On the classical reaction rate and the first-time problems of Brownian motion

Aihua Zhang; Sun Choi

doi:10.1016/j.physa.2023.128823

On the classical reaction rate and the first-time problems of Brownian motion

Aihua Zhang, Sun Choi

Department of Pharmaceutical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We have developed efficient techniques to solve the first-time problems of Brownian motion. Based on a time-scale separation of recrossings, we show that Eyring's transmission coefficient (κ) equals to the one (κ_V) corresponding to an absorbing boundary consistent with the transition state theory, which is greater than the one (κ_K) derived by Kramers. We also propose methods for reaction rate determination by analyzing short-time trajectories from the barrier maximum, and discuss the relation to the reactive flux method and the significance of reaction coordinates.

Original language	English
Article number	128823
Journal	Physica A: Statistical Mechanics and its Applications
Volume	622
DOIs	https://doi.org/10.1016/j.physa.2023.128823
State	Published - 15 Jul 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

First-time Problems
Kramers’ coefficient
Langevin equation
Reaction rate theory
Transition state theory

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10.1016/j.physa.2023.128823

Cite this

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abstract = "We have developed efficient techniques to solve the first-time problems of Brownian motion. Based on a time-scale separation of recrossings, we show that Eyring's transmission coefficient (κ) equals to the one (κV) corresponding to an absorbing boundary consistent with the transition state theory, which is greater than the one (κK) derived by Kramers. We also propose methods for reaction rate determination by analyzing short-time trajectories from the barrier maximum, and discuss the relation to the reactive flux method and the significance of reaction coordinates.",

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AU - Zhang, Aihua

AU - Choi, Sun

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N2 - We have developed efficient techniques to solve the first-time problems of Brownian motion. Based on a time-scale separation of recrossings, we show that Eyring's transmission coefficient (κ) equals to the one (κV) corresponding to an absorbing boundary consistent with the transition state theory, which is greater than the one (κK) derived by Kramers. We also propose methods for reaction rate determination by analyzing short-time trajectories from the barrier maximum, and discuss the relation to the reactive flux method and the significance of reaction coordinates.

AB - We have developed efficient techniques to solve the first-time problems of Brownian motion. Based on a time-scale separation of recrossings, we show that Eyring's transmission coefficient (κ) equals to the one (κV) corresponding to an absorbing boundary consistent with the transition state theory, which is greater than the one (κK) derived by Kramers. We also propose methods for reaction rate determination by analyzing short-time trajectories from the barrier maximum, and discuss the relation to the reactive flux method and the significance of reaction coordinates.

KW - First-time Problems

KW - Kramers’ coefficient

KW - Langevin equation

KW - Reaction rate theory

KW - Transition state theory

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VL - 622

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 128823

ER -

On the classical reaction rate and the first-time problems of Brownian motion

Abstract

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Keywords

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