Conceptual Density-Functional Theory for General Chemical Reactions, Including Those That Are Neither Charge- nor Frontier-Orbital-Controlled. 1. Theory and Derivation of a General-Purpose Reactivity Indicator
Bibliographic record
Abstract
A new general-purpose reactivity indicator is derived. Unlike existing indicators, this indicator can describe the reactivity of molecules that lie between the electrostatic (or charge) control and electron-transfer (or frontier-orbital) control paradigms. Depending on the parameters in the indicator, it describes electrostatic control (where the electrostatic potential is the appropriate indicator), electron-transfer control (where the Fukui function's potential is the appropriate indicator), and intermediate cases (where linear combinations of the electrostatic potential and the Fukui function's potential are appropriate indicators). Our analysis gives some insight into the origins of the local hard/soft-acid/base principle. The "minimum Fukui function" rule for hard reagents also emerges naturally from our analysis: if (1) a reaction is strongly electrostatically controlled and (2) there are two sites that are equally favorable from an electrostatic standpoint, then the most reactive of the electrostatically equivalent sites is the site with the smallest Fukui function. An analogous electrostatic potential rule for soft reagents is also introduced: if (1) a reaction is strongly electron-transfer-controlled and (2) there are two sites where the Fukui function's potential are equivalent, then the most reactive of the Fukui-equivalent sites will be the one with greatest electrostatic potential (for electrophilic attack on a nucleophile) or smallest electrostatic potential (for nucleophilic attack on an electrophile).
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".