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How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?

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M.J.P. Hodgson, E. Kraisler, E.K.U. Gross

Atomic Physics · Submitted 2 Jun 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this Letter, we establish the common fundamental origin of these two features of the exact xc potential via an analytical derivation.

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arXiv ID1706.00586 (version 1)
Pith IDOYPRIDAE, Pith's permanent record of this paper and its review
CitationE. Kraisler, E.K.U. Gross, M.J.P. Hodgson. "How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?." arXiv:1706.00586 (2017). https://pith.science/paper/OYPRIDAE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,540 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.29 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The reliability of density-functional calculations hinges on accurately approximating the unknown exchange-correlation (xc) potential. Common (semi-)local xc approximations lack the jump experienced by the exact xc potential as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form in the potential as a result of the change in the decay rate of the density. These features are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Although well-known concepts, the exact relationship between them remained unclear. In this Letter, we establish the common fundamental origin of these two features of the exact xc potential via an analytical derivation. We support our result with an exact numerical solution of the many-electron Schroedinger equation for a single atom and a diatomic molecule in one dimension. Furthermore, we propose a way to extract the fundamental gap from the step structures in the potential.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The reliability of density-functional calculations hinges on accurately approximating the unknown exchange-correlation (xc) potential. background 1.00 0.04 0.02 asserted 1.00
s1 Common (semi-)local xc approximations lack the jump experienced by the exact xc potential as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form in the potential as a result of the change in the decay rate of the density. background 0.97 0.05 0.05 asserted 1.00
s2 These features are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. background 0.91 0.06 0.04 asserted 1.00
s3 Although well-known concepts, the exact relationship between them remained unclear. gap 1.00 0.06 0.03 asserted 0.94
s4 In this Letter, we establish the common fundamental origin of these two features of the exact xc potential via an analytical derivation. contribution 0.98 0.97 0.82 asserted 1.00
s5 We support our result with an exact numerical solution of the many-electron Schroedinger equation for a single atom and a diatomic molecule in one dimension. method 0.89 0.96 0.04 asserted 1.00
s6 Furthermore, we propose a way to extract the fundamental gap from the step structures in the potential. contribution 0.86 0.84 0.13 asserted 0.65

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The reliability of density-functional calculations hinges on accurately approximating the unknown exchange-correlation (xc) potential. Common (semi-)local xc approximations lack the jump experienced by the exact xc potential as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form in the potential as a result of the change in the decay rate of the density. These features are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Although well-known concepts, the exact relationship between them remained unclear. In this Letter, we establish the common fundamental origin of these two features of the exact xc potential via an analytical derivation. We support our result with an exact numerical solution of the many-electron Schroedinger equation for a single atom and a diatomic molecule in one dimension. Furthermore, we propose a way to extract the fundamental gap from the step structures in the potential.

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