Hyperfine coupling constants, electron-spin g-factors and vertical spectra of the X<sup>2</sup>Σ<sup>+</sup>radicals BeH, MgH, CaH and BZ<sup>+</sup>, AlZ<sup>+</sup>, GaZ<sup>+</sup>(Z = H, Li, Na, K). A theoretical study
Bibliographic record
Abstract
Hyperfine coupling constants (hfcc), electron-spin g-factors, excitation energies (ΔE) and oscillator strengths (f-values) are calculated for the X2Σ+ (1σ22σ) radicals YH (Y = Be, Mg, Ca) and BZ+, AlZ+, GaZ+ (Z = H, Li, Na, K). Single reference ab initio and density functional theory methods are used for the hfcc's, and multireference configuration interaction wavefunctions for ΔE's, f-values and g-shifts. In XZ+ (X = B to Ga; Z = Li to K), the 2σ unpaired electron is 60–90% pσ(X), resulting in |A⊥| being one order of magnitude larger than |A‖|. The Δg⊥'s are relatively large for just 3 valence electrons, from −3300 to −6100 ppm for BZ+, −14 100 to −29 600 ppm for AlZ+, and −93 700 to −198 300 ppm for GaZ+. Such large Δg⊥(XZ+)'s relate to the strong coupling between the close-lying X2Σ+ and 12Π(2σ → 1π) states, which results from the splitting of the 2P(s2p) state of X due to its interaction with Z+. ESR spectra are not available for any of the XZ+'s. Calculation on the hydrides YH/XH+ reproduce well the experimental hfcc's and g factors, except for AlH+, which appears to be strongly perturbed in Ar matrices. Several transitions X2Σ+ → n2Σ+ and X2Σ+ → n2Π in XZ+ have large oscillator strengths, mainly caused by intramolecular charge-transfer processes X ↔ Z and atomic-like sg ↔ pu excitations.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.003 | 0.003 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.005 |
| 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; both teacher heads agree on what is shown here.
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".