Necessary conditions for the <i>N</i>‐representability of pair distribution functions
Bibliographic record
Abstract
Abstract A necessary condition for the N ‐representability of the electron pair density proposed by one of the authors (E. R. D.) is generalized. This shows a link between this necessary condition and other, more widely known, N ‐representability conditions for the second‐order density matrix. The extension to spin‐resolved electron pair densities is considered, as is the extension to higher‐order distribution functions. Although quantum mechanical systems are our primary focus, the results are also applicable to classical systems, where they reduce to an inequality originally derived by Garrod and Percus. As a simple application, bounds to the average angle between an electron pair are derived. It is shown that computational methods based on variational minimization of the energy with respect to the electron pair density can give extremely poor results unless robust N ‐representability constraints are considered. For reference, constraints for the N ‐representability of the pair density are summarized. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.012 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".