Sequential short-time propagation of quantum classical dynamics

MacKernan, Donal; Kapral, Raymond; Ciccotti, Giovanni

doi:10.1088/0953-8984/14/40/301

Cited by 86 publications

(128 citation statements)

References 28 publications

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“…In the adiabatic basis the QCLE leads to a surfacehopping-type solution where segments of classical evolution are interspersed with energy-conserving quantum transitions [40,50]. The QCL operator may be written in this basis as a sum of diagonal (adiabatic) and offdiagonal (nonadiabatic) parts,…”

Section: Theorymentioning

confidence: 99%

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics

Kelly

Markland

2013

The Journal of Chemical Physics

110

115

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The quantum-classical Liouville equation offers a rigorous approach to nonadiabatic quantum dynamics based on surface hopping type trajectories. However, in practice the applicability of this approach has been limited to short times owing to unfavorable numerical scaling. In this paper we show that this problem can be alleviated by combining it with a formally exact generalized quantum master equation treatment. This allows dramatic improvements in the efficiency of the approach in nonadiabatic regimes, making it computationally tractable to treat the quantum dynamics of complex systems for long times. We demonstrate our approach by applying it to a model of condensed phase charge transfer where our method is shown to be numerically exact in regimes where fewest-switches surface hopping and mean field approaches fail to obtain the either the correct rates or long-time populations.

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Section: Theorymentioning

confidence: 99%

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics

Kelly

Markland

2013

The Journal of Chemical Physics

110

115

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“…18,[25][26][27][28][29][30]10 While the formal solution of this equation of motion is easily written as B W (t) ) exp(i Lˆt)B W (0), the construction of effective simulation algorithms for realistic many-body systems is not a simple task, and a number of different methods have been proposed. [29][30][31][32][33][34] In this paper, we describe a Trotter-based scheme for simulating quantum-classical Liouville dynamics in terms of an ensemble of surface-hopping trajectories. The method can be used to compute the dynamics for longer times with fewer trajectories than the sequential short-time propagation (SSTP) algorithm, which is also based on surface-hopping trajectories.…”

Section: B(t) ) Trb F(t) ) Trb (T)f(0)mentioning

confidence: 99%

Trotter-Based Simulation of Quantum-Classical Dynamics

2007

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Quantum rate processes in condensed phase systems are often computed by combining quantum and classical descriptions of the dynamics. An algorithm for simulating the quantum-classical Liouville equation, which describes the dynamics of a quantum subsystem coupled to a classical bath, is presented in this paper. The algorithm is based on a Trotter decomposition of the quantum-classical propagator, in conjunction with Monte Carlo sampling of quantum transitions, to yield a surface-hopping representation of the dynamics. An expression for the nonadiabatic propagator that is responsible for quantum transitions and associated bath momentum changes is derived in a form that is convenient for Monte Carlo sampling and exactly conserves the total energy of the system in individual trajectories. The expectation values of operators or quantum correlation functions can be evaluated by initial sampling of quantum states and use of quantum-classical Liouville dynamics for the time evolution. The algorithm is tested by calculations on the spin-boson model, for which exact quantum results are available, and is shown to reproduce the exact results for stronger nonadiabatic coupling and much longer times using fewer trajectories than other schemes for simulating quantum-classical Liouville dynamics.

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“…Recently it has been shown that partially linearizing the propagator for the electronic degrees of freedom, giving rise to the partially linearized density matrix (PLDM) [7] approach and the forward-backward trajectory solution (FBTS) to the quantum-classical Liouville equation [8], allows more dynamical correlation to be included at relatively little additional cost to fully linearized methods. Introduc- * Electronic address: tmarkland@stanford.edu ing further dynamical correlations between the subsystem and the bath adds further accuracy, at the expense of assigning weights and phase factors to the trajectories [10][11][12]. This in turn adds many orders of magnitude to the number of trajectories, which grows rapidly with system dimensionality and time, that must be generated in order to obtain converged properties.…”

Section: Introductionmentioning

confidence: 99%

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

Kelly

Brackbill

Markland

2015

The Journal of Chemical Physics

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In this article we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speedups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

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Sequential short-time propagation of quantum classical dynamics

Cited by 86 publications

References 28 publications

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics

Trotter-Based Simulation of Quantum-Classical Dynamics

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

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