On-the-Fly Symmetrical Quasi-Classical Dynamics with Meyer–Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

Da, Hu; Xie, Yu; Peng, Jiawei; Lan, Zhenggang

doi:10.1021/acs.jctc.0c01249

Cited by 25 publications

(30 citation statements)

References 134 publications

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“…For the particular case of the ethylene photo-dissociation dynamics, the ZPE correction does not further improve the results when the triangle window is used, similar to the recent work that utilized the kinematic momentum formulation of SQC. 64 With both ∆-SQC (panel b) and ∆-γ-SQC (panel d), we see a near quantitative agreement with AIMS, even slightly out-performing the commonly used dTSH (blue).…”

Section: Resultsmentioning

confidence: 60%

“…This new scheme has shown to provide a significant improvement for photo-dissociation problems with coupled Morse potentials 27 and has been combined with the kinematic momentum approach 63 to carry out on-the-fly simulations of the methaniminium cation. 64 The basic logic of this scheme is to choose an appropriate γ j for each state |j in a given individual trajectory, such that the initial population is forced to respect the initial electronic excitation focused onto a single excited state. If the initial electronic state is |i , then…”

Section: B Symmetric Quasi-classical (Sqc) Approachmentioning

confidence: 99%

“…Note that reformulating γ-SQC in the adiabatic representation (such as the kinematically transformed SQC 63 ) has been done recently to perform on-the-fly simulations. 64 However, formulating a quantum dynamics approach in the adiabatic representation introduces additional numerical issues as the molecular Hamiltonian in the adiabatic representation involves first and second derivative coupling elements that are typically sharply peaked around avoided crossings and become singular at a conical intersection (CI). In our previous work, 41 we showed that the kinematically transformed SQC (KT-SQC), formulated in the adiabatic representation, may require substantially small time step to converge dynamics due to the presence of sharply peaked first derivative coupling elements, even though the second derivative coupling elements are removed through mathematical transformation in this formalism.…”

Section: B Symmetric Quasi-classical (Sqc) Approachmentioning

confidence: 99%

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Ab-initio Symmetric Quasi-Classical Approach to Investigate Molecular Tully Models

Weight,

Mandal,

Huo

2021

Preprint

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We perform on-the-fly non-adiabatic molecular dynamics simulations using the symmetrical quasi-classical (SQC) approach with the recently suggested molecular Tully models: ethylene and fulvene. We attempt to provide benchmarks of the SQC methods using both the square and the triangle windowing schemes as well as the recently proposed electronic zero-point-energy correction scheme (so-called the γ correction). We use the quasi-diabatic propagation scheme to directly interface the diabatic SQC methods with adiabatic electronic structure calculations. Our results showcase the drastic improvement of the accuracy by using the trajectory-adjusted γ-corrections, which outperform the widely used trajectory surface hopping method with decoherence corrections. These calculations provide useful and non-trivial tests to systematically investigate the numerical performance of various diabatic quantum dynamics approaches, going beyond simple diabatic model systems that have been used as the major workhorse in the quantum dynamics field. At the same time, these available benchmark studies will also likely foster the development of new quantum dynamics approaches based on these techniques.

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Section: Resultsmentioning

confidence: 60%

Section: B Symmetric Quasi-classical (Sqc) Approachmentioning

confidence: 99%

Section: B Symmetric Quasi-classical (Sqc) Approachmentioning

confidence: 99%

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Ab-initio Symmetric Quasi-Classical Approach to Investigate Molecular Tully Models

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Mandal,

Huo

2021

Preprint

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“…42 .) We expect that the comprehensive mapping Hamiltonian with the commutator matrix will be useful for on-the-fly nonadiabatic dynamics 39,40 . The expression of the phase space mapping approach in the adiabatic representation is available in the Supporting Information of Ref.…”

Section: Discussionmentioning

confidence: 99%

Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics

Liu

2021

Acc. Chem. Res.

