Bifurcations of dividing surfaces in chemical reactions

Iñarrea, Manuel; Palacián, Jesús F.; Pascual, Ana I.; Salas, J. Pablo

doi:10.1063/1.3600744

Cited by 34 publications

(34 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the precise extent of this range, as well as the nature and consequences of any bifurcations of the phase space structures and invariant manifolds that might occur as energy is increased, is not known and is a topic of continuing research (73)(74)(75)(76).…”

Section: Periodic Orbit Dividing Surfaces Normally Hyperbolic Invarimentioning

confidence: 99%

Roaming: A Phase Space Perspective

Mauguière

Collins

Kramer

et al. 2017

Annu. Rev. Phys. Chem.

View full text Add to dashboard Cite

In this review we discuss the recently described roaming mechanism for chemical reactions from the point of view of nonlinear dynamical systems in phase space. The recognition of the roaming phenomenon shows the need for further developments in our fundamental understanding of basic reaction dynamics, as is made clear by considering some questions that cut across most studies of roaming: Is the dynamics statistical? Can transition state theory be applied to estimate roaming reaction rates? What role do saddle points on the potential energy surface play in explaining the behavior of roaming trajectories? How do we construct a dividing surface that is appropriate for describing the transformation from reactants to products for roaming trajectories? How should we define the roaming region? We show that the phase space perspective on reaction dynamics provides the setting in which these questions can be properly framed and answered. We illustrate these ideas by considering photodissociation of formaldehyde. The phase-space formulation allows an unambiguous description of all possible reactive events, which also allows us to uncover the phase space mechanism that explains which trajectories roam, as opposed to evolving toward a different reactive event.

show abstract

Section: Periodic Orbit Dividing Surfaces Normally Hyperbolic Invarimentioning

confidence: 99%

Roaming: A Phase Space Perspective

Mauguière

Collins

Kramer

et al. 2017

Annu. Rev. Phys. Chem.

View full text Add to dashboard Cite

show abstract

“…34 However, the precise extent of this range, as well as the nature and consequences of any bifurcations of the phase space structures and invariant manifolds that might occur as energy is increased, is not known and is a topic of continuing research. [36][37][38][39] While work relating phase space structures and invariant manifolds to saddle points on the potential energy surface has provided new insights and techniques for studying reaction dynamics, [22][23][24][25] it by no means exhausts all of the rich possibilities of dynamical phenomena associated with reactions. In fact, a body of work has called into question the utility of concepts such as the reaction path and/or transition state (TS).…”

Section: Introductionmentioning

confidence: 99%

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Mauguière

Collins

Kramer

et al. 2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories. C 2016 AIP Publishing LLC.[http://dx

show abstract

“…16 It defines a recrossing-free surface at energies below bifurcation thresholds. [23][24][25] Reactive trajectories are mediated by stable and unstable manifolds (reaction pathways) attached to the NHIM. These pathways persist even in reactions whose state-to-state transitions are not dictated by purely configurational changes.…”

Section: Introductionmentioning

confidence: 99%

Chemical reactions induced by oscillating external fields in weak thermal environments

Craven

Bartsch

Hernandez

2015

The Journal of Chemical Physics

View full text Add to dashboard Cite

Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally varying external field, the transition state that the reaction must pass through during the transformation from reactant to product is no longer a fixed geometric structure, but is instead timedependent. For a periodically forced model reaction, we develop a recrossing-free dividing surface that is attached to a transition state trajectory [T. Bartsch, R. Hernandez, and T. Uzer, Phys. Rev. Lett. 95, 058301 (2005)]. We have previously shown that for single-mode sinusoidal driving, the stability of the timevarying transition state directly determines the reaction rate [G. T. Craven, T. Bartsch, and R. Hernandez, J. Chem. Phys. 141, 041106 (2014)]. Here, we extend our previous work to the case of multi-mode driving waveforms. Excellent agreement is observed between the rates predicted by stability analysis and rates obtained through numerical calculation of the reactive flux. We also show that the optimal dividing surface and the resulting reaction rate for a reactive system driven by weak thermal noise can be approximated well using the transition state geometry of the underlying deterministic system. This agreement persists as long as the thermal driving strength is less than the order of that of the periodic driving. The power of this result is its simplicity. The surprising accuracy of the time-dependent noise-free geometry for obtaining transition state theory rates in chemical reactions driven by periodic fields reveals the dynamics without requiring the cost of brute-force calculations.

show abstract

Bifurcations of dividing surfaces in chemical reactions

Cited by 34 publications

References 35 publications

Roaming: A Phase Space Perspective

Roaming: A Phase Space Perspective

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Chemical reactions induced by oscillating external fields in weak thermal environments

Contact Info

Product

Resources

About