Invariant Manifolds and Rate Constants in Driven Chemical Reactions

Area of Science:

• Chemical Dynamics
• Computational Chemistry
• Reaction Rate Theory

Background:

• Determining reaction rates under nonequilibrium conditions is crucial for understanding chemical processes.
• The normally hyperbolic invariant manifold (NHIM) and moving dividing surface (DS) are key concepts for analyzing transition states.
• Previous methods for NHIM construction had limitations, especially in multidimensional systems.

Purpose of the Study:

• To extend and improve methods for accurately constructing the NHIM in multidimensional chemical systems.
• To advance the application of machine learning techniques for generating smooth NHIM representations.
• To compare the accuracy and applicability of different NHIM construction methods.

Main Methods:

• Developing accurate methods for constructing points on the NHIM for multidimensional cases.
• Implementing machine learning, including neural networks and Gaussian process regression, to build smooth NHIMs from discrete points.
• Applying these methods to a challenging two-dimensional model barrier system for validation.

Main Results:

• Successful accurate construction of NHIM points in multidimensional systems.
• Demonstrated the effectiveness of machine learning, particularly Gaussian process regression, in creating smooth NHIMs.
• Provided a comparative analysis of the developed methods on a model system, highlighting their accuracy and generalizability.

Conclusions:

• The enhanced methods provide accurate and generalizable approaches for constructing the NHIM in complex chemical systems.
• Machine learning techniques offer powerful tools for advancing the study of chemical reaction dynamics.
• These advancements facilitate a deeper understanding of reaction rates under nonequilibrium conditions.