On the environmental modes for the generalized Langevin equation

Kawai, Shinnosuke

doi:10.1063/1.4929710

Cited by 9 publications

(10 citation statements)

References 55 publications

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“…Note that, while Eqs. (B2a), (B2b), and (B2c) are similar to the generalized Langevin equation for classical non-Markovian dynamics via Markovian-type Lanvegin equations with virtual variables [87,88,91,92], our stochastic variables Ω = (. .…”

Section: (B1)mentioning

confidence: 99%

Low-Temperature Quantum Fokker–Planck and Smoluchowski Equations and Their Extension to Multistate Systems

Ikeda

Tanimura

2019

J. Chem. Theory Comput.

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10 -5 0 5 10 -5 0 5 -10 -5 0 5 10 -5 0 5 Non-Adiabatic Transition Electronic Coherence Excited State Ground StateSimulating 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 paper, 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 multi-state systems. The accuracy of these equations was numerically examined for a single-state Brownian system, while their applicability was examined for multi-state 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 non-adiabatic 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 multi-state potential forms, are provided as Supporting Information.

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Section: (B1)mentioning

confidence: 99%

Low-Temperature Quantum Fokker–Planck and Smoluchowski Equations and Their Extension to Multistate Systems

Ikeda

Tanimura

2019

J. Chem. Theory Comput.

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“…To elucidate the dynamical modes that are hidden in the environment but are still interacting with the subsystem, one of the present authors, following a long line of studies, 15,19,[26][27][28][29][30][31][32][33][34][35] has recently proposed a formulation that converts the GLE into multidimensional and memoryless equations of motion 36 . The idea of expressing the GLE by equivalent set of ordinary differential equations dates back to the continued-fraction expansion of the friction kernel introduced by Mori.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. 36 the theory was reformulated by starting with multi-exponential form of the friction kernel and provided explicit expression of these new variables in terms of the observed time series q 1 (t).…”

Section: Introductionmentioning

confidence: 99%

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Recovering hidden dynamical modes from the generalized Langevin equation

Kawai

Miyazaki

2016

The Journal of Chemical Physics

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In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection.

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“…We consider only Markovian solvent-solute interactions, although history-dependent effects can be included. 45,59,60 The noise is therefore white (uncorrelated in time) such that…”

Section: Description Of the Modelmentioning

confidence: 99%

Transition state theory for activated systems with driven anharmonic barriers

Revuelta

Craven

Bartsch

et al. 2017

The Journal of Chemical Physics

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Classical transition state theory has been extended to address chemical reactions across barriers that are driven and anharmonic. This resolves a challenge to the naive theory that necessarily leads to recrossings and approximate rates because it relies on a fixed dividing surface. We develop both perturbative and numerical methods for the computation of a time-dependent recrossing-free dividing surface for a model anharmonic system in a solvated environment that interacts strongly with an oscillatory external field. We extend our previous work, which relied either on a harmonic approximation or on periodic force driving. We demonstrate that the reaction rate, expressed as the long-time flux of reactive trajectories, can be extracted directly from the stability exponents, namely, Lyapunov exponents, of the moving dividing surface. Comparison to numerical results demonstrates the accuracy and robustness of this approach for the computation of optimal (recrossing-free) dividing surfaces and reaction rates in systems with Markovian solvation forces. The resulting reaction rates are in strong agreement with those determined from the long-time flux of reactive trajectories.

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On the environmental modes for the generalized Langevin equation

Cited by 9 publications

References 55 publications

Low-Temperature Quantum Fokker–Planck and Smoluchowski Equations and Their Extension to Multistate Systems

Low-Temperature Quantum Fokker–Planck and Smoluchowski Equations and Their Extension to Multistate Systems

Recovering hidden dynamical modes from the generalized Langevin equation

Transition state theory for activated systems with driven anharmonic barriers

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