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Title: Low-Temperature Quantum Fokker–Planck and Smoluchowski Equations and Their Extension to Multistate Systems
Authors: Ikeda, Tatsushi
Tanimura, Yoshitaka
Author's alias: 池田, 龍志
谷村, 吉隆
Keywords: Physical and Theoretical Chemistry
Computer Science Applications
Issue Date: 9-Apr-2019
Publisher: American Chemical Society
Journal title: Journal of Chemical Theory and Computation
Volume: 15
Issue: 4
Start page: 2517
End page: 2534
Abstract: Simulating electron–nucleus coupled dynamics poses a nontrivial challenge and an important problem in the investigation of ultrafast processes involving coupled electronic and vibrational dynamics. Because irreversibility of the system dynamics results from thermal activation and dissipation caused by the environment, in dynamical studies, it is necessary to include heat bath degrees of freedom in the total system. When the system dynamics involves high-energy electronic transitions, the environment is regarded to be in a low-temperature regime and we must treat it quantum mechanically. In this Article, we present rigorous and versatile approaches for investigating the dynamics of open systems with coupled electronic and vibrational degrees of freedom within a fully quantum mechanical framework. These approaches are based on a quantum Fokker–Planck equation and a quantum Smoluchowski equation employing a heat bath with an Ohmic spectral density, with non-Markovian low-temperature correction terms, and extensions of these equations to the case of multistate systems. The accuracy of these equations was numerically examined for a single-state Brownian system, while their applicability was examined for multistate double-well systems by comparing their results with those of the fewest-switch surface hopping and Ehrenfest methods with a classical Markovian Langevin force. Comparison of the transient absorption spectra obtained using these methods clearly reveals the importance of the quantum low-temperature correction terms. These equations allow us to treat nonadiabatic dynamics in an efficient way, while maintaining numerical accuracy. The C++ source codes that we developed, which allow for the treatment of the phase and coordinate space dynamics with any single-state or multistate potential forms, are provided as Supporting Information.
Rights: This document is the Accepted Manuscript version of a Published Work that appeared in final form in 'Journal of Chemical Theory and Computation', copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see
The full-text file will be made open to the public on 18 February 2020 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
DOI(Published Version): 10.1021/acs.jctc.8b01195
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