Extending the information-theoretic approach from the (one) electron density to the pair density
Bibliographic record
Abstract
Within the framework of chemical reactivity theory, information-theoretic descriptors have predominantly focused on global and local measures, while nonlocal descriptors beyond Shannon entropy remain largely unexplored. By extending the information carrier from the one-electron density to the two-electron distribution function (pair density), this work introduces information-theoretic descriptors rooted in both one-electron and pair densities. This broadens the scope of the information-theoretic approach (ITA) and introduces new types of ITA descriptors, notably the joint, conditional, and mutual ITA quantities. To elucidate the interaction between electron correlation and localization, we compute and analyze a suite of ITA descriptors for one-electron and pair electrons, including the Shannon entropy, Fisher information, and Rényi entropy, for neutral atoms ranging from helium (He) to argon (Ar). The results demonstrate how the pair-density ITA enhances the interpretation of electronic correlations and its connection to spatial localization.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".