Time-dependent wavepacket theory 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]. 

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... 

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 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. 

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