A reciprocal-space formulation of surface hopping

Krotz, Alex; Tempelaar, Roel

doi:10.1063/5.0076070

Cited by 12 publications

(25 citation statements)

References 55 publications

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“…In the following, we will first present FSSH calculations for a pristine lattice, by setting Δ = 0. As such, we will be revisiting a system that was addressed in Papers I 12 and II, 23 but with adjusted parameters. We will then consider the case of a single impurity model, by setting Δ = 2.0.…”

Section: Resultsmentioning

confidence: 99%

“…A key ingredient of FSSH is a stochastic switching of the active surface between instantaneous eigenstates. The switching from state α to state β is governed by the probability 23,24,29 i k j j j j j y…”

Section: T H Imentioning

confidence: 99%

“…We note that the switching probability commonly features a product of the classical momenta and the nonadiabatic coupling vectors within the physical basis. 24 By means of the chain rule, 23,29 we have replaced this product by an inner product of α and ∂β/∂t in eq 16, yielding a basis-independent form of the switching probability.…”

Section: T H Imentioning

confidence: 99%

“…2.3, we use the resulting formalism to rederive the equations of motion of reciprocal-space Ehrenfest dynamics and FSSH from Papers I 12 and II. 23 In Sec. 3 we introduce the single impurity model, and present FSSH results within transformed quantum and classical bases, subjected to basis truncations.…”

Section: Introductionmentioning

confidence: 99%

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Mixed Quantum–Classical Dynamics under Arbitrary Unitary Basis Transformations

Miyazaki,

Krotz,

Tempelaar

2024

J. Chem. Theory Comput.

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A common approach to minimizing the cost of quantum computations is by unitarily transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations and propose their integration into mixed quantum−classical dynamics, allowing this class of methods to be applied within arbitrary bases for both the quantum and classical coordinates. To this end, canonical positions and momenta of the classical degrees of freedom are combined into a set of complex-valued coordinates amenable to unitary transformations. We demonstrate the potential of the resulting approach by means of surface hopping calculations of an electronic carrier scattering onto a single impurity in the presence of phonons. Appropriate basis transformations, capturing both the localization of the impurity and the delocalization of higher-energy excitations, are shown to faithfully capture the dynamics within a fraction of the classical and quantum basis sets.

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Section: Resultsmentioning

confidence: 99%

Section: T H Imentioning

confidence: 99%

Section: T H Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mixed Quantum–Classical Dynamics under Arbitrary Unitary Basis Transformations

Miyazaki,

Krotz,

Tempelaar

2024

J. Chem. Theory Comput.

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“…One recent effort along these lines has been presented in Ref. 110. Therefore, in our work, we study the real-time dynamics in a paradigmatic condensed matter system, the Holstein model, 111 with methods of quantum chemistry, specifically the Ehrenfest and fewest-switches surface-hopping algorithms, 1,58,59 and the multiconfigurational Ehrenfest algorithm 112,113 and we benchmark them against exact diagonalization for small systems and DMRG-LBO 86,88 for large systems.…”

Section: Introductionmentioning

confidence: 99%

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

Brink,

Gräber,

Hopjan

et al. 2022

Preprint

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We benchmark a set of quantum-chemistry methods including the multitrajectory Ehrenfest, the fewest-switches surface-hopping, and the multiconfigurational Ehrenfest method against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method in general only captures the ultra-short time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior, but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

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Surface hopping dynamics in periodic solid-state materials with a linear vibronic coupling model

Xie

Wang

et al. 2022

The Journal of Chemical Physics

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We report a surface hopping approach in which the implemented linear vibronic coupling Hamiltonian is constructed and the electronic wavefunction is propagated in the reciprocal space. The parameters of the linear vibronic coupling model, including onsite energies, phonon frequencies, and electron-phonon couplings, are calculated with density-functional theory and density-functional perturbation theory, and interpolated in fine sampling points of the Brillouin zone with maximally localized Wannier functions. Using this approach, we studied the relaxation dynamics of the photo-excited hot carrier in a one-dimensional periodic carbon chain. The results show that the completeness of the number of Hilbert space k-points and the number of phonon q-points play important roles in the hot carrier relaxation processes. By calculating the relaxation times of hot carriers under different reciprocal space sampling and extrapolating with the stretched-compressed exponential function, the relaxation times of hot electrons and holes in the quasi-continuous energy band are obtained. By considering the feedback effect in the hopping processes and analyzing the time-dependent phonon energy in different normal modes, we found that the long-wave longitudinal optical phonons play a major role in the relaxation dynamics of hot electrons and holes. We therefore provided herein an efficient and accurate approach for modeling the photophysical processes in periodic solid-state material systems.

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A reciprocal-space formulation of surface hopping

Cited by 12 publications

References 55 publications

Mixed Quantum–Classical Dynamics under Arbitrary Unitary Basis Transformations

Mixed Quantum–Classical Dynamics under Arbitrary Unitary Basis Transformations

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

Surface hopping dynamics in periodic solid-state materials with a linear vibronic coupling model

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