Communication: Explicit construction of functional derivatives in potential-driven density-functional theory
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Bibliographic record
Abstract
We propose a method for imposing an important exact constraint on model Kohn-Sham potentials, namely, the requirement that they be functional derivatives of functionals of the electron density ρ. In particular, we show that if a model potential v(r) involves no ingredients other than ρ, ∇ρ, and ∇(2)ρ, then the necessary and sufficient condition for v(r) to be a functional derivative is ∂v/∂∇ρ=∇(∂v/∂∇(2)ρ). Integrability conditions of this type can be used to construct functional derivatives without knowing their parent functionals. This opens up possibilities for developing model exchange-correlation potentials that do not lead to unphysical effects common to existing approximations. Application of the technique is illustrated with examples.
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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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 it