Classical-Quantum correspondence in isomerization dynamics: quantum eigenstates and classical Arnol'd web

Recently, there has been a renaissance of sorts in chemical dynamics with researchers critically examining the validity of the two pillars of reaction rate theory - transition state theory and the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Since both theories have classical dynamics at their foundation, advances in our understanding of nonlinear dynamics and continuing efforts to characterize the phase space structure of systems with three or more degrees of freedom are beginning to yield crucial mechanistic insights into the dynamics. This talk focuses on a mechanistic understanding of the deviations from RRKM theory for a model isomerization problem with three degrees of freedom. Several studies have established that such systems are prime candidates for observing non-RRKM behavior\footnote{D. M. Leitner, Int. J. Quant. Chem. {\bf 75}, 523 (1999).}. The model is inspired, and generalized, from a much earlier study by De Leon and Berne\footnote{N. De Leon and B. J. Berne, J. Chem. Phys. {\bf 75}, 3495 (1981).}. We try to answer two of the questions posed in this early work by studying the intramolecular vibrational energy flow in the system from both classical and quantum viewpoints. Using a wavelet-based local frequency analysis it is possible to construct a useful representation of the classical phase space (Arnol'd web) highlighting the important dynamical structures. Insights into the dynamics originate from the various nonlinear resonances and phase space traps which potentially result in quantum eigenstates of varying degree of localization\footnote{D. M. Leitner and M. Gruebele, Mol. Phys. {\bf 106}, 433 (2008).}.