Coordinate scaling of the kinetic energy in pair density functional theory: A Legendre transform approach
Bibliographic record
Abstract
Abstract We show that the kinetic energy functional in pair density functional theory is homogeneous of degree 2 with respect to coordinate scaling. Although this result was already derived by Levy and Ziesche using the constrained search method (Levy and Ziesche, J Chem Phys 2001, 115, 9110 ), we derive our result using the Legendre transform formulation (Ayers et al., J Chem Phys 2006, 124, 054101 ). The advantage of this approach is that in the Legendre transform functional, the N ‐representability problem is solved by the functional. By contrast, in the Levy–Ziesche approach, the computationally impracticable N ‐representability constraints have to be imposed separately. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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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 | 0.000 | 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 | 0.000 | 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 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".