A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians

Subotnik, Joseph E.; Miao, Gaohan; Bellonzi, Nicole; Teh, Hung-Hsuan; Dou, Wenjie

doi:10.1063/1.5116210

Cited by 23 publications

(18 citation statements)

References 75 publications

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“…Recent dynamical work has suggested that the imaginary component of NADCs can yield very rich new physical behaviors. 42 In particular, whenever the derivative coupling d is complex, such complexity automatically introduces nontrivial Berry phase effects, 72,73 whereby a given trajectory moving on adiabat J with momentum ⃗ p should feel a force, 42,74…”

Section: Discussionmentioning

confidence: 99%

“…the real/imaginary nature of the NADC because if the NADC is truly imaginary, we should find interesting Berry phase physics. 42,74 However, it is clear (disappointingly) that in practice, for the case of benzaldehyde, after rotation there are little to no remaining imaginary components, and the NADCs can be rotated into an almost entirely real-valued vector; thus, no Berry phase effects will be strong here, using the formula in Eq. ( 50).…”

Section: Article Scitationorg/journal/jcpmentioning

confidence: 99%

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TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

Bellonzi

Alguire

Fatehi

et al. 2020

The Journal of Chemical Physics

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We present an algorithm for efficient calculation of analytic nonadiabatic derivative couplings between spin-adiabatic, time-dependent density functional theory states within the Tamm-Dancoff approximation. Our derivation is based on the direct differentiation of the Kohn-Sham pseudowavefunction using the framework of Ou et al. Our implementation is limited to the case of a system with an even number of electrons in a closed shell ground state, and we validate our algorithm against finite difference at an S 1 /T 2 crossing of benzaldehyde. Through the introduction of a magnetic field spin-coupling operator, we break time-reversal symmetry to generate complex valued nonadiabatic derivative couplings. Although the nonadiabatic derivative couplings are complex valued, we find that a phase rotation can generate an almost entirely real-valued derivative coupling vector for the case of benzaldehyde.

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Section: Discussionmentioning

confidence: 99%

Section: Article Scitationorg/journal/jcpmentioning

confidence: 99%

TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

Bellonzi

Alguire

Fatehi

et al. 2020

The Journal of Chemical Physics

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“…Note that another branching criterion was recently proposed by Shi and coworkers 49 and may be useful to further improve the performance of BCMF. (3) Previous studies show that the mean field approach can automatically characterize the Berry phase 58,59 and naturally treat trivial crossings, 15,19 while traditional surface hopping does not. [60][61][62][63][64][65] This also justifies the urgent demand to develop robust mean field methods like BCMF.…”

Section: Pd Ppmentioning

confidence: 99%

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

Xu¹,

Wang²

2020

Preprint

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When describing nonadiabatic dynamics based on trajectories, severe trajectory branching occurs when the nuclear wave packets on some potential energy surfaces are reflected while those on the remaining surfaces are not. As a result, the traditional Ehrenfest mean field (EMF) approximation breaks down. In this study, two versions of the branching corrected mean field (BCMF) method are proposed. Namely, when trajectory branching is identified, BCMF stochastically selects either the reflected or the non-reflected group to build the new mean field trajectory or splits the mean field trajectory into two new trajectories with the corresponding weights. As benchmarked in six standard model systems and an extensive model base with two hundred diverse scattering models, BCMF significantly improves the accuracy while retaining the high efficiency of the traditional EMF. In fact, BCMF closely reproduces the exact quantum dynamics in all investigated systems, thus highlighting the essential role of branching correction in nonadiabatic dynamics simulations of general systems.

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“…Hamiltonian, we would need to discuss Berry's force and an approximate hopping direction, 30,31 which would only complicate the present paper (and will be addressed in a future publication).…”

Section: B Testing the Algorithm With A Simple Model Problem In The mentioning

confidence: 99%

A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the Cases of Trivial and Near-Trivial Crossings

Zhou

Jin

Qiu

et al. 2019

J. Chem. Theory Comput.

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We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon consideration of the overlap matrix (U) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of log(U). In so doing, one can extend the concept of parallel transport to cases with sharp curve crossings. We demonstrate that this algorithm performs well under extreme situations where dozens of states cross each other either through trivial crossings (where there is zero effective diabatic coupling), or through nontrivial crossings (when there is a nonzero diabatic coupling), or through a combination of both. In all cases, we compute the time-derivative coupling matrix elements (or equivalently non-adiabatic derivative coupling matrix elements) that are as smooth as possible.Our results should be of interest to all who are interested in either non-adiabatic dynamics, or more generally, parallel transport in large systems.

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A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians

Cited by 23 publications

References 75 publications

TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the Cases of Trivial and Near-Trivial Crossings

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