Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians

Joubert-Doriol, Loïc; Izmaylov, Artur F.

doi:10.1021/acs.jpca.8b03404

Cited by 20 publications

(19 citation statements)

References 77 publications

(212 reference statements)

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“…For an excellent review of the Gaussian wavepacket approach to nonadiabatic electronic effects, see [49]. This paper aims to investigate and compare the hydrodynamic approaches for both the mean-field models and the exact factorization ansatz in the context of geometric mechanics.…”

Section: Factorized Wave Functions In Quantum Molecular Dynamicsmentioning

confidence: 99%

Geometry of Nonadiabatic Quantum Hydrodynamics

2019

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The Hamiltonian action of a Lie group on a symplectic manifold induces a momentum map generalizing Noether's conserved quantity occurring in the case of a symmetry group. Then, when a Hamiltonian function can be written in terms of this momentum map, the Hamiltonian is called 'collective'. Here, we derive collective Hamiltonians for a series of models in quantum molecular dynamics for which the Lie group is the composition of smooth invertible maps and unitary transformations. In this process, different fluid descriptions emerge from different factorization schemes for either the wavefunction or the density operator. After deriving this series of quantum fluid models, we regularize their Hamiltonians for finite by introducing local spatial smoothing. In the case of standard quantum hydrodynamics, the = 0 dynamics of the Lagrangian path can be derived as a finite-dimensional canonical Hamiltonian system for the evolution of singular solutions called 'Bohmions', which follow Bohmian trajectories in configuration space. For molecular dynamics models, application of the smoothing process to a new factorization of the density operator leads to a finite-dimensional Hamiltonian system for the interaction of multiple (nuclear) Bohmions and a sequence of electronic quantum states.

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Section: Factorized Wave Functions In Quantum Molecular Dynamicsmentioning

confidence: 99%

Geometry of Nonadiabatic Quantum Hydrodynamics

2019

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“…The second step involves an approximation and subsequent truncation of the coherent state basis [23]. Despite its accompanying issues [47], this type of representation is the basis of most current models in molecular dynamics [24]. However, this representation leads to cumbersome equations of motion, which are often simplified by specifically devised methods and uncontrolled approximations [25].…”

Section: Generalized Born-oppenheimer Theorymentioning

confidence: 99%

Regularized Born-Oppenheimer molecular dynamics

Rawlinson

Tronci

2020

Phys. Rev. A

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While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of Mead-Truhlar minimal coupling, this paper presents a new closure of the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics scheme capturing geometric phase effects. Specifically, a semiclassical closure of the nuclear Ehrenfest dynamics is obtained through a convenient prescription for the nuclear Bohmian trajectories. The conical intersections are suitably regularized in the resulting nuclear particle motion and the associated Lorentz force involves a smoothened Berry curvature identifying a loop-dependent geometric phase. In turn, this geometric phase rapidly reaches the usual topological index as the loop expands away from the original singularity. This feature reproduces the phenomenology appearing in recent exact nonadiabatic studies, as shown explicitly in the Jahn-Teller problem for linear vibronic coupling. Likewise, a newly proposed regularization of the diagonal correction term is also shown to reproduce quite faithfully the energy surface presented in recent nonadiabatic studies.

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“…. 57 The single set formulation is a natural choice when Ehrenfest trajectories are employed, since all electronic states are involved in propagation of a single trajectory, and this formulation was reported to provide a better description of nonadiabatic dynamics. 55 The multidimensional coherent state |z n is a direct product of one-dimensional coherent states corresponding to single nuclear DoFs…”

Section: Working Equationsmentioning

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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Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians

Cited by 20 publications

References 77 publications

Geometry of Nonadiabatic Quantum Hydrodynamics

Geometry of Nonadiabatic Quantum Hydrodynamics

Regularized Born-Oppenheimer molecular dynamics

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

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