Potential energy surface final state distributions

The purpose of this chapter is a detailed comparison of these systems and the elucidation of the transition from regular to irregular dynamics or from mode-specific to statistical behavior. The main focus will be the intimate relationship between the multidimensional PES on one hand and observables like dissociation rate and final-state distributions on the other. Another important question is the rigorous test of statistical methods for these systems, in comparison to quantum mechanical as well as classical calculations. The chapter is organized in the following way The three potential-energy surfaces and the quantum mechanical dynamics calculations are briefly described in Sections II and III, respectively. The results for HCO, DCO, HNO, and H02 are discussed in Sections IV-VII, and the overview ends with a short summary in Section VIII. 

This list, which is by no means complete, clearly demonstrates that the generic type of final state distribution is not only observed for atom-diatom systems but also if the recoiling partner is a large polyatomic molecule. In contrast to the many experimental examples, there are only a few systems for which rotational excitation has been analyzed by means of ab initio potential energy surfaces and exact quantum mechanical or classical calculations. In the following we discuss two of them. 

Fig. 9.1. Left-hand side Representation of an elastic potential energy surface. It has the general form (6.35) with coupling strength parameter e = 0. In case (a), the equilibrium bond distance in the electronic ground state equals the equilibrium separation of the free BC fragment. The heavy arrows schematically indicate two representative trajectories starting at the respective FC points. Right-hand side The corresponding final state distributions.

On the other hand, the dynamics of the bond dissociations (i.e. the motion of the representative wave packet on the potential energy surfaces of ground and excited states for the various molecular entities) turns out to be always the same. This is concluded from the fact that the final state of the desorbing NO stays constant all energy distributions, translational, rotational, and vibrational, as well as their correlations, are identical despite the strong variations of cross sections [14, 96], These characteristics are compatible with the proposed TNI mechanism (see item 2 in... 

The basic question posed in reactive scattering theory today is simple. Given a potential energy surface for the interacting molecules, what will be the outcome of a collision between them. The outcome is described in various terms such as a reaction probability, distribution of final states, differential cross section, rate constant etc. All of these quantities depend on the initial state of the colliders. 

The laws of physics needed to answer the question are well known. Since the potential energy surface is given, one knows the masses of the colliders and so one only needs to solve the SchrUdinger equation. The problem of course is that the number of coupled equations that need to be solved is enormous and not yet within reach of present day computers. Necessarily then the theorist is restricted to studying model systems and construction of approximations. One type of approximation is to solve the exact classical mechanical equations of motion. One selects initial conditions which correspond to the experimental initial state, integrates the equations of motion forward in time till the process is over and then obtains cross sections, product distributions etc. In essence, Hamilton s equations of motion serve as a black box , whose structure is determined by the masses and the potential energy surface. This black box provides the necessary transformation from initial conditions to final conditions. 

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