Kohn-Sham potential for a strongly correlated finite system with fractional occupancy

Solving the fundamental and optical gap problems, which yield information about charged and neutral excitations in electronic systems, is one of the biggest challenge in density-functional theory (DFT). Despite their intrinsic difference, we show that the two problems can be made formally identical by introducing a universal and canonical ensemble weight dependent exchange-correlation (xc) density functional. The weight dependence of the xc energy turns out to be the key ingredient for describing the infamous derivative discontinuity and represents a new path for its approximation.

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“…Moreover, as readily seen from Eq. (17), the N + -and N − -electron energies can be extracted separately from the ensemble energy as follows,…”

Section: Exact Extraction Of Individual Energiesmentioning

confidence: 99%

Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles

2018

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“…In the appendix, we show that, using (33) and (34) in (31) and inserting the result in (30), δF ZPE /δρ(x) can be expressed as (see Appendix for details)…”

Section: B Explicit Expressionmentioning

confidence: 99%

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

Grossi¹,

Seidl²,

Gori‐Giorgi³

et al. 2019

Phys. Rev. A

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We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy-Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.

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“…It is well known that the exact KS potential for ground state of an interacting two-electron system can be constructed if the electron density n (2) gs (r) of the spin-singlet ground state is known [31,35,36]:…”

Section: Kohn-sham Green's Functionmentioning

confidence: 99%

One-particle Green’s function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn–Sham system

Kosugi¹,

Matsushita²

2018

J. Phys.: Condens. Matter

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For a three-electron system with finite-strength interactions confined to a one-dimensional harmonic trap, we solve the Schrödinger equation analytically to obtain the exact solutions, from which we construct explicitly the simultaneous eigenstates of the energy and total spin for the first time. The solutions for the three-electron system allow us to derive analytic expressions for the exact one-particle Green's function (GF) for the corresponding two-electron system. We calculate the GF in frequency domain to examine systematically its behavior depending on the electronic interactions. We also compare the pole structure of non-interacting GF using the exact Kohn-Sham (KS) potential with that of the exact GF to find that the discrepancy of the energy gap between the KS system and the original system is larger for a stronger interaction. We perform numerical examination on the behavior of GFs in real space to demonstrate that the exact and KS GFs can have shapes quite different from each other. Our simple model will help to understand generic characteristics of interacting GFs.

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Kohn-Sham potential for a strongly correlated finite system with fractional occupancy

Cited by 30 publications

References 24 publications

Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles

Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

One-particle Green’s function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn–Sham system

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