Electron-Spin Magnetic Moment (<i>g</i> Factor) of X<sup>2</sup>Σ<sup>+</sup> Diatomic Radicals MX<sup>(±)</sup> with Nine Valence Electrons (M = Be, B, Mg, Al; X = N, O, F, P, S, Cl). An ab Initio Study
Bibliographic record
Abstract
The electron-spin g shifts (magnetic moments μ S ) of X 2 Σ + (1π 4 3σ) radicals MX (±) with nine valence electrons are calculated at their equilibrium geometries, using second-order perturbation theory, a Hamiltonian based on Breit−Pauli theory, and correlated (MRCI) wave functions. Eighteen diatomics have been studied: BeF, BeO -, BeCl, MgF, MgO -, and MgCl (class I); BF +, BCl +, AlF +, and AlCl + (class II); and BO, BN -, BS, BP -, AlO, AlN -, AlS, and AlP - (class III). Most radicals have small Δ g ∥ values (≈−100 ppm) and large negative Δ g ⊥ values (−800 to −8500 ppm), except for AlN - and AlP -, which have positive Δ g ⊥ values (1400 and 10 000 ppm) due to the quasi-degeneracy X 2 Σ + /1 2 Π i . The sum-over-states expansions for Δ g ⊥ are dominated in classes I and II by the coupling with 1 2 Π r, and in class III with both 1 2 Π i and 2 2 Π r . The 2 Π r (3σ→2π) state always contributes negatively, whereas 2 Π i (1π→3σ) contributes positively for most radicals but negatively for the boron series BO, BN -, BS, and BP - . Experimental g shifts, which are available for eight of the radicals studied here, are generally well reproduced by the Δ g values calculated at R e . However, for radicals having a very-low-lying 1 2 Π i state, such as AlN - and AlP -, our study suggests that future calculations should include vibrational averaging to describe the (unknown) experimental data correctly. Theoretical and experimental g ⊥ shifts are compared with those estimated from spin−rotation coupling constants γ, via Curl's equation.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".