, Hyperspherical description of collinear reactive scattering, J. Phys. B At. Mol. Phys. 15 (1982) L455. 

Poliak, E. and Child, M.S. (1981). A simple classical prediction of quanta resonances in collinear reactive scattering, Chem. Phys. 60, 23-32. 

Romelt, J. (1983). Prediction and interpretation of collinear reactive scattering resonances by the diagonal corrected vibrational adiabatic hyperspherical model, Chem. Phys. 79, 197-209. 

DIVAH model for collinear reactive scattering resonances... 

N. Abu-Salbi, D. J. Kouri, M. Baer, and E. Poliak, A study of the quantal time delay matrix in collinear reactive scattering, /. Chem. Phys. 82 4500 (1985). 

E. Poliak and M. S. Child, Chem. Phys., 60, 23 (1981). A Simple Prediction of Quantal Resonances in Collinear Reactive Scattering. 

In the next section (Sec. 2), we will develop the theory of the BCRLM. We discuss the solution of the coupled-channel equations in both natural collision coordinates " and hyperspherical coordinates. " Both coordinate systems are widely used to treat collinear reactive scattering processes. We will discuss the projection " of the hyperspherical equations on coordinate surfaces appropriate for applying scattering boundary conditions and review the definition of integral and differential scattering cross sections in this model. 

One of the intriguing facts uncovered by numerical computations for collinear reactive scattering of an atom on a diatom was the existence of sharp spikes in the reaction probability as a function of energy. 

The reason for this is that the collinear reactive scattering Hamiltonian can be written equivalently in terms of the mass-scaled Jacobi coordinates of either arrangement a = a or c as... 

The main advantage that hyperspherical coordinates have over natural collision coordinates is that the kinetic energy operator and volume element are far simpler in hyperspherical coordinates. The collinear reactive scattering Hamiltonian can be written in terms of p and 9, for example, as... 

The Kohn variational method described above for potential scattering extends in a straightforward way to the collinear reactive scattering problem described in Section 2 without the need to introduce any special coordinates (i.e., one can continue to work with the optimum mass-scaled Jacobi coordinates of the reactant and product arrangements). Moreover, the extensions that are required are comparatively minor, and the overall structure of the method remains the same. 

One important application to collinear reactive scattering was recently reported by Kuppermann et who used hyperspherical... 

A. Kuppermann, J. A. Kaye, and J. P. Dwyer, Hyperspherical coordinates in quantum mechanical collinear reactive scattering, Chem. Phys. Lett., in press. 

A. Kuppermann and J. P. Dwyer, A simple model of dynamic resonances in collinear reactive scattering, in "Electronic and Atomic Collisions, Abstracts of Contributed Papers, XIth... 

International Conference on the Physics of Electronic and Atomic Collisions, Kyoto , K. Takayanagi and N. Oda, eds., The Society for Atomic Collision Research, Japan (1979), pp. 888-889 J. P. Dwyer and A. Kuppermann, Resonances in collinear reactive scattering A simple hyperspherical coordinate model, manuscript in preparation. 

The F + H2 — HF + FI reaction is one of the most studied chemical reactions in science, and interest in this reaction dates back to the discovery of the chemical laser.79 In the early 1970s, a collinear quantum scattering treatment of the reaction predicted the existence of isolated resonances.80 Subsequent theoretical investigations, using various dynamical approximations on several different potential energy surfaces (PESs), essentially all confirmed this prediction. The term resonance in this context refers to a transient metastable species produced as the reaction occurs. Transient intermediates are well known in many kinds of atomic and molecular processes, as well as in nuclear and particle physics.81 What makes reactive resonances unique is that they are not necessarily associated with trapping... 

G.C. Schatz, A. Kuppermann, Dynamical resonances in collinear, coplanar, and three-dimensional quantum mechanical reactive scattering, Phys. Rev. Lett. 35 (1975) 1266. 

C. C. Marston, G. G. Balint-Kurti, and R. N. Dixon, Theor. Chim. Acta, 79, 313 (1991). Time-Dependent Quantum Dynamics of Reactive Scattering and the Calculation of Product Distributions—A Study of the Collinear F -I- H, (v = 0) — HF (v ) -I- FI Reaction. 

A few examples may demonstrate this. The approximation has been used to treat the photodissociation processes of NOHCl [33] and NO2 [34] which include three internal modes. Five dimensional time dependent calculations were performed on the photodissociation of CH3I [35, 36]. The state-to-state chemistry has been investigated for the reactive scattering of H-1-H2 (v=0,l) —> H2 (v=0,l) -1- H collinear system [37]. The MCTDSCF approach has also been applied to surface chemistry, in particular H2 dissociation on a transition metal surface [38] the photodissociation of CH3I on MgO surface [39, 40] and to inelastic molecule-surface scattering [41, 42]. Recently, the MCTDSCF method has been used to investigate multimode effects in the absorption spectrum of pyrazine taking into account 14 vibrational modes [43]. 

A. Jackie and H.-D. Meyer, Reactive scattering using the multiconfiguration time-dependent Hartee approximation General aspects and application to the collinear H+H2 -> H2+H reaction, J. Chem. Phys., 102 (1995) 5605. 

Light J.C. and Walker. E.B. (1976) An B matrix approach to the solution of coupled equations for atom-molecule reactive scattering, J. Chem. Phys. 65. 4272-4282. Halavee, U. and Shapiro, M. (1976) A collinear analytic model for atom-diatom chemical reactions, J. Chem. Phys. 64, 2826-2839. 

A scattering calculation gives the most complete description of resonances in reactive and non-reactive systems. However, if the resonances are the major features of interest a more direct approach to obtain them is desirable. A number of such aproaches exist and are reviewed in this volume and in the following sections of this paper. These have been applied mainly to non-reactive systems, however, they are beginning to be used in reactive systems. Thus far they have been applied to collinear reactive systems where their accuracy is being tested. The status of these calculations is discussed in a paper by Garrett et al. in this volume. 

We have performed the first (piantum reactive scattering ealculations for the C( D) + H2 —> CH + H reaction on a recent ab initio PES [46] calculated in our group. The C2, geometry shows no barrier and a deep well (4.32 eV) corresponding to the l Ai electronic state of the CH2 species. In contrast the collinear barrier is very large (0.535 eV). This reaction is similar to the 0( D) + H2 reaction because no barrier occurs for the perpendicular geometry. However there are three main differences, the well is less deep, the collinear barrier is larger and the exothermicity is much smaller (0.273 eV). 

A. Goussev, R. Schubert, H. Waalkens, S. Wiggins, The quantum normal form approach to reactive scattering The cumulative reaction probability for collinear exchange reactions,... 

The main objective of any theory is to be able to understand and predict the results of experiments. Since the world is three dimensional one cannot limit oneself to the study of collinear systems. In section IV we show how the collinear analysis based on periodic orbits may be generalised to three dimensional systems.We provide a 3D adiabatic transition state theory which is used to analyse numerical computations as well as experimental results. A 3D analysis of quantal resonances predicts that one should hope that quantal resonances will provide a new spectroscopy of transition states. A discussion of the future role of periodic orbits and reactive scattering is given in section V. 

As has been shown in the last years [5,9,10,17-19] FEM is a very useful and accurate tool for the solution of reactive scattering problems. In the collinear case we can calculate the whole scattering wavefunction with FEM in one step and the FEM procedure allows to obtain realistic estimates of the accuracy and convergence properties [17]. 

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