Semiclassical Moyal dynamics

Shen, Yifan; Wang, Linjun

doi:10.1063/1.5067005

“…When strong nuclear quantum effects emerge, however, better semiclassical dynamics approaches may be useful. 66,67 (5) To get reliable populations in the asymptotic region, BCMF resets wavefunction coefficients considering the energy conservation. Note that similar algorithms have been utilized in the Liouville space surface hopping.…”

Section: Associated Contentmentioning

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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“…It is generally assumed that in more general situations, a proper description of the dynamics may require high order solutions (or QHD-N ), although except in a small number of cases, e.g. [20], [21], such solutions have rarely been tested.…”

Section: Introductionmentioning

confidence: 99%

“…More recently Shen and Wang have developed a phase space approach [21] to the same general problems, which they refer to as semi-classical Moyal dynamics (SMD), This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.…”

Section: Introductionmentioning

confidence: 99%

Generalized quantum cumulant dynamics

Bowen

¹

,

Everitt

²

,

Phillips

³

et al. 2019

The Journal of Chemical Physics

2

0

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A means of unifying some semiclassical models of computational chemistry is presented; these include Quantized Hamiltonian Dynamics (QHD), Quantal Cumulant Dynamics (QCD) and Semiclassical Moyal Dynamics (SMD). A general method for creating the infinite hierarchy of operator dynamics in the Heisenberg picture is derived together with a general method for truncation (or closure) of that series, and in addition we provide a simple link to the phase space methods of SMD. Operator equations of arbitrary order may be created readily, avoiding the tedious algebra identified previously. Truncation is based on a simple recurrence formula which is related to, but avoids the more complex contractions of, Wick's theorem. This generalised method is validated against a number of trial problems considered using the previous methods. We also touch on some of the limitations involved using such methods; noting, in particular, that any truncation will lead to a state which is in some sense unphysical. Finally, we briefly introduce our quantum algebra package QuantAL which provides an automated method for: generation of the required equation set; the initial conditions for all variables from an any start; and all the higher order approximations necessary for truncation of the series, at essentially arbitrary order.

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“…When strong nuclear quantum effects emerge, however, better semiclassical dynamics approaches may be useful. 66,67 (5) To get reliable populations in the asymptotic region, BCMF resets wave function coefficients considering the energy conservation. Note that similar algorithms have been utilized in the Liouville space surface hopping.…”

mentioning

confidence: 99%

“…(4) In some sense, the present BCMF algorithm for nonadiabatic dynamics is analogous to the classical Wigner approximation for adiabatic dynamics. , Both approaches benefit from the initial Wigner sampling to consider most of the nuclear quantum effects. When strong nuclear quantum effects emerge, however, better semiclassical dynamics approaches may be useful. , (5) To get reliable populations in the asymptotic region, BCMF resets wave function coefficients considering the energy conservation. Note that similar algorithms have been utilized in the Liouville space surface hopping. , A slow decoherence effect due to traditional decay of mixing may be responsible for this. − Relevant studies are currently under way.…”

mentioning

confidence: 99%

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

Xu

¹

,

Wang

²

2020

J. Phys. Chem. Lett.

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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. 2Nonadiabatic dynamics have attracted substantial interest in the past decades.Many important phenomena in chemistry, physics, biology, and material sciences (e.g., proton transfer, 1,2 photoisomerization, 3,4 charge transport, 5,6 exciton dissociation, 7,8 and nonradiative energy relaxation 9,10 ) all fall into the category of nonadiabatic dynamics.Compared with adiabatic dynamics, nonadiabatic dynamics involve strongly coupled electronic and nuclear motion, and thus are generally difficult to deal with theoretically.The fully quantum simulations give accurate description but are normally too expensive to carry out in complex systems. Comparatively, mixed quantum-classical dynamics (MQCD) methods are widely utilized due to the potentially good balance between efficiency and reliability. Nowadays, the Ehrenfest mean field (EMF), 11 Tully's fewest switches surface hopping (FSSH), 12 and their many variants have become the most popular approaches for nonadiabatic dynamics simulations in different fields. [13][14][15][16][17][18][19][20] Both EMF and FSSH utilize the time-dependent Schrödinger equation (TDSE) to characterize the electronic wavefunction evolution. 11,12 Their major difference lies in the description of nuclear motion. In EMF, the nuclei evolve on a single effective potential energy surface (PES), which is obtained through averaging over all the electronic states and using the quantum populations as weights. In comparison, FSSH forces the nuclei to move on an active PES at any time and allows stochastic surface hops between PESs according to the nonadiabatic coupling. As a result, FSSH can take into account the different motion of nuclear wave packets (WPs) on different PESs.FSSH has shown higher reliability, 12,21,22 better detailed balance, [23][24][25] and the ability to describe both strong and weak polaronic effects, [26][27][28] implying that surface hops play an

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Semiclassical Moyal dynamics

Cited by 8 publications

References 54 publications

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

Generalized quantum cumulant dynamics

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

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