The shell model for the exchange-correlation hole in the strong-correlation limit
Bibliographic record
Abstract
We present a model for the exchange-correlation hole and the exchange-correlation energy in the strong-correlation (SC) limit of density functional theory. The SC limit is useful in the construction of exchange-correlation functionals through interpolation of the adiabatic connection. The new approximation (referred to as shell model) is an improvement of the non-local radius (NLR) model recently proposed by Wagner and Gori-Giorgi [Phys. Rev. A 90, 052512 (2014)]. The NLR model does not correctly reproduce the limit of the strongly correlated homogeneous electron gas and this shortcoming is remedied by the shell model. As in the case of the NLR model, the spherically averaged electron density ρ(r,u)=∫dΩu4πρ(r+u) is the starting point for the construction of the shell model and it is also its computational bottleneck. We show how ρ(r, u), the NLR, and the shell model can be implemented efficiently. For this purpose, analytical integrals for the normalization and the energy density of the underlying holes are provided. Employing the shell model, we illustrate how improved adiabatic connection interpolations can be constructed.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".