Proton Spin−Spin Coupling and Electron Delocalization
Bibliographic record
Abstract
The spin−spin coupling of protons measured by the constant J HH ‘ in NMR experiments is dominated by a term proportional to the product of the electron spin densities at the two nuclei, the Fermi contact term. The probability of β electrons being in excess over α electrons at the position of nucleus n ‘, given that there is an α electron at n, is proportional to the negative of the exchange density, the total Fermi correlation between n and n ‘. Thus the delocalization of the Fermi hole between n and n ‘ is the mechanism whereby the spin perturbation caused by the magnetic interaction of an electron with nucleus n is transmitted to n ‘. The density and exchange density within the basin of a hydrogen atom are described primarily in terms of s-type basis functions, and one may approximate the exchange density between two protons at n and n ‘ by the exchange between the two associated atomic basins determined by the delocalization index δ(A,B) within the quantum theory of atoms in molecules. It is shown that this model yields good linear regression equations relating J HH ‘ to δ(H,H‘) for hydrogen atoms bonded to different carbons in alkanes, alkenes, their cyclic congeners, and polybenzenoid hydrocarbons.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".