Revisiting the Concept of Equivalence in Solid-State NMR
Bibliographic record
Abstract
The concepts of chemical and magnetic equivalence have profound impacts on the understanding and interpretation of NMR phenomena. In solution, magnetic equivalence between spin-1/2 nuclei is generally associated with the lack of an observable spectral J-splitting. We examine here the concept of equivalence between quadrupolar nuclei with an emphasis on solid powdered samples. In this context, magnetic equivalence means that the coupled nuclei have identical NMR interaction tensor magnitudes and orientations. Contrary to the spin-1/2 case, J-couplings between magnetically equivalent quadrupolar nuclei are manifested as spectral splittings in solids and in aligned media. Following an overview of the relevant theory, examples employing double-rotation NMR, MQMAS NMR, ultrahigh-field NMR, and two-dimensional J-resolved experiments under both spinning and stationary conditions are discussed. The dependence of the observed splittings on the type of equivalence shared by the coupled nuclei (none, chemical, or magnetic) provides a unique experimental handle on crystallographic symmetry, which is of value for structure elucidation.
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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 | 0.010 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.022 |
| Scholarly communication | 0.004 | 0.016 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".