Xin He

Xin He

PhD. in Physical Chemistry and Theoretical Chemistry

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publications

A new perspective for nonadiabatic dynamics with phase space mapping models

Published in Journal of Chemical Physics, 2019

Based on the recently developed unified theoretical framework [J. Liu, J. Chem. Phys. 145(20), 204105 (2016)], we propose a new perspective for studying nonadiabatic dynamics with classical mapping models (CMMs) of the coupled multistate Hamiltonian onto the Cartesian phase space. CMMs treat the underlying electronic state degrees of freedom classically with a simple physical population constraint while employing the linearized semiclassical initial value representation to describe the nuclear degrees of freedom. We have tested various benchmark condensed phase models where numerically exact results are available, which range from finite temperature to more challenging zero temperature, from adiabatic to nonadiabatic domains, and from weak to strong system-bath coupling regions. CMMs demonstrate overall reasonably accurate dynamics behaviors in comparison to exact results even in the asymptotic long time limit for various spin-boson models and site-exciton models. Further investigation of the strategy used in CMMs may lead to practically useful approaches to study nonadiabatic processes in realistic molecular systems in the condensed phase.

Recommended citation: He, X.; Liu, J. A New Perspective for Nonadiabatic Dynamics with Phase Space Mapping Models. The Journal of Chemical Physics 2019, 151 (2), 024105. https://doi.org/10.1063/1.5108736.
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Negative zero-point-energy parameter in the Meyer-Miller mapping model for nonadiabatic dynamics

Published in Journal of Physical Chemistry Letter, 2021

The celebrated Meyer–Miller mapping model has been a useful approach for generating practical trajectory-based nonadiabatic dynamics methods. It is generally assumed that the zero-point-energy (ZPE) parameter is positive. The constraint implied in the conventional Meyer–Miller mapping Hamiltonian for an F-electronic-state system actually requires γ∈(−1/F, ∞) for the ZPE parameter for each electronic degree of freedom. Both negative and positive values are possible for such a parameter. We first establish a rigorous formulation to construct exact mapping models in the Cartesian phase space when the constraint is applied. When nuclear dynamics is approximated by the linearized semiclassical initial value representation, a negative ZPE parameter could lead to reasonably good performance in describing dynamic behaviors in typical spin-boson models for condensed-phase two-state systems, even at challenging zero temperature.

Recommended citation: He, X.; Gong, Z.; Wu, B.; Liu, J. Negative Zero-Point-Energy Parameter in the Meyer-Miller Mapping Model for Nonadiabatic Dynamics. The Journal of Physical Chemistry Letters 2021, 12 (10), 2496–2501. https://doi.org/10.1021/acs.jpclett.1c00232.
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Commutator matrix in phase space mapping models for nonadiabatic quantum dynamics

Published in Journal of Physical Chemistry A, 2021

We show that a novel, general phase space mapping Hamiltonian for nonadiabatic systems, which is reminiscent of the renowned Meyer–Miller mapping Hamiltonian, involves a commutator variable matrix rather than the conventional zero-point-energy parameter. In the exact mapping formulation on constraint space for phase space approaches for nonadiabatic dynamics, the general mapping Hamiltonian with commutator variables can be employed to generate approximate trajectory-based dynamics. Various benchmark model tests, which range from gas phase to condensed phase systems, suggest that the overall performance of the general mapping Hamiltonian is better than that of the conventional Meyer–Miller Hamiltonian.

Recommended citation: He, X.; Wu, B.; Gong, Z.; Liu, J. Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics. The Journal of Physical Chemistry A 2021, 125 (31), 6845–6863. https://doi.org/10.1021/acs.jpca.1c04429.
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Unified formulation of phase space mapping approaches for nonadiabatic quantum dynamics

Published in Accounts of Chemical Research, 2021

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-point-energy 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 photodissociation 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.

Recommended citation: Liu, J.; He, X.; Wu, B. Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics. Accounts of Chemical Research 2021, 54 (23), 4215–4228. https://doi.org/10.1021/acs.accounts.1c00511.
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New phase space formulations and quantum dynamics approaches

Published in WIREs Computational Molecular Science, 2022

We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems. This leads to a general coordinate-momentum phase space formulation of composite quantum systems, where conventional representations on infinite phase space are employed for continuous variables. It is convenient to utilize (weighted) constraint coordinate-momentum phase space for representing the quantum state and describing nonclassical features. Various numerical tests demonstrate that new trajectory-based quantum dynamics approaches derived from the (weighted) constraint phase space representation are useful and practical for describing dynamical processes of composite quantum systems in the gas phase as well as in the condensed phase.

Recommended citation: He, X.; Wu, B.; Shang, Y.; Li, B.; Cheng, X.; Liu, J. New Phase Space Formulations and Quantum Dynamics Approaches. WIREs Comput. Mol. Sci. 2022, 12 (6). https://doi.org/10.1002/wcms.1619.
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Transition Path Flight Times and Nonadiabatic Electronic Transitions

Published in Journal of Physical Chemistry Letter, 2022

Transition path flight times are studied for scattering on two electronic surfaces with a single crossing. These flight times reveal nontrivial quantum effects such as resonance lifetimes and nonclassical passage times and reveal that nonadiabatic effects often increase flight times. The flight times are computed using numerically exact time propagation and compared with results obtained from the Fewest Switches Surface Hopping (FSSH) method. Comparison of the two methods shows that the FSSH method is reliable for transition path times only when the scattering is classically allowed on the relevant adiabatic surfaces. However, where quantum effects such as tunneling and resonances dominate, the FSSH method is not adequate to accurately predict the correct times and transition probabilities. These results highlight limitations in methods which do not account for quantum interference effects, and suggest that measuring flight times is important for obtaining insights from the time-domain into quantum effects in nonadiabatic scattering.

