Quantum mechanical scattering

The theory of chemical reactions has many facets including elaborate quantum mechanical scattering approaches that treat the kinetic energy of atoms by proper wave mechanical methods. These approaches to chemical reaction theory go far beyond the capabilities of a product like HyperChem as many of the ideas are yet to have wide-spread practical implementations. 

A chemical reaction is then described as a two-fold process. The fundamental one is the quantum mechanical interconverting process among the states, the second process is the interrelated population of the interconverting state and the relaxation process leading forward to products or backwards to reactants for a given step. These latter determine the rate at which one will measure the products. The standard quantum mechanical scattering theory of rate processes melds both aspects in one [21, 159-165], A qualitative fine tuned analysis of the chemical mechanisms enforces a disjointed view (for further analysis see below). 

As it was said above (Section 3.2), for the elastic interaction this coefficient coincides with the effective radius of recombination, Reff = b, whereas for the Coulomb interaction Re ff is defined in equation (3.2.51). Therefore the problem of obtaining the steady-state reaction rate is reduced to the finding the asymptotic coefficient b of the solution of equation (4.2.25). Formally it coincides with the quantum-mechanical scattering length on the potential... 

The basis for the semiclassical description of kinetics is the existence of two well separated time scales, one of which describes a slow classical evolution of the system and the other describes fast quantum processes. For example, the collision integral in the Boltzmann equation may be written as local in time because quantum-mechanical scattering is assumed to be fast as compared to the evolution of the distribution function. 

T.N. Rescigno, C.W. McCurdy, Numerical grid methods for quantum-mechanical scattering problems, Phys. Rev. A 62 (3) (2000) 032706. 

The Born aj)])roximation was developed originally to describe quantum mechanical scattering (Born, 1933 Born and Wolf, 1980). Since the basic idea behind this method has broad applications, it is po.ssible to apply the Born approximation to different geophysical problems as well. For example, it has been used quite extensively and successfully in seismic geophysics (Bleistein, 1984 Bleistcin and Gray, 1985 Tarantola, 1987). 

Kosloff, R. and Cerjan. C. (1984) Dynamical atom/surface eftects Quantum mechanical scattering and desorption, J. Chem. Phys. 81, 3722-3729. 

V. Aquilanti, S. Cavalli, G. Grossi, and R.W. Anderson, Stereodirected states in molecular dynamics A discrete basis representation for the quantum mechanical scattering matrix. J. Phys. Chem., 95 8184-8193, 1991. 

Resonances in reactive collisions were first observed in quantum mechanical scattering calculations for the colllnear H + H2 reaction (1-9 for a review of early calculations on this system see reference 22. recent review of the quantum mechanical... 

The steplike CRP originally obtained (8) from quantum mechanical scattering calculations has also been reproduced by a trace formula that avoids explicit specification of asymptotic states (98,99) and by a method based on eigenvalues of a reaction probability operator (100). 

The authors are grateful to Yuri Volobuev for participation in early stages of the DH2 analysis and to Professor Ken Leopold for helpful discussions. The quantum mechanical scattering calculations were supported in part by the National Science Foundation. The variational transition state theory calculations were supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences. 

Y. Sun, D. J. Kouri, D. G. Truhlar, and D. W. Schwenke, Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory, Phys. Rev. A 41 4857 (1990). 

Chemical reactions and their rates are central to chemical research. The quantum mechanical theory of reaction rates invokes quantum mechanical scattering theory and statistical mechanics. Thus, one considers the propagation of a system from an initial situation to a different one. Expressions for such processes are developed by means of quasi stationary nonequilibrium theory. 

This is a consequence of the strongly decreased elastic scattering cross-section for the high-atomic number materials at low energies. As shown by Re-imer, these effects can only be predicted by extensive quantum mechanical scattering cross-section calculations based on the partial wave expansion method. For a compound material the backscatter coefficient can be obtained by weighting the elemental backscatter coefficients with their mass fractions, c according to eqn [6] ... 

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. 

In order to reliably predict the rates for these processes, it is necessary to perform accurate dynamical calculations using accurate potential energy surfaces (PES). However, one is faced with difficulties realizing these ideals. Quantum mechanical scattering methods are not yet advanced to the point where 3-dimensional calculations can be performed on three and four atom systems at elevated temperatures and accurate PES information is rarely available. Fortunately it is often possible to ameliorate these difficulties and in this paper we discuss recent advances in this area. 

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