Detecting reactive islands in a system-bath model of isomerization

Naik, Shibabrat; Wiggins, Stephen

doi:10.1039/d0cp01362e

Cited by 25 publications

(12 citation statements)

References 99 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…SVM is known to work well even with small amounts of data, therefore our approach is computationally better suited than existing methods for high-dimensional systems and systems where integrating trajectories is expensive. This makes SVM suitable for the reactive island theory of three DoF 21 and system-bath models of isomerization 22 which has been developed recently and supports the case for a computationally efficient approach to phase space structures presented here.…”

Section: Introductionsupporting

confidence: 73%

See 1 more Smart Citation

Support vector machines for learning reactive islands

Naik¹,

Krajňák²,

Wiggins³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We develop a machine learning framework that can be applied to data sets derived from the trajectories of Hamilton's equations. The goal is to learn the phase space structures that play the governing role for phase space transport relevant to particular applications. Our focus is on learning reactive islands in two degrees-of-freedom Hamiltonian systems. Reactive islands are constructed from the stable and unstable manifolds of unstable periodic orbits and play the role of quantifying transition dynamics. We show that support vector machines (SVM) is an appropriate machine learning framework for this purpose as it provides an approach for finding the boundaries between qualitatively distinct dynamical behaviors, which is in the spirit of the phase space transport framework. We show how our method allows us to find reactive islands directly in the sense that we do not have to first compute unstable periodic orbits and their stable and unstable manifolds. We apply our approach to the Hénon-Heiles Hamiltonian system, which is a benchmark system in the dynamical systems community. We discuss different sampling and learning approaches and their advantages and disadvantages.

show abstract

Section: Introductionsupporting

confidence: 73%

“…and other application of this method includes celestial mechanics, ship dynamics, models of dissociation and isomerization reaction 22,24,42,43 ).…”

Section: The Linearized Hamiltonian Systemmentioning

confidence: 99%

Support vector machines for learning reactive islands

Naik¹,

Krajňák²,

Wiggins³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The method of Lagrangian descriptors turns this problem on its head by emphasizing the initial conditions of trajectories, rather than the precise location of their futures and pasts, after a specified amount of time. In fact, Lagrangian descriptors have already been used to reveal reactive islands in 2 DoF Hamiltonian systems [39,[45][46][47]. A low-dimensional "slice" of phase space can be selected and sampled with a grid of initial conditions of high resolution.…”

Section: B Three Degrees-of-freedom Hamiltonian Systemsmentioning

confidence: 99%

Reactive Islands for Three Degrees-of-Freedom Hamiltonian Systems

Krajňák,

García-Garrido,

Wiggins

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We develop the geometrical, analytical, and computational framework for reactive island theory for three degrees-of-freedom time-independent Hamiltonian systems. In this setting, the dynamics occurs in a 5-dimensional energy surface in phase space and is governed by four-dimensional stable and unstable manifolds of a three-dimensional normally hyperbolic invariant sphere. The stable and unstable manifolds have the geometrical structure of spherinders and we provide the means to investigate the ways in which these spherinders and their intersections determine the dynamical evolution of trajectories. This geometrical picture is realized through the computational technique of Lagrangian descriptors. In a set of trajectories, Lagrangian descriptors allow us to identify the ones closest to a stable or unstable manifold. Using an approximation of the manifold on a surface of section we are able to calculate the flux between two regions of the energy surface.

show abstract

“…In this study, we use Lagrangian descriptors [71][72][73] (see Appendix C for details on the method) to identify the changes in the phase space structures with the changes in the coupling strengths and frequency of the third mode. In the case of three or more degrees of freedom systems, this method has been used to detect invariant manifolds and reactive islands [74][75][76], discovering structure in the nuclear phase space in nonadiabatic quantum dynamics [77], while there is an increasing number of analysis for one and two degrees of freedom system with and without dissipation and time dependence. We refer the reader to the references in the open-source book on Lagrangian descriptors [73].…”

Section: Phase Space Viewpoint: Lagrangian Descriptors Are Correlated...mentioning

confidence: 99%

Influence of low frequency modes on dynamical concertedness in double proton transfer dynamics

Pandey,

Naik,

Keshavamurthy

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We analyze the classical phase space dynamics of a three degree of freedom Hamiltonian that models multiple bond breaking and forming reactions. The model Hamiltonian, inspired from studies on double proton transfer reactions, allows for exploring the dynamical consequences of higher index saddles on multidimensional potential energy surfaces. Studies have shown that coupling of low frequency transverse modes to the reaction coordinate can significantly influence the reaction mechanism, concerted or sequential, as inferred from a reduced dimensional analysis. Using the notion of dynamically concerted and sequential pathways, we provide insights into the role of the transverse modes by studying the delay times between the formation of two bonds. The delay time distribution, used extensively in earlier studies, is placed on a firm dynamical footing by correlating it with the phase space manifolds, determined using the technique of Lagrangian descriptors. We establish the utility of Lagrangian descriptors in identifying the phase space manifolds responsible for the dynamically concerted and dynamically sequential pathways.

show abstract

Detecting reactive islands in a system-bath model of isomerization

Abstract: Reactive islands in a system-bath model of isomerization detected by the singular features in the Lagrangian descriptor contour map.

Cited by 25 publications

References 99 publications

Support vector machines for learning reactive islands

Support vector machines for learning reactive islands

Reactive Islands for Three Degrees-of-Freedom Hamiltonian Systems

Influence of low frequency modes on dynamical concertedness in double proton transfer dynamics

Contact Info

Product

Resources

About