### Abstract

The results of transition state theory are derived rigorously in the general context of ergodic dynamical systems defined by a vector field on a Riemannian manifold. A new perspective on how to compute the dynamical corrections to the transition state theory transition frequency is given. Hamiltonian dynamical systems are considered a special case and the so-called Marcus formula for the rate constant is re-derived.

Original language | English (US) |
---|---|

Pages (from-to) | 501-509 |

Number of pages | 9 |

Journal | Nonlinearity |

Volume | 19 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2006 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Nonlinearity*,

*19*(2), 501-509. https://doi.org/10.1088/0951-7715/19/2/014

**Transition state theory and dynamical corrections in ergodic systems.** / Tal, Fabio A.; Vanden Eijnden, Eric.

Research output: Contribution to journal › Article

*Nonlinearity*, vol. 19, no. 2, pp. 501-509. https://doi.org/10.1088/0951-7715/19/2/014

}

TY - JOUR

T1 - Transition state theory and dynamical corrections in ergodic systems

AU - Tal, Fabio A.

AU - Vanden Eijnden, Eric

PY - 2006/2/1

Y1 - 2006/2/1

N2 - The results of transition state theory are derived rigorously in the general context of ergodic dynamical systems defined by a vector field on a Riemannian manifold. A new perspective on how to compute the dynamical corrections to the transition state theory transition frequency is given. Hamiltonian dynamical systems are considered a special case and the so-called Marcus formula for the rate constant is re-derived.

AB - The results of transition state theory are derived rigorously in the general context of ergodic dynamical systems defined by a vector field on a Riemannian manifold. A new perspective on how to compute the dynamical corrections to the transition state theory transition frequency is given. Hamiltonian dynamical systems are considered a special case and the so-called Marcus formula for the rate constant is re-derived.

UR - http://www.scopus.com/inward/record.url?scp=30644466750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30644466750&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/19/2/014

DO - 10.1088/0951-7715/19/2/014

M3 - Article

AN - SCOPUS:30644466750

VL - 19

SP - 501

EP - 509

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 2

ER -