Recommended citation: He, X.; Wu, B.; Rivlin, T.; Liu, J.; Pollak, E. Transition Path Flight Times and Nonadiabatic Electronic Transitions. J. Phys. Chem. Lett. 2022, 13 (30), 6966–6974. https://doi.org/10.1021/acs.jpclett.2c01425.
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Restriction of crossing conical intersections: the intrinsic mechanism of aggregation-induced emission

Published in Physical Chemistry Chemical Physics, 2023

Elucidating the mechanism of aggregation-induced emission (AIE) is a prerequisite for designing more AIE-gens. The diphenylethylene (DPE) featured molecules are one of the most important AIE-gens due to their propeller structure. Three representative DPE-featured AIE-gens, triphenylethylene, cis-stilbene, and trans-stilbene, are explored via ultrafast ultraviolet/infrared (UV/IR) spectroscopy and theoretical calculations. Both experimental and computational results suggest that readily crossing conical intersections (CIs) with flexible structural evolutions in solutions significantly reduces fluorescence, whereas crossing CIs is restricted because of high energy cost, and therefore no fast nonradiative decay can compete with spontaneous emission in solids. The mechanism also well explains the different emission quantum yields and interconversion ratios between cis-stilbene and trans-stilbene after photoexcitation.

Recommended citation: Peng, J.; He, X.; Li, Y.; Guan, J.; Wu, B.; Li, X.; Yu, Z.; Liu, J.; Zheng, J. Restriction of Crossing Conical Intersections: The Intrinsic Mechanism of Aggregation-Induced Emission. Phys. Chem. Chem. Phys. 2023, 25 (17), 12342–12351. https://doi.org/10.1039/D2CP05256C.
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Nonadiabatic Field on Quantum Phase Space: A Century after Ehrenfest

Published in Journal of Physical Chemistry Letter, 2024

Nonadiabatic transition dynamics lies at the core of many electron/hole transfer, photoactivated, and vacuum field-coupled processes. About a century after Ehrenfest proposed “Phasenraum” and the Ehrenfest theorem, we report a conceptually novel trajectorybased nonadiabatic dynamics approach, nonadiabatic field (NAF), based on a generalized exact coordinate−momentum phase space formulation of quantum mechanics. It does not employ the conventional Born−Oppenheimer or Ehrenfest trajectory in the nonadiabatic coupling region. Instead, in NAF the equations of motion of the independent trajectory involve a nonadiabatic nuclear force term in addition to an adiabatic nuclear force term of a single electronic state. A few benchmark tests for gas phase and condensed phase systems indicate that NAF offers a practical tool to capture the correct correlation of electronic and nuclear dynamics for processes where the states remain coupled all the time as well as for the asymptotic region where the coupling of electronic states vanishes.

Recommended citation: Wu, B.; He, X.; Liu, J. Nonadiabatic Field on Quantum Phase Space: A Century after Ehrenfest. J. Phys. Chem. Lett. 2024, 15 (2), 644–658. https://doi.org/10.1021/acs.jpclett.3c03385.
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Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space

Published in Journal of Physical Chemistry Letter, 2024

Recent progress on the constraint coordinate-momentum phase space (CPS) formulation of finite-state quantum systems has revealed that the triangle window function approach is an isomorphic representation of the exact population–population correlation function of the two-state system. We use the triangle window (TW) function and the CPS mapping kernel element to formulate a novel useful representation of discrete electronic degrees of freedom (DOFs). When it is employed with nonadiabatic field (NaF) dynamics, a new variant of the NaF approach (i.e., NaF-TW) is proposed. The NaF-TW expression of the population of any adiabatic state is always positive semidefinite. Extensive benchmark tests of model systems in both the condensed phase and gas phase demonstrate that the NaF-TW approach is able to faithfully capture the dynamical interplay between electronic and nuclear DOFs in a broad region, including where the states remain coupled all the time, as well as where the bifurcation characteristic of nuclear motion is important

Recommended citation: He, X.; Cheng, X.; Wu, B.; Liu, J. Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space. J. Phys. Chem. Lett. 2024, 5452–5466. https://doi.org/10.1021/acs.jpclett.4c00793.
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A Novel Class of Phase Space Representations for the Exact Population Dynamics of Two-State Quantum Systems and the Relation to Triangle Window Functions

Published in Chinese Journal of Chemical Physics, 2024

Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart. We use the constraint phase space developed in J. Chem. Phys. 145, 204105 (2016); 151, 024105 (2019); J. Phys. Chem. Lett. 12, 2496 (2021), non-covariant phase space functions, time-dependent weight functions, and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system. The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation. The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite. We also prove that the triangle window function approach, albeit proposed as a heuristic empirical model in J. Chem. Phys. 145, 144108 (2016), is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.

Recommended citation: Cheng, X.; He, X.; Liu, J. A Novel Class of Phase Space Representations for the Exact Population Dynamics of Two-State Quantum Systems and the Relation to Triangle Window Functions. Chinese Journal of Chemical Physics 2024. https://doi.org/10.1063/1674-0068/cjcp2403033.
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