Chemical dynamics between wells across a time-dependent barrier: Self-similarity in the Lagrangian descriptor and reactive basins

Abstract

In chemical or physical reaction dynamics, it is essential to distinguish precisely between reactants and products for all time. This task is especially demanding in time-dependent or driven systems because therein the dividing surface (DS) between these states often exhibits a nontrivial time-dependence. The so-called transition state (TS) trajectory has been seen to define a DS which is free of recrossings in a large number of one-dimensional reactions across time-dependent barriers, and, thus, allows one to determine exact reaction rates. A fundamental challenge to applying this method is the construction of the TS trajectory itself. The minimization of Lagrangian descriptors (LDs) provides a general and powerful scheme to obtain that trajectory even when perturbation theory fails. Both approaches encounter possible breakdowns when the overall potential is bounded, admitting the possibility of returns to the barrier long after trajectories have reached the product or reactant wells. Such global dynamics cannot be captured by perturbation theory. Meanwhile, in the LD-DS approach, it leads to the emergence of additional local minima which make it difficult to extract the optimal branch associated with the desired TS trajectory. In this work, we illustrate this behavior for a time-dependent double-well potential revealing a self-similar structure of the LD, and we demonstrate how the reflections and side-minima can be addressed by an appropriate modification of the LD associated with the direct rate across the barrier.

7 pages, 6 figures, 50 references

References in corpus (9)

• Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
• The Transition State in a Noisy Environment
• Stochastic Transition States: Reaction Geometry amidst Noise
• Identifying reactive trajectories using a moving transition state
• Chemical reactions induced by oscillating external fields in weak thermal environments
• Transition state trajectory stability determines barrier crossing rates in chemical reactions induced by time-dependent oscillating fields
• Local phase space control and interplay of classical and quantum effects in dissociation of a driven Morse oscillator
• Persistence of transition state structure in chemical reactions driven by fields oscillating in time
• Chemical Reaction Dynamics within Anisotropic Solvents in Time-Dependent Fields

Cited by in corpus (22)

• Finding NHIM: Identifying High Dimensional Phase Space Structures in Reaction Dynamics using Lagrangian Descriptors
• Detection of Dynamical Matching in a Caldera Hamiltonian System using Lagrangian Descriptors
• Phase Space Analysis of the Dynamics on a Potential Energy Surface with an Entrance Channel and Two Potential Wells
• The Dynamical Matching Mechanism in Phase Space for Caldera-Type Potential Energy Surfaces
• The Phase Space Mechanism for Selectivity in a Symmetric Potential Energy Surface with a Post-Transition-State Bifurcation
• Finding NHIM in 2 and 3 degrees-of-freedom with Hénon-Heiles type potential
• Invariant Manifolds and Rate Constants in Driven Chemical Reactions
• Global dynamics visualisation from Lagrangian Descriptors. Applications to discrete and continuous systems
• Tilting and Squeezing: Phase space geometry of Hamiltonian saddle-node bifurcation and its influence on chemical reaction dynamics
• Neural network approach to time-dependent dividing surfaces in classical reaction dynamics
• Visualizing the Phase Space of the HeI_2 van der Waals Complex using Lagrangian Descriptors
• Detection of separatrices and chaotic seas based on orbit amplitudes
• Phase-space resolved rates in driven multidimensional chemical reactions
• From Poincare Maps to Lagrangian Descriptors: The Case of the Valley Ridge Inflection Point Potential
• Unveiling the Fractal Structure of Julia Sets with Lagrangian Descriptors
• Using Lagrangian descriptors to uncover invariant structures in Chesnavich's Isokinetic Model with application to roaming
• An Extension of Discrete Lagrangian Descriptors for Unbounded Maps
• Reactive Islands for Three Degrees-of-Freedom Hamiltonian Systems
• Controlling reaction dynamics in chemical model systems through external driving
• Dynamics and decay rates of a time-dependent two-saddle system
• Hamiltonian pitchfork bifurcation in transition across index-1 saddles
• Using Lagrangian descriptors to calculate the Maslov index of periodic orbits