### Abstract

We develop a first passage time description for the kinetics of reactions involving diffusive barrier crossing in a bistable (and also in a more general) potential, a situation realized, for example, in some photoisomerization processes. In case the reactant is in thermal equilibrium, the first passage times account well for the reaction dynamics as shown by comparison with exact numerical calculations. A simple integral expression for the rate constants is presented. For a case involving a reactant initially far off equilibrium, a two relaxation time description for the particle number N(t) is derived and compared with the results of an "exact" calculation. This description results from a knowledge of N(t=0), N(t=0), ∫_{0}^{∞}dt N(t), i.e., the first passage time, and ∫_{0}^{∞}dt t N(t).

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

Pages (from-to) | 4426-4432 |

Number of pages | 7 |

Journal | The Journal of Chemical Physics |

Volume | 74 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 1981 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*The Journal of Chemical Physics*,

*74*(8), 4426-4432. https://doi.org/10.1063/1.441684

**Dynamics of reactions involving diffusive barrier crossing.** / Schulten, Klaus J; Luthey-Schulten, Zaida Ann; Szabo, Attila.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 74, no. 8, pp. 4426-4432. https://doi.org/10.1063/1.441684

}

TY - JOUR

T1 - Dynamics of reactions involving diffusive barrier crossing

AU - Schulten, Klaus J

AU - Luthey-Schulten, Zaida Ann

AU - Szabo, Attila

PY - 1981/1/1

Y1 - 1981/1/1

N2 - We develop a first passage time description for the kinetics of reactions involving diffusive barrier crossing in a bistable (and also in a more general) potential, a situation realized, for example, in some photoisomerization processes. In case the reactant is in thermal equilibrium, the first passage times account well for the reaction dynamics as shown by comparison with exact numerical calculations. A simple integral expression for the rate constants is presented. For a case involving a reactant initially far off equilibrium, a two relaxation time description for the particle number N(t) is derived and compared with the results of an "exact" calculation. This description results from a knowledge of N(t=0), N(t=0), ∫0∞dt N(t), i.e., the first passage time, and ∫0∞dt t N(t).

AB - We develop a first passage time description for the kinetics of reactions involving diffusive barrier crossing in a bistable (and also in a more general) potential, a situation realized, for example, in some photoisomerization processes. In case the reactant is in thermal equilibrium, the first passage times account well for the reaction dynamics as shown by comparison with exact numerical calculations. A simple integral expression for the rate constants is presented. For a case involving a reactant initially far off equilibrium, a two relaxation time description for the particle number N(t) is derived and compared with the results of an "exact" calculation. This description results from a knowledge of N(t=0), N(t=0), ∫0∞dt N(t), i.e., the first passage time, and ∫0∞dt t N(t).

UR - http://www.scopus.com/inward/record.url?scp=0001069331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001069331&partnerID=8YFLogxK

U2 - 10.1063/1.441684

DO - 10.1063/1.441684

M3 - Article

AN - SCOPUS:0001069331

VL - 74

SP - 4426

EP - 4432

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

ER -