Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions

Abstract

Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific assumptions about the extent of intramolecular vibrational energy flow in the system. However, the nature of the transition to the statistical regime as a function of the molecular parameters is far from being completely understood. Here, we use tools from nonlinear dynamics to study the transition to statisticality in a model unimolecular reaction by explicitly visulaizing the high dimensional classical phase space. We identify generic features in the phase space involving the intersection of two or more independent anharmonic resonances and show that the presence of correlated, but chaotic, intramolecular dynamics near such junctions leads to nonstatisticality. Interestingly, akin to the stability of asteroids in the Solar System, molecules can stay protected from dissociation at the junctions for several picoseconds due to the phenomenon of stable chaos.

Cavity-modified unimolecular dissociation reactions via intramolecular vibrational energy redistribution

“…For instance, the ensembles of initial states used to calculate the dissociation dynamics can be selected through a variety of means. Here we study ensembles of trajectories picked from constant energy hypersurfaces [35]. Our approach can easily be generalized to differently chosen ensembles of initial states, however.…”

“…1a in Ref. 35. As Karmakar et al note, under these conditions, distribution of vibrational energy occurs mostly statistically, meaning that the space of nonlinear frequency resonances between vibrational modes is widely explored with little trapping in any particular nonlinear resonance.…”

“…We use a classical triatomic model with three degrees of freedom and anharmonic potentials. This model was previously used by Karmakar et al to understand the onset of chaos in IVR processes [35] and is itself based on the approach pioneered by D. L. Bunker and others who studied the ozone molecule in a series of computational studies on unimolecular dissociation reactions [36][37][38]. Importantly, this model is minimal while still demonstrating chaotic dynamics through an interconnected Arnold web [39,40], or network of nonlinear resonances, and therefore serves as a fundamental starting point for IVR studies of larger molecules.…”

“…Here, the initial energy is 34 kcal/mol > D 1 = D 2 = 24 kcal/mol, (ω 1 , ω 2 , ω 3 ) = (1112, 1040, 632) cm −1 , α 1 = 2.212 Bohr −1 , α 2 = 2.069 Bohr −1 , and equilibrium values q 0 i and G (0) ij are as defined in Table I in Appendix A and in Ref. 35. The trajectory exhibits chaotic i are in atomic units.…”

“…2, we plot the frequency spectra for molecules initialized with energy 34 kcal/mol > D i = 24 kcal/mol, sufficient to dissociate the bond. To statistically characterise the influence of model parameters on the dissociation lifetimes and the chaotic dynamics of the IVR processes [35][36][37], we propagate the trajectories for ∼ 10 4 − 10 5 initial states of identical energies [35] and bin them by their dissociation lifetimes.…”