Hyperfine coupling constants and electron-spin <i>g</i>-factors of B2+, Al2+, Ga2+, BAl+, BGa+, and AlGa+: An <i>ab initio</i> study
Bibliographic record
Abstract
The hyperfine coupling constants (hfcc) and electron-spin g-factors (magnetic moments) calculated for B2+, Al2+, Ga2+, BAl+, BGa+, and AlGa+ are reported. The hfcc’s are obtained with single-reference configuration interaction, second-order Møller–Plesset, density functional (B3LYP, PW91PW91) methods, and 6-311+G(2df ) basis sets. The 2σg/3σ SOMOs of X 2Σg+(1σg21σu22σg)/X 2Σ+(1σ22σ23σ) mainly have a pσ–pσ composition, leading in most cases to similar values of Adip and Aiso. As a result, |A∥| is up two orders of magnitude larger than |A⊥|. The A⊥’s are slightly negative (ca. −10 MHz) for Al2+, Ga2+, and AlGa+. The g-shifts (Δg=g−ge) are evaluated with multireference CI wave functions, perturbation expansions up to second-order, and 6-311+G(2d) basis sets. Both Δg∥ and Δg⊥ are negative, but Δg∥ lies close to zero. The Δg⊥’s of B2+, Al2+, Ga2+ are about −1 300, −12 800, −97 300 ppm, respectively, while for BGa+, BAl+, AlGa+, they are much smaller (−800, −2 800, −47 400 ppm). The reduced Δg⊥’s for XY+ result from the mutual cancellation between a positive contribution from the 1 2Π(3σ→1π) state but a negative one from 2 2Π(3σ→2π). The positive contribution is at variance with the rule-of-thumb stating that SOMO→virtual MO excitations should contribute negatively. The variation of the hfcc’s with bond distance is analyzed for all systems, and that of the Δg⊥ component for B2+ and BAl+. Experimental or previous theoretical electron-spin resonance data are not available for comparison.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".