Correlation Functions in Open Quantum-Classical Systems

Hsieh, Chang‐Yu; Kapral, Raymond

doi:10.3390/e16010200

Cited by 10 publications

(15 citation statements)

References 73 publications

(110 reference statements)

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“…The method is also inexpensive, non-perturbative, and provides a superior description of branching processes and detailed balance when compared to other approaches, such as the Ehrenfest method. 16 Despite these appealing features, surface hopping naturally suffers from several deficiencies. [17][18][19][20] Clearly the description of nuclear motion as classical renders the approach incapable of capturing low temperature effects such as nuclear tunneling on a single potential surface.…”

Section: Introductionmentioning

confidence: 99%

On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems

Chen

Reichman

2016

The Journal of Chemical Physics

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We perform extensive benchmark comparisons of surface hopping dynamics with numerically exact calculations for the spin-boson model over a wide range of energetic and coupling parameters as well as temperature. We find that deviations from golden-rule scaling in the Marcus regime are generally small and depend sensitively on the energetic bias between electronic states. Fewest switches surface hopping (FSSH) is found to be surprisingly accurate over a large swath of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic, at least for the case of an environment modeled with the commonly used Debye spectral density.

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Section: Introductionmentioning

confidence: 99%

On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems

Chen

Reichman

2016

The Journal of Chemical Physics

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“…In this section, we provide a summary of the FBTS method and refer the reader to Refs [30,31,47] for more details. Starting from the formal solution of the mapping QCLE in terms of forward and backward propagators, one can derive another approximate solution to the QCLE by representing these propagators in the coherent state basis [38] and assuming that, at a given time step, the overlap integral between two coherent states decays rapidly if their phase space coordinates are substantially different (see Ref.…”

Section: The Forward -Backward Trajectory Solutionmentioning

confidence: 99%

Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments

Martinez

Hanna

2014

Molecular Simulation

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The quantum-classical Liouville equation (QCLE) provides a rigorous approach for modelling the dynamics of systems that can be effectively partitioned into a quantum subsystem and a classical environment. Several surface-hopping algorithms have been developed for solving the QCLE and successfully applied to simple model systems, but simulating the long-time dynamics of complex, realistic systems using these schemes has proven to be computationally demanding. Motivated by the need for computationally efficient algorithms, two approximate solutions of the QCLE, the Poisson bracket mapping equation (PBME) solution and the forward-backward trajectory solution (FBTS), were developed. These solutions involve simple algorithms in which both the quantum and classical degrees of freedom are described in terms of continuous variables and evolve according to classical-like equations of motion. However, since these schemes are approximate, they must be benchmarked against the exact quantum and QCLE surface-hopping solutions for a variety of simple and complex systems to determine the conditions under which they are valid. To illustrate the validity of the PBME and FBTS approaches, we review the results of a simple model for a condensed-phase photo-induced electron transfer and present new results for a realistic model for a proton transfer in a hydrogen-bonded complex dissolved in a polar nanocluster. Overall, the results demonstrate that caution must be taken when applying these approximate methods, since they can manifest nonphysical behaviour for systems where a mean-field-like description is not valid.

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“…Then, starting with these exact quantum expressions, one may approximate the quantum dynamics by quantum-classical dynamics. [53][54][55][56] In this framework the expectation value of an observable BW (X) is given by,…”

Section: Some Properties Of the Qclementioning

confidence: 99%

“…Expressions for reaction rate constants in this framework have been formulated. 53,55,56,[145][146][147] The QCL expression for the time-…”

Section: ): Proton Transfer (Ah-bmentioning

confidence: 99%

Quantum dynamics in open quantum-classical systems

Kapral

2015

J. Phys.: Condens. Matter

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Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

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Correlation Functions in Open Quantum-Classical Systems

Cited by 10 publications

References 73 publications

On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems

On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems

Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments

Quantum dynamics in open quantum-classical systems

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