Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics

Albert, J.; Kaiser, Dustin; Engel, Volker

doi:10.1063/1.4948777

Cited by 19 publications

(9 citation statements)

References 26 publications

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“…Even when energy conservation does not allow internal excitations, virtual transitions between internal states cannot be neglected. Such mechanisms turn out to be essential in determining scattering coefficients, and should be carefully included for a quantitative evaluation of, e.g., reaction cross sections in heavy-nuclei fusion [1], chemisorption/backscattering ratio in diatomic molecule/surface collisions [3], non-adiabatic electronuclear quantum dynamics [4], lightwave-driven quasiparticle collisions [5], or resonant tunneling of two-particle systems [6].…”

Section: Introductionmentioning

confidence: 99%

Time-dependent scattering of a composite particle: A local self-energy approach for internal excitations

2016

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When composite particles - such as small molecules, nuclei, or photogenerated excitons in semiconductors - are scattered by an external potential, energy may be transferred between the c.m. and the internal degrees of freedom. An accurate dynamical modeling of this effect is pivotal in predicting diverse scattering quantities and reaction cross sections, and allows us to rationalize time-resolved energy and localization spectra. Here, we show that time-dependent scattering of a quantum composite particle with an arbitrary, nonperturbative external potential can be obtained by propagating the c.m. degrees of freedom with a properly designed local self-energy potential. The latter embeds the effect of internal virtual transitions and can be obtained by the knowledge of the stationary internal states. The case is made by simulating Wannier-Mott excitons in one- and two-dimensional semiconductor heterostructures. The self-energy approach shows very good agreement with numerically exact Schrödinger propagation for scattering potentials where a mean-field model cannot be applied, at a dramatically reduced computational cost

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Section: Introductionmentioning

confidence: 99%

Time-dependent scattering of a composite particle: A local self-energy approach for internal excitations

2016

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“…We also note that purely classical description of electron and nuclear dynamics may also yield reasonable results (at least for an one-electron system). 28 The quantum propagation on a grid, the straightforward approach to quantum dynamics, being numerically exact is subjected to a socalled "exponential curse", i.e. the number of grid points needed to cover a volume of interest rises as N d , with the number of grid points per dimension N and the number of dimensions d. Therefore, the propagation on a grid becomes unfeasible for systems with many degrees of freedom (DoFs).…”

Section: Introductionmentioning

confidence: 99%

Comparison of moving and fixed basis sets for nonadiabatic quantum dynamics at conical intersections

2020

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We assess the performance of two different types of basis sets for nonadiabatic quantum dynamics at conical intersections. The basis sets of both types are generated using Ehrenfest trajectories of nuclear coherent states. These trajectories can either serve as a moving (timedependent) basis or be employed to sample a fixed (time-independent) basis. We demonstrate on the example of two-state two-dimensional and three-state five-dimensional models that both basis set types can yield highly accurate results for population transfer at intersections, as compared with reference quantum dynamics. The details of wave packet evolutions are discussed for the case of the two-dimensional model. The fixed basis is found to be superior to the moving one in reproducing nonlocal spreading and maintaining correct shape of the wave packet upon time evolution. Moreover, for the models considered, the fixed basis set outperforms the moving one in terms of computational efficiency.

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“…The celebrated Born-Oppenheimer approximation, 1 which treats the electronic and nuclear motions in molecules separately, is no longer valid for describing processes involving two or more strongly vibronically coupled electronic states. A common approach that goes beyond this approximation [2][3][4][5][6][7][8][9] consists in solving the time-dependent Schrödinger equation with a truncated molecular Hamiltonian that includes only a few, most significantly coupled 10,11 Born-Oppenheimer electronic states. [12][13][14] The "adiabatic" states, obtained directly from the electronic structure calculations, are, however, not adequate for representing the molecular Hamiltonian in the region of strong nonadiabatic couplings; in particular, the couplings between the states diverge to infinity at conical intersections, 2,[14][15][16][17][18][19] where potential energy surfaces of two or more adiabatic states intersect.…”

Section: Introductionmentioning

confidence: 99%

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Choi,

Vaníček

2020

Preprint

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Quasidiabatization of the molecular Hamiltonian is a standard approach to remove the singularity of nonadiabatic couplings at a conical intersection of adiabatic potential energy surfaces. Typically, the residual nonadiabatic couplings between quasidiabatic states are simply neglected. Here, we investigate the validity of this potentially drastic approximation by comparing the quantum dynamics simulated either with or without these couplings. By comparing the two simulations in the same quasidiabatic representation, we entirely avoid errors due to the transformation between representations. To eliminate grid and time discretization errors even in simulations with the nonseparable quasidiabatic Hamiltonian, we use the highly accurate and general eighth-order composition of the implicit midpoint method. To show that the importance of the residual couplings can depend on the employed quasidiabatization scheme, we compare the first-and second-order regular diabatizations applied to the cubic E ⊗e Jahn-Teller model, whose parameters were chosen so that the magnitudes of the residual couplings differed by a factor of 200. As a consequence, neglecting the residual couplings in the first-order scheme results in very unreliable dynamics, while it has almost no effect in the second-order scheme. In contrast, the simulation with the exact quasidiabatic Hamiltonian is accurate regardless of the quasidiabatization scheme.

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Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics

Cited by 19 publications

References 26 publications

Time-dependent scattering of a composite particle: A local self-energy approach for internal excitations

Time-dependent scattering of a composite particle: A local self-energy approach for internal excitations

Comparison of moving and fixed basis sets for nonadiabatic quantum dynamics at conical intersections

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

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