A unified theoretical framework for mapping models for the multi-state Hamiltonian

Liu, J.

doi:10.1063/1.4967815

Cited by 61 publications

(151 citation statements)

References 13 publications

(28 reference statements)

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“…26 Unfortunately, this approach did not reduce to the correct dynamics for isolated subsystems either, which has lead some authors to believe that spin is not a good classical analogue for a quantum system. 9 In the present paper we demonstrate how a spin mapping can indeed be generalized to multi-level systems, in a way that gives identical results to the Schrödinger equation for an isolated subsystem.…”

Section: Introductionmentioning

confidence: 61%

“…This quantity is independent of basis representation and controls the overall strength of the nuclear forces. In contrast with previous spin mapping attempts, 9,25,26 we have shown how the dynamics can be generated by a quadratic Hamiltonian of the same form as in the standard harmonic-oscillator mapping, but with a new formula for the zero-point energy parameter γ. Originally γ was included as a Langer correction, then justified through the commutation relations of a set of harmonic-oscillator operators.…”

Section: Discussionmentioning

confidence: 83%

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Generalized spin mapping for quantum-classical dynamics

Runeson

Richardson

2020

The Journal of Chemical Physics

207

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We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system and a spin-1/2 particle. In the present paper, we generalize this method to describe the dynamics of N -level systems. This is done via a mapping to a classical phase space that preserves the SU (N )-symmetry of the original quantum problem. The theory reproduces the standard Meyer-Miller-Stock-Thoss Hamiltonian without invoking an extended phase space, and we thus avoid leakage from the physical subspace. In contrast with the standard derivation of this Hamiltonian, the generalized spin mapping leads to an N -dependent value of the zero-point energy parameter that is uniquely determined by the Casimir invariant of the N -level system. Based on this mapping, we derive a simple way to approximate correlation functions in complex nonadiabatic molecular systems via classical trajectories, and present benchmark calculations on the seven-state Fenna-Matthews-Olson complex. The results are significantly more accurate than conventional Ehrenfest dynamics, at a comparable computational cost, and can compete in accuracy with other state-ofthe-art mapping approaches.

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Section: Introductionmentioning

confidence: 61%

Section: Discussionmentioning

confidence: 83%

Generalized spin mapping for quantum-classical dynamics

Runeson

Richardson

2020

The Journal of Chemical Physics

207

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“…In this paper we focus on QC/MH methods, 19,44,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69] which represent the electronic population and coherence operators, whose expectation values correspond to the diagonal and off-diagonal electronic density matrix elements, respectively, using mapping operators. The latter have the same commutation relations as the original electronic operators.…”

Section: Introductionmentioning

confidence: 99%

Benchmarking Quasiclassical Mapping Hamiltonian Methods for Simulating Electronically Nonadiabatic Molecular Dynamics

Gao

Saller

Liu

et al. 2020

J. Chem. Theory Comput.

141

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Quasi-classical mapping Hamiltonian methods have recently emerged as a promising approach for simulating electronically nonadiabatic molecular dynamics. The classicallike dynamics of the overall system within these methods makes them computationally feasible and they can be derived based on well-defined semiclassical approximations.However, the existence of a variety of different quasi-classical mapping Hamiltonian methods necessitates a systematic comparison of their respective advantages and limitations. Such a benchmark comparison is presented in this paper. The approaches compared include the Ehrenfest method, the symmetrical quasi-classical (SQC) method, and five variations of the linearized semiclassical (LSC) method, three of which employ a modified identity operator. The comparison is based on a number of popular nonadiabatic model systems; the spin-boson model, a Frenkel bi-exciton model and 1

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“…To apply methods like path-integral molecular dynamics (or dynamic extensions like ring-polymer molecular dynamics) to multilevel systems when the nonadiabatic effects cannot be neglected, a popular strategy is to use the mapping variable approach [18,19], see also the review article [2] and more recent developments in [20][21][22][23][24][25][26]. The idea is to replace the multi-level system by a single level system with higher dimension by mapping the discrete electronic states to continuous variables using uncoupled harmonic oscillators [19].…”

Section: Introductionmentioning

confidence: 99%

Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems

Zhou

2017

The Journal of Chemical Physics

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In this work, a novel ring polymer representation for multi-level quantum system is proposed for thermal average calculations. The proposed representation keeps the discreteness of the electronic states: besides position and momentum, each bead in the ring polymer is also characterized by a surface index indicating the electronic energy surface. A path integral molecular dynamics with surface hopping (PIMD-SH) dynamics is also developed to sample the equilibrium distribution of ring polymer configurational space. The PIMD-SH sampling method is validated theoretically and by numerical examples.

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A unified theoretical framework for mapping models for the multi-state Hamiltonian

Abstract: b) The manuscript has been accepted by J. Chem. Phys.

Cited by 61 publications

References 13 publications

Generalized spin mapping for quantum-classical dynamics

Generalized spin mapping for quantum-classical dynamics

Benchmarking Quasiclassical Mapping Hamiltonian Methods for Simulating Electronically Nonadiabatic Molecular Dynamics

Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems

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