Abstract
A reduced two-dimensional model is used to study ketene isomerization reaction. In light of recent results by Ulusoy et al. (J Phys Chem A 117, 7553, 2013), the present work focuses on the generalization of the roaming mechanism to the ketene isomerization reaction by applying our phase space approach previously used to elucidate the roaming phenomenon in ion–molecule reactions. Roaming is again found be associated with the trapping of trajectories in a phase space region between two dividing surfaces; trajectories are classified as reactive or nonreactive, and are further naturally classified as direct or nondirect (roaming). The latter long-lived trajectories are trapped in the region of nonlinear mechanical resonances, which in turn define alternative reaction pathways in phase space. It is demonstrated that resonances associated with periodic orbits provide a dynamical explanation of the quantum mechanical resonances found in the isomerization rate constant calculations by Gezelter and Miller (J Chem Phys 103, 7868–7876, 1995). Evidence of the trapping of trajectories by ‘sticky’ resonant periodic orbits is provided by plotting Poincaré surfaces of section, and a gap time analysis is carried out in order to investigate the statistical assumption inherent in transition state theory for ketene isomerization.
Highlights
The photodissociation of ketene, CH2CO, has been the subject of many studies, both experimental and theoretical
If we consider that the system is initially in the ketene well located on the part of the potential for which qF\ À 3 a0, isomerization is completed if the system passes to the other ketene well located on the part of the potential for which qF [ 3 a0
The strategy followed to understand the motions of nonlinear dynamical systems is to reveal the geometry of phase space in a systematic way by first locating equilibria, and from them the emanating principal families of periodic orbits, tori, normally hyperbolic invariant manifolds (NHIMs) andstable manifolds associated with NHIMs. The latter are key protagonists in controlling reaction fluxes. Both for the isomerization dynamics of ketene and in our previous work on the Chesnavich model for ion–molecule reactions, we have shown that, by defining transition states using the appropriate NHIMs, ordinary (MEP) and roaming reaction pathways emerge within a phase space framework
Summary
The photodissociation of ketene, CH2CO, has been the subject of many studies, both experimental and theoretical. Ulusoy et al [6, 7] studied the effect of roaming trajectories on the reaction rates for the isomerization of ketene. By investigating the dynamics in its appropriate setting, phase space, we examined the roaming phenomenon in the presence of well-defined dividing surfaces (DSs) and associated reaction pathways in phase space. This approach enabled us to interpret roaming as a trapping phenomenon of trajectories between two DSs and the enhancement of this trapping by the presence of nonlinear mechanical resonances between the different degrees of freedom (DoF) of the system.
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