Approximate non-relativistic energy expression and the rotational–vibrational constants of the Tietz–Hua potential: a semiclassical approach
Bibliographic record
Abstract
The low- and high-lying rovibrational energy levels of the Schrodinger equation with the molecular Tietz–Hua potential are obtained via the Wentzel–Kramers–Brilluoin (WKB) quantization approach. The Pekeris-type approximation scheme is applied to deal with the orbital centrifugal term of the effective potential function. The obtained energy spectra and the rotational–vibrational (rovibrational) coefficients for [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] diatomic molecules were compared with the ones obtained by other analytical methods and available experimental data in the literature. The results revealed that the accuracy of the energy spectra for the high-lying rovibrational quantum states may depend on the rotational-vibrational constants.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".