Scattering calculations systems, reactive collisions

Of the various decoupling approximations, the simplest (and concommitantly least accurate) is the lOS approximation.It has been developed and applied in several versions for reactive systems. These different versions relate, in part, to the manner in which the CS orbital angular momentum parameter is chosen. 5Most recent work on inelastic (nonreactive) scattering shows that a S3rrametric choice is best (since otherwise time-reversal S3rmmetry is violated).Calculations on reactive collisions also indicate the same conclusion holds. 

The preferable theoretical tools for the description of dynamical processes in systems of a few atoms are certainly quantum mechanical calculations. There is a large arsenal of powerful, well established methods for quantum mechanical computations of processes such as photoexcitation, photodissociation, inelastic scattering and reactive collisions for systems having, in the present state-of-the-art, up to three or four atoms, typically. " Both time-dependent and time-independent numerically exact algorithms are available for many of the processes, so in cases where potential surfaces of good accuracy are available, excellent quantitative agreement with experiment is generally obtained. In addition to the full quantum-mechanical methods, sophisticated semiclassical approximations have been developed that for many cases are essentially of near-quantitative accuracy and certainly at a level sufficient for the interpretation of most experiments.These methods also are com-... 

In a collision process, it is the relative position of the atoms that matters, not the absolute positions, when external fields are excluded, and the potential energy E will depend on the distances between atoms rather than on the absolute positions. It will therefore be natural to change from absolute Cartesian position coordinates to a set that describes the overall motion of the system (e.g., the center-of-mass motion for the entire system) and the relative motions of the atoms in a laboratory fixed coordinate system. This can be done in many ways as described in Appendix D, but often the so-called Jacobi coordinates are chosen in reactive scattering calculations because they are convenient to use. The details about their definition are described in Appendix D. The salient feature of these coordinates is that the kinetic energy remains diagonal in the momenta conjugated to the Jacobi coordinates, as it is when absolute position coordinates are used. 

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... 

In gas-phase dynamics, the discussion is focused on the TD quantum wave packet treatment for tetraatomic systems. This is further divided into two different but closed related areas molecular photofragmentation or half-collision dynamics and bimolecular reactive collision dynamics. Specific methods and examples for treating the dynamics of direct photodissociation of tetraatomic molecules and of vibrational predissociation of weakly bound dimers are given based on different dynamical characters of these two processes. TD methods such as the direct projection method for direct photodissociation, TD golden rule method and the flux method for predissociation are presented. For bimolecular reactive scattering, the use of nondirect product basis and the computation of the initial state-selected total reaction probabilities by flux calculation are discussed. The descriptions of these methods are supported by concrete numerical examples and results of their applications. 

Several other related aspects of TCFs can be mentioned, but will not be covered here to concentrate instead on calculational methods and applications of collisional TCFs. An earlier alternative approach in terms of superoperators [18] suggests ways of extending the formalism to include phenomena where the total energy is not conserved due to interactions with external fields or media. It has led to different TCFs which however have not been used in calculations. Information-theory concepts can be combined with TCFs [10] to develop useful expressions for collisional problems [19]. Collisional TCFs can also be expressed as overlaps of time-dependent transition amplitude functions that satisfy differential equations and behave like wavepackets. This approach to the calculation of TCFs was developed for Raman scattering [20] and has more recently been extended using collisional TCFs for general interactions of photons with molecules [21] and for systems coupled to an environment [22-25]. This approach has so far been only applied to the interaction of photons with molecular systems. Flux-flux TCFs [26-28] have been applied to reactive collision and molecular dynamics problems, but their connection to collisional TCFs have not yet been studied. 

The answer to many questions that arise in binary collision processes lies in a knowledge of detailed potential energy surfaces which for the three atom systems are now attainable, however, at considerable effort and expense.85 Until such surfaces become available, we must rely on approximate or schematic potential energy curves constructed from empirical calculations and experimental information to interpret reactive scattering and rate data of ion-molecule reactions. 

The results reported correspond to Rg- H2 model systems,but where the mass of the rare gas atom Rg has been set to 1 a.u.m. Amongst these systems is included the H-H2 one using a L.E.P.S. potential energy surface, as studied by Kulander et al., because it displays no reactive scattering for the collision energies considered. All these calculations lead to the similar trends exemplified on figure 2,namely ... 

Our aim is to use FEM for the investigation of dynamical problems, especially the reactive scattering dynamics between atoms and diatomic molecules. There has been significant progress in treating molecular collisions theoretically [1], but up to now the H + H2 system is the only one where accurate 3D calculations [2-10] have been performed. 

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