Residual dipolar coupling in the CP/MAS nuclear magnetic resonance spectra of spin-1/2 nuclei coupled to quadrupolar nuclei application of floquet theory
Bibliographic record
Abstract
The CP/MAS spectra of spins-1/2 directly bonded to a quadrupolar nucleus (for example, C13 coupled to N14) often show fine structure, due to dipolar coupling. As the magnetic field is increased, splittings decrease and disappear. For the C13–N14 system, spectra appear as doublets with an intensity ration of 1:2. The mechanism for this is well-understood. Internuclear dipolar coupling, normally averaged out by spinning, appears because the N14 nucleus is not quantized exactly along the static magnetic field—the molecule-fixed quadrupolar interaction is not negligible compared to the lab-frame Zeeman interaction. Sample spinning cannot remove dipolar coupling if the quantization direction depends on molecular orientation. While the principle is clear, a fully detailed theory is lacking. Perturbation theory or average Hamiltonian theory work well if the quadrupolar interaction is small, or is very large, with respect to Zeeman term. However, there is little available that permits the calculation of the full spinning sideband spectra for all strengths of the quadrupolar interaction. In this paper, the spin system is solved exactly, by full matrix diagonalization, for a given orientation. This involves a careful analysis of the definition of quantization. Floquet theory is adopted to handle sample spinning—the time-dependent Hamiltonian is replaced by an expanded time-independent “Floquet” Hamiltonian. Due to the time-dependent quantization direction resulting from quadrupolar coupling, off-diagonal blocks must be computed by numerical Fourier transformation. Once the Floquet matrix is set up, and dephasing of coherences accounted, the result is a comprehensive means of simulating spectra, valid for all ranges of parameters.
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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 | 0.000 | 0.001 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".