Invariant Manifolds and Rate Constants in Driven Chemical Reactions

Abstract

Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets, and introduce the use of Gaussian process regression for the determination of the NHIM. Finally, we compare and contrast all of these methods for a challenging two-dimensional model barrier case so as to illustrate their accuracy and general applicability.

28 pages, 13 figures, table of contents figure

References in corpus (10)

• Mayavi: a package for 3D visualization of scientific data
• 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
• Chaotic Dynamics in Multidimensional Transition States
• Transition state trajectory stability determines barrier crossing rates in chemical reactions induced by time-dependent oscillating fields
• Persistence of transition state structure in chemical reactions driven by fields oscillating in time
• Transition state theory for wave packet dynamics. II. Thermal decay of Bose-Einstein condensates with long-range interaction
• Transition state theory for wave packet dynamics. I. Thermal decay in metastable Schrödinger systems

Cited by in corpus (3)

• Finding NHIM: Identifying High Dimensional Phase Space Structures in Reaction Dynamics using Lagrangian Descriptors
• Phase-space resolved rates in driven multidimensional chemical reactions
• Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems