Polyad intramolecular dynamics

The unzipping procedure reveals the diagnostically significant trends in fractionation widths and patterns illustrated by Figure 3. These trends can lead to qualitative insights into IVR mechanisms and can suggest optimal schemes for external control over intramolecular dynamics. The unzipped polyads can also yield quantitative least-squares refinements of anharmonic coupling constants, from which any dynamical quantity based on (Q, 0 may be calculated. 

Trajectories in action/angle polyad phase space convey all of the most important qualitative relationships between a quantum spectrum and classical intramolecular dynamics. However, coordinate space trajectories are both more easily visualized and more directly comparable to quantum probability densities, ip(Qi,Q2,... ( 3jv-6) 2 Xiao and Kellman (1989) describe how the action/angle phase space trajectories for each eigenstate may be converted into a coordinate space trajectory. The key to this is the exact relationship between Morse oscillator displacement coordinates, rit and the action, angle variables, Ii,4>i (Rankin and Miller, 1971). Figure 9.17 shows, for the 6 eigenstates in the I = 3 (N = vs + va = 5) polyad of H20, the correspondences between the phase space trajectories, the coordinate space trajectories, and the probability densities. The resemblance between the classical coordinate space trajectories and the quantum probability densities is striking ... 

The phase space structures for two identical coupled anharmonic oscillators are relatively simple because the trajectories lie on the surface of a 2-dimensional manifold in a 4-dimensional phase space. The phase space of two identical 2-dimensional isotropic benders is 8-dimensional, the qualitative forms of the classifying trajectories are far more complicated, and there is a much wider range of possibilities for qualitative changes in the intramolecular dynamics. The classical mechanical polyad 7feff conveys unique insights into the dynamics encoded in the spectrum as represented by the Heff fit model. 

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