Reactive scattering, wavepacket theory

This chapter deals with the theory underlying the apphcation of wavepackets to molecular photodissociation and reactive scattering. The objective will be to derive and gather together the equations and theoretical methods needed in such calculations. No attempt will be made to reference aU calculations that have been undertaken in this very popular field. Several alternative related methods will be discussed, but it will not be possible to do full justice to all the different methods that have been proposed, many of which are being successfully used. 

The first part of the review deals with aspects of photodissociation theory and the second, with reactive scattering theory. Three appendix sections are devoted to important technical details of photodissociation theory, namely, the detailed form of the parity-adapted body-fixed scattering wavefunction needed to analyze the asymptotic wavefunction in photodissociation theory, the definition of the initial wavepacket in photodissociation theory and its relationship to the initial bound-state wavepacket, and finally the theory of differential state-specific photo-fragmentation cross sections. Many of the details developed in these appendix sections are also relevant to the theory of reactive scattering. 

Exciting new developments, not discussed in the review are the extension of time-dependent wavepacket reactive scattering theory to full dimensional four-atom systems [137,199-201], the adaptation of the codes to use the power of parallel computers [202], and the development of new computational techniques for acting with the Hamiltonian operator on the wavepacket [138]. 

The first part of the chapter deals with aspects of photodissociation theory and the second with reactive scattering theory. Key topics covered in the chapter are the anal sis of the wavepacket in the exit channel to ield product (piantuin state distributions, photofragmentation T matrix elements, state-to-state S matrices and the real wavepacket method, which we have applied only to reactive scattering calculations. 

Balint-Kurti, G.G., Wavepacket theory of photodissociation and reactive scattering, Adv. Chem. Phys., (irr press). 

There are two classes in applications of quantum nuclear dynamics one is the stationary-state scattering theory to treat reactive scattering (chemical reactions), and the other is time-dependent wavepacket method. Here... 

The energy is a constant of the motion. So each portion of the wavepacket with a definite energy may be considered to scatter independently of other parts of the same wavepacket which have diflferent energies. In time-dependent reactive scattering theory we analyse the final wavepacket so as to find out what happened to different energy components of it. In order to find the reaction probability we need to know what portion of the original wavepacket had a particular energy. 

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. 

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