### Abstract

We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

Original language | English |
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Title of host publication | AIP Conference Proceedings |

Pages | 1597-1600 |

Number of pages | 4 |

Volume | 1281 |

DOIs | |

Publication status | Published - 2010 |

Event | International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece Duration: 2010 Sep 19 → 2010 Sep 25 |

### Other

Other | International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 |
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Country | Greece |

City | Rhodes |

Period | 10/9/19 → 10/9/25 |

### Fingerprint

### Keywords

- cluster
- diffusion
- dimension reduction
- hyperspherical coordinates
- non-RRKM
- reaction coordinate
- reaction rate

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1281, pp. 1597-1600) https://doi.org/10.1063/1.3498120

**A nonequilibrium rate formula for collective motions of complex molecular systems.** / Yanao, Tomohiro; Koon, Wang Sang; Marsden, Jerrold E.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AIP Conference Proceedings.*vol. 1281, pp. 1597-1600, International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010, Rhodes, Greece, 10/9/19. https://doi.org/10.1063/1.3498120

}

TY - GEN

T1 - A nonequilibrium rate formula for collective motions of complex molecular systems

AU - Yanao, Tomohiro

AU - Koon, Wang Sang

AU - Marsden, Jerrold E.

PY - 2010

Y1 - 2010

N2 - We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

AB - We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

KW - cluster

KW - diffusion

KW - dimension reduction

KW - hyperspherical coordinates

KW - non-RRKM

KW - reaction coordinate

KW - reaction rate

UR - http://www.scopus.com/inward/record.url?scp=79954466808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954466808&partnerID=8YFLogxK

U2 - 10.1063/1.3498120

DO - 10.1063/1.3498120

M3 - Conference contribution

VL - 1281

SP - 1597

EP - 1600

BT - AIP Conference Proceedings

ER -