Nuclear spin–spin coupling constants from regular approximate relativistic density functional calculations. I. Formalism and scalar relativistic results for heavy metal compounds
Bibliographic record
Abstract
We present a relativistic formulation of the spin–spin coupling hyperfine terms based on the two component zeroth-order regular approximate Hamiltonian. The scalar relativistic parts of the resulting operators were used for an implementation into the Amsterdam density functional program. Application of the code for the calculation of one-bond metal-ligand couplings of systems containing W183, Pt195, Hg199, and Pb207 shows that scalar relativistic calculations are able to reproduce major parts of the relativistic effects on the coupling constants, which can be even larger in magnitude than the respective total nonrelativistic values. The spatial origin of the regular approximate relativistic analogue of the Fermi-contact contribution, which is usually responsible for the strong relativistic increase of the couplings, is analyzed. Its relativistic effects can be described by the relativistic increase of valence orbital density in the very vicinity of the heavy nucleus.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".