Wiggins S. Phase Space Structures in Reaction Dynamics. A Dynamical Systems 2025

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Wiggins S. Phase Space Structures in Reaction Dynamics. A Dynamical Systems 2025

Textbook in PDF format Chemical reaction dynamics is crucial for the study of chemical processes and the mechanisms which governthem. Most frameworks, however, remain static when representing the landscape of chemical reactions, fallingshort of capturing fully the evolution over time of the reaction profile. This book presents an application of fundamental mathematical theories — dynamical systems theory and phase space — tochemical reaction dynamics. These concepts are relevant to the analysis of chemical transformations which always involve changeover time. Exploiting the real-time evolution of molecular systems will enable better understanding and prediction of reactioncharacteristics, including reaction rates and product distributions. Traditional methods to quantify reactions rates do not alwayscapture this complex snapshot from reactants to products. In this book, the study of potential energy surfaces (PES) and other configurational landscapes is combined with phase space anddynamical systems theory, especially using the predictive value of the Hamiltonian. Introductory chapters focus on Hamiltoniandynamical systems and the crucial concepts in phase space and reaction dynamics, such as invariant manifolds, reactive islandsand transition state theory. They are followed by examples with various degrees of freedom in numerous models, such as theMorse oscillator, the De Leon-Berne Isomerization Model, and the Caldera Model. Advanced examples are also included for higherdimensional systems. With the aim of bridging the gap between traditional static models and a more comprehensive, dynamic perspective, this bookintroduces dynamical systems theory in a more accessible and unified language. It should be relevant for applied mathematiciansas well as computational chemists interested in chemical reaction dynamics