Chapter 3. A New Look at the Transition State: Wigner's Dynamical Perspective Revisited

  1. M. Toda5,
  2. T. Komatsuzaki6,
  3. T. Konishi7,
  4. R. S. Berry8 and
  5. S. A. Rice9
  1. Charles Jaffé1,
  2. Shinnosuke Kawai2,
  3. Jesús Palacián3,
  4. Patricia Yanguas3 and
  5. Turgay Uzer4

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch3

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

How to Cite

Jaffé, C., Kawai, S., Palacián, J., Yanguas, P. and Uzer, T. (2005) A New Look at the Transition State: Wigner's Dynamical Perspective Revisited, in Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130 (eds M. Toda, T. Komatsuzaki, T. Konishi, R. S. Berry and S. A. Rice), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471712531.ch3

Editor Information

  1. 5

    Physics Department, Nara Women's University, Nara, 630-8506, Japan

  2. 6

    Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan

  3. 7

    Department of Physics, Nagoya University, Nagoya, 464-8602, Japan

  4. 8

    Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA

  5. 9

    Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

Author Information

  1. 1

    Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA

  2. 2

    Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan

  3. 3

    Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain

  4. 4

    Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA

Publication History

  1. Published Online: 27 JAN 2005
  2. Published Print: 21 JAN 2005

Book Series:

  1. Advances in Chemical Physics

Book Series Editors:

  1. Stuart A. Rice

Series Editor Information

  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

ISBN Information

Print ISBN: 9780471711582

Online ISBN: 9780471712534

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Keywords:

  • classical reaction dynamics;
  • transition state theory;
  • saddles;
  • separatrices;
  • transition states;
  • normally hyperbolic invariant manifolds

Summary

In this article we review our general formulation of the nonlinear dynamics and geometry of classical reaction dynamics. Our formalism hinges on finding, for the first time, the dynamically exact higher dimensional structures (separatrices, dividing surfaces) which regulate transport between qualitatively different states (“reactants” and “products”) in three or more degrees of freedom. The work explained in this article has been a long-standing and often-expressed aspiration of the science and mathematics communities, but it is only now that we have the theoretical and computational tools for its fulfillment. We illustrate the theory on the isomerization of HCN.