Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics

He, Xin; Wu, Baihua; Gong, Zhihao; Liu, J.

doi:10.1021/acs.jpca.1c04429

Cited by 24 publications

(108 citation statements)

References 158 publications

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“…In addition, the EOMs used in Spin-LSC and eCMM are identical as well. Considering all of the above, eCMM 56 is an identical approach compared to Spin-LSC. 29 (6).…”

Section: E Connections With Previous Methodsmentioning

confidence: 99%

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Non-adiabatic Dynamics using the Generators of the su(N) Lie Algebra

Bossion

Chowdhury

Huo

2022

Preprint

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We present the rigorous theoretical framework of the generalized spin mapping representation for non- adiabatic dynamics. This formalism is based on the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space in the state representation. We use the generalized spin coherent states representation and the Stratonovich-Weyl transform to describe these electronic spin-mapping variables in the continuous variables space. Wigner representation is used to de- scribe the nuclear degrees of freedom. Using the above representations, we derived an exact expression of the time-correlation function as well as the exact quantum Liouvillian. Making the linearization approximation, this exact Liouvillian is reduced to the Liouvillian of the recently proposed spin-Linearized Semi-Classical (spin-LSC) dynamics. These expressions lead to a self-consistent trajectory-based method to simulate non- adiabatic dynamics, which is based entirely on the generalized spin mapping formalism to treat the electronic states without the necessity of converting back to the cartesian mapping variables of the bosonic DOF (which are commonly referred to as the Meyer-Miller-Stock-Thoss mapping variables). The accuracy of this approach is tested with several challenging non-adiabatic model systems.

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“…In addition, the EOMs used in Spin-LSC and eCMM are identical as well. Considering all of the above, eCMM 56 is an identical approach compared to Spin-LSC. 29 (6).…”

Section: E Connections With Previous Methodsmentioning

confidence: 99%

“…7 of Ref. 55) derived in the extended classical mapping model (eCMM), 55,56 when adding an additional total population constraint in the MMST mapping phase space. Here, the total population constraint is naturally satisfied in the su(N ) framework and within the SW transform.…”

Section: Connections With the Mmst Mapping Formalismmentioning

confidence: 99%

Non-adiabatic Dynamics using the Generators of the su(N) Lie Algebra

Bossion

Chowdhury

Huo

2022

Preprint

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“…From the unified framework, the extended classical mapping model 30,77,122 uses the Meyer-Miller Hamiltonian:…”

Section: Extended Classical Mapping Model (Ecmm)mentioning

confidence: 99%

NQCDynamics.jl: A Julia Package for Nonadiabatic Quantum Classical Molecular Dynamics in the Condensed Phase

Gardner,

Douglas-Gallardo,

Stark

et al. 2022

Preprint

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Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in condensed phase. To facilitate effective development, code sharing and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon. Using the Julia programming language, we have developed the NQCDynamics.jl package which provides a framework for established and emerging methods for performing semiclassical and mixed quantum-classical dynamics in condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit. We further demonstrate the capabilities of the package on two examples of chemical dynamics in condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semi-classical and mixed quantum-classical nonadiabatic methods and the reactive scattering of H 2 on Ag(111) using the Molecular Dynamics with Electronic Friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems. Methods FSSH NRPMD Ehrenfest MDEF Classical Langevin eCMM Simulation Parameters Atoms Elements Masses Models Analytic model ASE calculator ML model Keywords Simulation cell Temperature Method extras Simulation Method (atoms , model; kwargs¡ ) { } FIG. 1. The user inputs required to define the parameters for a simulation. This diagram along with Figs. 2 and 3 was created using the Excalidraw 65 online tool.

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“…21,23 Moreover, projecting the Hilbert space to the SEO subspace also ruins the original simple commutation relations among the MMST mapping operators in their full Hilbert space, 24 making the mapping Hamiltonian potentially containing more terms that require additional approximations to parameterize. 25 Mathematically, the idea of mapping relation is referred to as the generalized Weyl correspondence, in which Lie groups and Lie algebras are the central components. [26][27][28] Lie algebras are formed by commutation relations among generators with given structure constants; the elements of a connected matrix Lie group 29 can be expressed as the exponential of the Lie algebra generators, i.e., the exponential map.…”

Section: Introductionmentioning

confidence: 99%

“…This is a reasonable choice for constructing an algorithm for approximate quantum dynamics, as it avoids deriving the EOMs in the generalized Euler angles of the spin coherent state, which is highly non-trivial. However, this choice also brings the potential confusions 25 that the MMST mapping Hamiltonian is a necessary and essential ingredient in the SU (N ) mapping formalism. 43 Further, the EOMs of the spin-LSC approach 43 were not rigorously derived, and there is a lack a rigorous derivation of the timecorrelation function as well.…”

Section: Introductionmentioning

confidence: 99%

Non-adiabatic Mapping Dynamics in the Phase Space of the SU(N) Lie Group

Bossion

Ying

Chowdhury

et al. 2022

Preprint

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We present the rigorous theoretical framework of the generalized spin mapping representation for non- adiabatic dynamics. This formalism is based on the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space in the state representation. The Stratonovich-Weyl transform is then used to map an operator in the Hilbert space to a continuous func- tion on the SU(N) Lie Group manifold which is a phase space of continuous variables. Wigner representation is used to describe the nuclear degrees of freedom. Using the above representations, we derived an exact expression of the time-correlation function as well as the exact quantum Liouvillian. Making the linearization approximation, this exact Liouvillian is reduced to the Liouvillian of the several recently proposed meth- ods. These expressions lead to a self-consistent trajectory-based method to simulate non-adiabatic dynamics, which is based entirely on the generalized spin mapping formalism to treat the electronic states without the necessity of converting back to the cartesian Meyer-Miller-Stock-Thoss mapping variables. We envision that the theoretical work presented in this work provides a rigorous and unified framework to formally derive non-adiabatic quantum dynamics approaches with continuous variables.

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Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics

Cited by 24 publications

References 158 publications

Non-adiabatic Dynamics using the Generators of the su(N) Lie Algebra

Non-adiabatic Dynamics using the Generators of the su(N) Lie Algebra

NQCDynamics.jl: A Julia Package for Nonadiabatic Quantum Classical Molecular Dynamics in the Condensed Phase

Non-adiabatic Mapping Dynamics in the Phase Space of the SU(N) Lie Group

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