Machine learning phase space quantum dynamics approaches.
11 May 2021-Journal of Chemical Physics (AIP Publishing LLCAIP Publishing)-Vol. 154, Iss: 18, pp 184104-184104
TL;DR: Proof-of-concept applications to realistic molecules demonstrate that machine learning phase space dynamics approaches are possible as well as competent in producing reasonably accurate results with a modest computation effort.
Abstract: Derived from phase space expressions of the quantum Liouville theorem, equilibrium continuity dynamics is a category of trajectory-based phase space dynamics methods, which satisfies the two critical fundamental criteria: conservation of the quantum Boltzmann distribution for the thermal equilibrium system and being exact for any thermal correlation functions (even of nonlinear operators) in the classical and harmonic limits. The effective force and effective mass matrix are important elements in the equations of motion of equilibrium continuity dynamics, where only the zeroth term of an exact series expansion of the phase space propagator is involved. We introduce a machine learning approach for fitting these elements in quantum phase space, leading to a much more efficient integration of the equations of motion. Proof-of-concept applications to realistic molecules demonstrate that machine learning phase space dynamics approaches are possible as well as competent in producing reasonably accurate results with a modest computation effort.
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TL;DR: This work introduces a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data.
Abstract: We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is first-principles based in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DPMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size.
254 citations
TL;DR: In this paper, 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 is presented.
Abstract: ConspectusNonadiabatic 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.
16 citations
TL;DR: In this article, a general phase space mapping Hamiltonian for nonadiabatic systems, which is reminiscent of the renowned Meyer-Miller mapping Hamiltonians, involves a commutator variable matrix rather than the conventional zero-point-energy parameter.
Abstract: 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.
12 citations
TL;DR: In this paper , the authors report progress on the phase space formulation of quantum mechanics with coordinatemomentum variables, focusing more on new theory of (weighted) constraint coordinate momentum phase space for discrete variable quantum systems.
Abstract: 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.
7 citations
Journal Article•
TL;DR: Four new approximate treatments are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" and the full Donoso-Martens dynamics ( full DMD and thesecond order DMD based on 'Donoso- Martens trajectories'--all of which can be viewed as generalizations of the original LSC-IVR method.
Abstract: Real time correlation function in a single phase space integral—beyond the linearized semiclassical initial value representation Jian Liu and William H. Miller Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry University of California, and Chemical Science Division, Lawrence Berkeley National Laboratory Berkeley, California 94720-1460 Abstract It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper— the full Wigner dynamics (full WD) and the 2 nd order WD based on “Winger trajectories”, and the full Donoso-Martens dynamics (full DMD) and the 2 nd order DMD based on “Donoso-Martens trajectories”—all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of these four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation
6 citations
References
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TL;DR: In this article, the Boltzmann formula for the probability of a configuration is given in classical theory by means of a probability function, and the result discussed is developed for the correction term.
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TL;DR: In this article, the Boltzmann formula for lower temperatures has been developed for a correction term, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.
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5,865 citations
01 Jan 1949
TL;DR: In this article, an attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics, which may hence be considered as an interpretation of quantum kinematics.
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TL;DR: In this article, a discrete variable representation (DVR) is introduced for use as the L2 basis of the S-matrix version of the Kohn variational method for quantum reactive scattering.
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1,575 citations