Adiabatic Approximation in Nonperturbative Time-Dependent Density-Functional Theory

Thiele, M.; Gross, E. K. U.; Kümmel, Stephan

doi:10.1103/physrevlett.100.153004

Cited by 135 publications

(137 citation statements)

References 39 publications

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“…The mRKS technique can also be used for construction of exchange-correlation potentials of adiabatic time-dependent density-functional theory. [60][61][62] Extensions of the mRKS method to spinpolarized post-HF wave functions and to systems that are not pure-state v-representable remain the subject of future work.…”

Section: Discussionmentioning

confidence: 99%

Improved method for generating exchange-correlation potentials from electronic wave functions

Ospadov

Ryabinkin

Staroverov

2017

The Journal of Chemical Physics

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Ryabinkin, Kohut, and Staroverov (RKS) [Phys. Rev. Lett. 115, 083001 (2015)] devised an iterative method for reducing many-electron wave functions to Kohn-Sham exchange-correlation potentials, vXC(r). For a given type of wave function, the RKS method is exact (Kohn-Sham-compliant) in the basis-set limit; in a finite basis set, it produces an approximation to the corresponding basisset-limit vXC(r). The original RKS procedure works very well for large basis sets but sometimes fails for commonly used (small and medium) sets. We derive a modification of the method's working equation that makes the RKS procedure robust for all Gaussian basis sets and increases the accuracy of the resulting exchange-correlation potentials with respect to the basis-set limit.

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Section: Discussionmentioning

confidence: 99%

Improved method for generating exchange-correlation potentials from electronic wave functions

Ospadov

Ryabinkin

Staroverov

2017

The Journal of Chemical Physics

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“…In the linear response regime, the xc kernel for charge-transfer excitations displays frequency-dependent steps [26]. However we argue that the dynamical step structures we are seeing are generic, and moreover, unlike most of the above cases [18,[22][23][24], cannot be captured by an adiabatic approximation. They appear with no need for ionization nor subsystems of fractional charge, nor any applied field (see next example), unlike in Refs.…”

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confidence: 92%

“…[18,22] showed they appear in ionization processes, and linked them to a time-dependent derivative discontinuity, related to fractional charges. In time-resolved transport, step structures have been shown to be essential for describing Coulomb-blockade phenomena [23], again related to the discontinuity.…”

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confidence: 99%

Universal Dynamical Steps in the Exact Time-Dependent Exchange-Correlation Potential

et al. 2012

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We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of non-equilibrium dynamical situations relevant for modeling of photo-chemical/physical processes: field-free evolution of a non-stationary state, resonant local excitation, resonant complete charge-transfer, and evolution under an arbitrary field. Lack of these steps in usual approximations yield inaccurate dynamics, for example predicting faster dynamics and incomplete charge transfer.The vast majority of applications of time-dependent density functional theory (TDDFT) today deal with the calculation of the linear electronic spectra and response of molecules and solids, and provide an unprecedented balance between accuracy and efficiency [1,2]. The theorems of TDDFT also apply to any real-time electron dynamics, not necessarily starting in a ground-state, and possibly subject to strong or weak time-dependent fields. Time-resolved dynamics are particularly important and topical for TDDFT for two reasons. First, there is really no alternative practical method for accurately describing correlated electron dynamics, and second, many fascinating new phenomena and technological applications lie in this realm. These include: attosecond control of electron dynamics [3], photo-induced coupled electron-ion dynamics (for example in describing lightharvesting and artificial photosyntheses), and photochemical/physical processes [4,5] in general. TDDFT in theory yields all observables exactly, solely in terms of the time-dependent density, however in practice, approximations must be made both for the observable as a functional of the density, and for the exchangecorrelation (xc) functional. Thus the question arises as to whether the approximate functionals that have been successful for excitations predict equally well the dynamics in the more general time-dependent context. In particular, the exact xc contribution to the Kohn-Sham (KS) potential at time t functionally depends on the history of the density n(r, t ′ < t), the initial interacting many-body state Ψ 0 , and the choice of the initial KS state Φ 0 : v XC [n; Ψ 0 , Φ 0 ](r, t). However, almost all calculations today use an adiabatic approximation, v A XC = v g.s. XC

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“…Whereas most of the studies so far have relied on the local density approximation, 1,[32][33][34] a big effort has also been taken on the direction of capturing memory effects. [33][34][35][36][37][38] Furthermore, there has been considerable interest in the extension of TDDFT to study situations where there is an interplay between electronic and nuclear degrees of freedom and both are explicitly included in the simulation. [39][40][41][42][43][44][45] An alternative approach to this problem relies on Open Quantum Systems (OQS) theory, where the electronic degrees of freedom are evolved as a quantum master equation (ME), with the bath of phonons affecting the electrons via fluctuations and dissipation.…”

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confidence: 99%

Remarks on time-dependent [current]-density functional theory for open quantum systems

Yuen-Zhou

Aspuru‐Guzik

2013

Phys. Chem. Chem. Phys.

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Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems.Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particleparticle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.

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Adiabatic Approximation in Nonperturbative Time-Dependent Density-Functional Theory

Cited by 135 publications

References 39 publications

Improved method for generating exchange-correlation potentials from electronic wave functions

Improved method for generating exchange-correlation potentials from electronic wave functions

Universal Dynamical Steps in the Exact Time-Dependent Exchange-Correlation Potential

Remarks on time-dependent [current]-density functional theory for open quantum systems

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