Elastic, Inelastic, and Reactive Scattering

The relations discussed above can be generalized to elastic, inelastic, and reactive scattering of two molecules for any initial conditions. A detailed discussion of these results is presented in Appendix C. 

Summary. An introduction to the field of time-independent quantum reactive scattering is given, focussing on triatomic (A-hBC) systems. Concepts of elastic, inelastic and reactive scattering as well as coordinate systems are discussed and the developments are outlined which led to the first numerically exact calculations for H-hH2. 

The intention of this review is to give an introduction into the field of time-independent quantum reactive scattering which will be exemplified mostly in form of triatomic systems (A+BC). Nowadays four-atom systems (AB-fCD, A+BCD) constitute the state-of-the-art of the field, but including them would burst the size of this contribution. As a consequence, new developments will be quoted only in a shorter way. In the present Part I we will give an introduction of what is meant by elastic, inelastic and reactive scattering, then we will discuss coordinate systems and finally we will present the historical way how the first numerically exact calculations for H+H2 had been performed in the 1970 s. 

In the next three subsections (extracted from the work of Miller [13]) we will discuss briefly molecular collision processes (elastic, inelastic and reactive scattering), perhaps the most well-defined and rigorous approach to studying chemical dynamics. 

Another motivation for pursuing these semiclassical approaches to inelastic and reactive scattering is the well-known success that semiclassical theory has had in describing quantum effects in simpler elastic (potential) scattering.5,6 Here one now knows that essentially all quantum effects can be adequately described in a semiclassical framework. 

Toennies JP. 1974. Molecular beam scattering experiments on elastic, inelastic, and reactive collisions . In Physical Chemistry, An Advanced Treatise, vol. VI A, lost W (ed.). Academic Press New York, NY 228-381. 

Equations (16) and (17) for Tpa are exact results. In particular it does not matter how Vy Is partitioned into Vy Vy provided only that Vy gives rise to elastic or inelastic non-reactive scattering (otherwise, another term has to be added to the right hand sides of Eqs. (16) and (17)). 

Just as for gas-phase molecular collisions, gas-surface encounters can be elastic, inelastic, or reactive in nature. A wide range of scattering behavior is observed depending upon the gas molecules, the composition, structure, and temperature... 

As one would expect, developments in the theory of such phenomena have employed chemical models chosen more for analytical simplicity than for any connection to actual chemical reactions. Due to the mechanistic complexity of even the simplest laboratory systems of interest in this study, moreover, application of even approximate methods to more realistic situations is a formidable task. At the same time a detailed microscopic approach to any of the simple chemical models, in terms of nonequilibrium statistical mechanics, for example, is also not feasible. As is well known, the method of molecular dynamics discussed in detail already had its origin in a similar situation in the study of classical fluids. Quite recently, the basic MD computer model has been modified to include inelastic or reactive scattering as well as the elastic processes of interest at equilibrium phase transitions (18), and several applications of this "reactive" molecular dynamicriRMD) method to simple chemical models involving chemical instabilities have been reported (L8j , 22J. A variation of the RMD method will be discussed here in an application to a first-order chemical phase transition with many features analogous to those of the vapor-liquid transition treated earlier. 

The theory of reactive scattering is more complicated than that for elastic and inelastic scattering [70], because of coordinates, and different formulations of reactive scattering turn on how one deals with this coordinate problem. Fig. 1.2 depicts the situation for the collinear A+BC->AB-fC reaction. If only an inelastic scattering process (i.e. vibrational excitation) is treated. 

Whilst semi-classical theories have been successful in describing non-reactive processes such as elastic and inelastic scattering, they have had less impact on calculations for reactions. The majority of calculations have been for simple reactions such as H + H2, F + H2 or H + Cl2 which have been treated collinearly for the most part. The most successful use of semi-classical theory is for treating tunnelling and it has found use extending the scope of purely classical calculations by describing classically forbidden processes and threshold effects [156]. 

From the above example, it should be clear that all the elementary excitations are the result of the collective interactions of the bare fields in the system, and therefore pertain to the system as a whoIe24). Elementary excitations, which will be identified with the physical particles we observe, correspond to superpositions of large numbers of exact stationary states of the field Hamiltonian it, Eq. (2.3), with a narrow spread in energy i.e. they are wave-packets. An equivalent way of saying this is that the elementary excitations interact with one another, and so have finite lifetimes their interactions may lead to reactive, inelastic or elastic scattering processes. 

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