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

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

Funding Information:
This work was supported by the Mid-career Researcher Program ( NRF-2020R1A2C2101636 ), Bio & Medical Technology Development Program ( NRF-2022M3E5F3080873 ), Medical Research Center (MRC) grant ( NRF-2018R1A5A2025286 ), and the Brain Pool Program ( NRF-2021H1D3A2A02081370 ) funded by the Ministry of Science and ICT (MSIT) through the National Research Foundation of Korea (NRF) . It was also supported by the Ewha Womans University Research Grant of 2021. We thank T. N. L. Vũ for helpful discussions.

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

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title = "On the classical reaction rate and the first-time problems of Brownian motion",

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.",

keywords = "First-time Problems, Kramers{\textquoteright} coefficient, Langevin equation, Reaction rate theory, Transition state theory",

author = "Aihua Zhang and Sun Choi",

note = "Funding Information: This work was supported by the Mid-career Researcher Program ( NRF-2020R1A2C2101636 ), Bio & Medical Technology Development Program ( NRF-2022M3E5F3080873 ), Medical Research Center (MRC) grant ( NRF-2018R1A5A2025286 ), and the Brain Pool Program ( NRF-2021H1D3A2A02081370 ) funded by the Ministry of Science and ICT (MSIT) through the National Research Foundation of Korea (NRF) . It was also supported by the Ewha Womans University Research Grant of 2021. We thank T. N. L. Vũ for helpful discussions. Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

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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

Bibliographical note

Keywords

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