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Density Functional Theory Based on the Electron Distribution on the Energy Coordinate

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Hideaki Takahashi

Chemical Physics · Submitted 25 Jan 2016

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

The authors' main claim By taking advantage of this property we developed a prototype of the static correlation functional employing no empirical parameters, which realized a reasonable dissociation curve for H2 molecule.

how it is stated · asserted 0.99 read the record →

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arXiv ID1601.06553 (version 1)
Pith ID7OKGSHYK, Pith's permanent record of this paper and its review
CitationHideaki Takahashi. "Density Functional Theory Based on the Electron Distribution on the Energy Coordinate." arXiv:1601.06553 (2016). https://pith.science/paper/7OKGSHYK
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,323 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.16 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We introduced a new electron density n({\epsilon}) by projecting the spatial electron density n(r) onto the energy coordinate {\epsilon} defined with the external potential \upsion (r) of interest. Then, a density functional theory (DFT) was formulated, where n({\epsilon}) serves as a fundamental variable for the electronic energy. It was demonstrated that the Kohn-Sham equation can also be adapted to the DFT that employs the density n({\epsilon}) as an argument to the exchange energy functional. An important attribute of the energy density is that it involves the spatially non-local population of the spin-adapted density n(r) at the bond dissociation. By taking advantage of this property we developed a prototype of the static correlation functional employing no empirical parameters, which realized a reasonable dissociation curve for H2 molecule.

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 We introduced a new electron density n({\epsilon}) by projecting the spatial electron density n(r) onto the energy coordinate {\epsilon} defined with the external potential \upsion (r) of interest. contribution 0.87 0.94 0.08 asserted 1.00
s1 Then, a density functional theory (DFT) was formulated, where n({\epsilon}) serves as a fundamental variable for the electronic energy. contribution 0.78 0.90 0.18 asserted 1.00
s2 It was demonstrated that the Kohn-Sham equation can also be adapted to the DFT that employs the density n({\epsilon}) as an argument to the exchange energy functional. result 0.45 0.84 0.15 asserted 1.00
s3 An important attribute of the energy density is that it involves the spatially non-local population of the spin-adapted density n(r) at the bond dissociation. interpretation 0.49 0.77 0.12 asserted 1.00
s4 By taking advantage of this property we developed a prototype of the static correlation functional employing no empirical parameters, which realized a reasonable dissociation curve for H2 molecule. result 0.67 0.96 0.45 asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.94 · evidence from simulation or computation 0.58.

What was examined, and what was not

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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

We introduced a new electron density n({\epsilon}) by projecting the spatial electron density n(r) onto the energy coordinate {\epsilon} defined with the external potential \upsion (r) of interest. Then, a density functional theory (DFT) was formulated, where n({\epsilon}) serves as a fundamental variable for the electronic energy. It was demonstrated that the Kohn-Sham equation can also be adapted to the DFT that employs the density n({\epsilon}) as an argument to the exchange energy functional. An important attribute of the energy density is that it involves the spatially non-local population of the spin-adapted density n(r) at the bond dissociation. By taking advantage of this property we developed a prototype of the static correlation functional employing no empirical parameters, which realized a reasonable dissociation curve for H2 molecule.

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