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Record W4299358577 · doi:10.17615/b915-bb97

Necessary and sufficient conditions for the N -representability of density functionals

2021· article· en· W4299358577 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueUNC Libraries · 2021
Typearticle
Languageen
FieldMathematics
TopicGraph theory and applications
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of CanadaCanada Research Chairs
KeywordsMathematicsStatistical physicsApplied mathematicsPhysics

Abstract

fetched live from OpenAlex

It is well known that variational optimization of the energy using approximate density functionals can give results below the true ground-state energy. This can be attributed to the fact that many approximate density functionals are not N-representable. This paper presents a general method for deriving N-representability conditions in density-functional theory and presents specific results for the kinetic energy, the electron-electron interaction energy, the Hohenberg-Kohn functional, and the exchange-correlation energy functional. The method can be extended to energy densities, and specific results are presented for two different choices of the kinetic-energy density. Max-min variational principles for minimizing the energy subject to N-representability constraints are presented. Some constraints on exchange-correlation density functionals are among our secondary findings. In particular, we construct an exact meta-generalized-gradient-approximation (meta-GGA) functional using a Legendre transform and use this expression to show that (a) meta-GGAs should be convex functionals of the kinetic-energy density and (b) the sum of the Coulomb energy and the meta-GGA exchange-correlation energy should be a convex functional of the electron density.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.035
Threshold uncertainty score0.197

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.060
GPT teacher head0.315
Teacher spread0.255 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it