Multinuclear Magnetic Resonance Crystallographic Structure Refinement and Cross-Validation Using Experimental and Computed Electric Field Gradients: Application to Na<sub>2</sub>Al<sub>2</sub>B<sub>2</sub>O<sub>7</sub>
Bibliographic record
Abstract
An NMR crystallographic method is presented for the refinement of structures using electric field gradient (EFG) tensors measured using solid-state NMR spectroscopy and those calculated using the projector-augmented wave DFT method. As the calculated EFG data often overestimate the experimental data, the former are scaled to yield optimal agreement for a test set of compounds having highly accurate NMR data. A least-squares optimization procedure is then performed to minimize the difference between the experimental and the scaled calculated EFG tensors. This procedure yields high-quality crystal structures comparable to those obtained from pure DFT energy minimizations, as judged by their rmsd from single-crystal X-ray structures, and is based on experimental observables. Further improvement is obtained by simultaneously refining the structures against the experimental EFG tensor parameters and optimizing the lattice energy with DFT. We use this hybrid experimental–theoretical approach to refine the crystal structure of Na 2 Al 2 B 2 O 7, a member of an important family of nonlinear optical materials, which has been the focus of study due to its tendency to form stacking faults. The resulting structures are subjected to a systematic cross-validation process using experimental 23 Na, 11 B, 17 O, and 27 Al EFG and chemical shift data, thereby demonstrating the validity of our strategy. This approach may be useful for the refinement of crystal structures of intrinsically polycrystalline materials for which typically only low quality structures are obtainable through traditional diffraction-based methods.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".