The Fukui Potential and the Capacity of Charge and the Global Hardness of Atoms
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Bibliographic record
Abstract
In the course of a reaction it is the shape of the Fukui potential that guides a distant reagent toward the site where an electrophile/nucleophile is willing to accept/donate charge. In this paper we explore the mathematical characteristics of the Fukui potential and demonstrate its relationship to the hardness and the ability of an atom in a molecule to change its charge. The Fukui potential not only determines the active site for electron transfer, but it also approximates the distribution of hardness of a molecule: it is the Coulomb contribution to the frontier local hardness. The Fukui potential at the position of the nuclei is equal to the variation of the chemical potential with the nuclear charge and therefore measures the sensitivity of the system to changes in atom type. In the specific case of atoms and slightly charged ions, the Fukui potential at the nucleus measures the hardness. The strong correlation between the hardness and the Fukui potential at the nucleus suggests that the Fukui potential at the nucleus is an alternative definition for the chemical hardness.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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 it