Gauge invariance of the spin-other-orbit contribution to the g-tensors of electron paramagnetic resonance
Bibliographic record
Abstract
The spin-other-orbit (SOO) contribution to the g-tensor (DeltagSOO) of electron paramagnetic resonance arises due to the interaction of electron-spin magnetic moment with the magnetic field produced by the orbital motion of other electrons. A similar mechanism is responsible for the leading term in nuclear magnetic-shielding tensors sigma. We demonstrate that analogous to sigma, paramagnetic DeltagSOO contribution exhibits a pronounced dependence on the choice of the magnetic-field gauge. The gauge corrections to DeltagSOO are similar in magnitude, and opposite in sign, to the paramagnetic SOO term. We calculate gauge-invariant DeltagSOO values using gauge-including atomic orbitals and density-functional theory. For organic radicals, complete gauge-invariant DeltagSOO values typically amount to less than 500 parts per million (ppm), and are small compared to other g-tensor contributions. For the first-row transition-metal compounds, DeltagSOO may contribute several thousand ppm to the g-tensor, but are negligible compared to the remaining deviations from experiment. With popular choices for the magnetic-field gauge, the individual gauge-variant contributions may be an order of magnitude higher, and do not provide a reliable estimation of DeltagSOO.
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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 | 0.002 |
| 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 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".