Scaling properties of information-theoretic quantities in density functional reactivity theory
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Bibliographic record
Abstract
Density functional reactivity theory (DFRT) employs the electron density and its related quantities to describe reactivity properties of a molecular system. Quantities from information theory such as Shannon entropy, Fisher information, and Ghosh-Berkowitz-Parr entropy are natural descriptors within the DFRT framework. They have been previously employed to quantify electrophilicity, nucleophilicity and the steric effect. In this work, we examine their scaling properties with respect to the total number of electrons. To that end, we considered their representations in terms of both the electron density and the shape function for isolated atoms and neutral molecules. We also investigated their atomic behaviors in different molecules with three distinct partitioning schemes: Bader's zero-flux, Becke's fuzzy atom, and Hirshfeld's stockholder partitioning. Strong linear relationships of these quantities as a function of the total electron population are reported for atoms, molecules, and atoms in molecules. These relationships reveal how these information-theoretic quantities depend on the molecular environment and the electron population. These trends also indicate how these quantities can be used to explore chemical reactivity for real chemical processes.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| 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