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Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent in the molecular structure or induced by the (intense) external field. The curse of dimensionality indicates the intractable exponential scaling of calculation effort with system size and restricts the implementation of "numerically exact" approaches for realistic large systems. The phase space formulation of quantum mechanics offers an important theoretical framework for constructing practical approximate trajectory-based methods for quantum dynamics. This Account reviews our recent progress in phase space mapping theory: a unified framework for constructing the mapping Hamiltonian on phase space for coupled F-state systems where the renowned Meyer-Miller Hamiltonian model is a special case, a general phase space formulation of quantum mechanics for nonadiabatic systems where the electronic degrees of freedom are mapped onto constraint space and the nuclear degrees of freedom are mapped onto infinite space, and an isomorphism between the mapping phase space approach for nonadiabatic systems and that for nonequilibrium electron transport processes. While the zero-point-energy parameter is conventionally assumed to be positive, we show that the constraint implied in the conventional Meyer-Miller mapping Hamiltonian requires that such a parameter can be negative as well and lies in   1 , F   for each electronic degree of freedom. More importantly, the zero-pointenergy parameter should be interpreted as a special case of a commutator matrix in the comprehensive phase space mapping Hamiltonian for nonadiabatic systems. From the rigorous formulation of mapping phase space, we propose approximate but practical trajectory-based nonadiabatic dynamics methods. The applications to both gas phase and condensed phase problems include the spin-boson model for condensed phase dissipative two-state systems, the three-state photo-dissociation models, the seven-site model of the Fenna-Matthews-Olson monomer in photosynthesis of green sulfur bacteria, the strongly-coupled molecular/atomic matter-optical cavity systems designed for controlling and manipulating chemical dynamical processes, and the Landauer model for a quantum dot state coupled with two electrodes. In these applications the overall performance of our phase space mapping dynamics approach is superior to two prevailing trajectory-based methods, Ehrenfest dynamics and fewest switches surface hopping.

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“…Within the system-plus-bath model, the quantum evolution of the reduced system under study is far more important than that of environmental DOFs; thus, it is rather essential to develop a suitable dynamics approach for the correct description of the quantum evolution of open systems. Along this idea, various dynamics approaches were proposed in several decades. ,,− However, these available dynamics methods behave well in some situations, while they suffer from some disadvantages in other cases. For instance, some approximated approaches, such as mixed-quantum-classical Ehrenfest dynamics and its extensions, , and widely used trajectory surface-hopping methods, − have rather low computational costs, while the inconsistent descriptions of the quantum and classical parts always bring some deficiencies, such as overcoherence problems. ,, The perturbative approaches, such as Redfield theory, , work well in weak system–bath coupling cases but fail in strong coupling situations.…”

mentioning

confidence: 99%

Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network

Lin

Peng

et al. 2021

J. Phys. Chem. Lett.

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The recurrent neural network with the long short-term memory cell (LSTM-NN) is employed to simulate the long-time dynamics of open quantum systems. The bootstrap method is applied in the LSTM-NN construction and prediction, which provides a Monte Carlo estimation of a forecasting confidence interval. Within this approach, a large number of LSTM-NNs are constructed by resampling time-series sequences that were obtained from the early stage quantum evolution given by numerically exact multilayer multiconfigurational time-dependent Hartree method. The built LSTM-NN ensemble is used for the reliable propagation of the long-time quantum dynamics, and the simulated result is highly consistent with the exact evolution. The forecasting uncertainty that partially reflects the reliability of the LSTM-NN prediction is also given. This demonstrates the bootstrap-based LSTM-NN approach is a practical and powerful tool to propagate the long-time quantum dynamics of open systems with high accuracy and low computational cost.

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On-the-Fly Symmetrical Quasi-Classical Dynamics with Meyer–Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

Cited by 25 publications

References 134 publications

Ab-initio Symmetric Quasi-Classical Approach to Investigate Molecular Tully Models

Ab-initio Symmetric Quasi-Classical Approach to Investigate Molecular Tully Models

Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics

Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network

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