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 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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".