Exact time-dependent density-functional potentials for strongly correlated tunneling electrons

Hodgson, M. J. P.; Ramsden, J. D.; Chapman, Jacob B. J.; Lillystone, Piers; Godby, R. W.

doi:10.1103/physrevb.88.241102

Cited by 53 publications

(95 citation statements)

References 13 publications

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“…We find that in the system studied in Ref. 12 there are density minima, and thus peaks in the velocity field, that do not correspond to steps in the time-dependent xc potential. We have confirmed that this is because these density minima do not correspond to KS single-particle densities crossing.…”

Section: A Time-dependencementioning

confidence: 83%

“…Steps in the xc potential (a jump in the level of the xc potential over a relatively short distance) have been shown to be crucial for an accurate description of the electron density for a variety of ground-state and timedependent systems [5][6][7][8][9][10][11][12][13][14][15] , such as tunneling electrons and charge transfer/excitations. Atomic structure calculations by van Leeuwen et al 6 demonstrated that steps arise at the boundaries between atomic shells.…”

Section: Introductionmentioning

confidence: 99%

“…We derive, from these principles, arguments for the position and magnitude of steps, to aid the development of approximate functionals which have the ability to produce steps in v xc , such as the mixed localization potential (MLP) 14 . In Sections III-VI we model finite systems in one dimension using our iDEA code 12 in which we find the exact xc potential by first solving the time-dependent many-electron Schrödinger equation to obtain the fully correlated wavefunction. From this we calculate the exact electron density for ground-state, and subsequently timedependent, systems.…”

Section: Introductionmentioning

confidence: 99%

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Origin of static and dynamic steps in exact Kohn-Sham potentials

2016

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Knowledge of exact properties of the exchange-correlation (xc) functional is important for improving the approximations made within density functional theory. Features such as steps in the exact xc potential are known to be necessary for yielding accurate densities, yet little is understood regarding their shape, magnitude and location. We use systems of a few electrons, where the exact electron density is known, to demonstrate general properties of steps. We find that steps occur at points in the electron density where there is a change in the 'local effective ionization energy' of the electrons. We provide practical arguments, based on the electron density, for determining the position, shape and height of steps for ground-state systems, and extend the concepts to time-dependent systems. These arguments are intended to inform the development of approximate functionals, such as the mixed localization potential (MLP), which already demonstrate their capability to produce steps in the Kohn-Sham potential.PACS numbers: 31.15. 71.15.Mb, 31.15.A,

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Section: A Time-dependencementioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Origin of static and dynamic steps in exact Kohn-Sham potentials

2016

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“…Approximate functionals can not capture the step, and it is known [17,19,[52][53][54] that they yield poor CT dynamics, failing to transfer the charge, even when the functional yields a good prediction for the CT excitation energy. This is borne out in the dipole dynamics shown in the upper panel Fig.…”

Section: B Charge-transfer From a Ground Statementioning

confidence: 99%

Studies of spuriously shifting resonances in time-dependent density functional theory

Luo

Fuks

Maitra

2016

The Journal of Chemical Physics

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Adiabatic approximations in time-dependent density functional theory (TDDFT) will in general yield unphysical time-dependent shifts in the resonance positions of a system driven far from its ground-state. This spurious time-dependence is explained in [J. I. Fuks, K. Luo, E. D. Sandoval and N. T. Maitra, Phys. Rev. Lett. 114, 183002 (2015)] in terms of the violation of an exact condition by the non-equilibrium exchange-correlation kernel of TDDFT. Here we give details on the derivation and discuss reformulations of the exact condition that apply in special cases. In its most general form, the condition states that when a system is left in an arbitrary state, the TDDFT resonance position for a given transition in the absence of time-dependent external fields and ionic motion, is independent of the state. Special cases include the invariance of TDDFT resonances computed with respect to any reference interacting stationary state of a fixed potential, and with respect to any choice of appropriate stationary Kohn-Sham reference state. We then present several case studies, including one that utilizes the adiabatically-exact approximation, that illustrate the conditions and the impact of their violation on the accuracy of the ensuing dynamics. In particular, charge-transfer across a long-range molecule is hampered, and we show how adjusting the frequency of a driving field to match the time-dependent shift in the charge-transfer resonance frequency, results in a larger charge transfer over time.

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“…In order to test the LDAs, we employ our iDEA code [29] which solves the many-electron Schrödinger equation exactly for model finite systems to determine the exact, fully correlated, many-electron wave function. Using this to obtain the exact electron density, we then utilize our reverse engineering algorithm to find the exact KS system.…”

Section: Introductionmentioning

confidence: 99%

Comparison of local density functionals based on electron gas and finite systems

2018

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Article:Entwistle, M. T., Casula, Michele and Godby, R. W. orcid.org/0000-0002- 1012-4176 (2018) Comparison of local density functionals based on electron gas and finite systems. A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced a set of alternative LDAs constructed from one-dimensional systems of one, two, and three electrons that resemble the HEG within a finite region. We now construct a HEG-based LDA appropriate for spinless electrons in one dimension and find that it is remarkably similar to the finite LDAs. As expected, all LDAs are inadequate in low-density systems where correlation is strong. However, exploring the small but significant differences between the functionals, we find that the finite LDAs give better densities and energies in high-density exchange-dominated systems, arising partly from a better description of the self-interaction correction.

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Exact time-dependent density-functional potentials for strongly correlated tunneling electrons

Cited by 53 publications

References 13 publications

Origin of static and dynamic steps in exact Kohn-Sham potentials

Origin of static and dynamic steps in exact Kohn-Sham potentials

Studies of spuriously shifting resonances in time-dependent density functional theory

Comparison of local density functionals based on electron gas and finite systems

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