Dissociation guided by an unstable periodic orbit

Time-resolved coordinate distribution Pri(Ru-ou, a t) obtaine ing over a large number of classical trajectories. In order to reveal 

The excited complex breaks apart very rapidly and only a minor fraction performs, on the average, one single internal vibration. Therefore, the total stationary wavefunction does not exhibit a clear change of its nodal structure when the energy is tuned from one peak to another (Weide and Schinke 1989). In the light of Section 7.4.1 we can argue that the direct part of the total wavefunction, S dir-, dominates and therefore obscures the more interesting indirect part, Sind- The superposition of the direct and the indirect parts makes it difficult to analyze diffuse structures in the time-independent approach. In contrast, the time-dependent theory allows, by means of the autocorrelation function, the separation of the direct and resonant contributions and it is therefore much better suited to examine diffuse structures. 

Because of the very short lifetime the time-dependent approach provides the more illuminating explanation of diffuse structures. It allows the separation of the indirect part of the dissociation from the less interesting direct one, which dominates the overall fragmentation dynamics. 

This is inherently impossible in the time-independent approach because the wavefunction contains the entire history of the wavepacket. The real understanding, however, is provided by classical mechanics. Plotting individual trajectories easily shows the type of internal motion leading to the recurrences which subsequently cause the diffuse structures in the energy domain. The next obvious step, finding the underlying periodic orbits, is rather straightforward. 

The main purpose of this chapter is to emphasize the intimate relation between the topology of the dissociative PES and the vibrational excitation of the fragment molecule. In Sections 9.1 and 9.2 we consider exclusively direct processes. The photodissociation of symmetric molecules with two equivalent product channels is the topic of Section 9.3. Finally, vibrational state distributions following the decay of a long-lived intermediate complex will be discussed in Section 9.4. The theory 

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