Classical and Mexican hat-type potential energy curve for the hydrogen molecule from a confined Kratzer oscillator
Bibliographic record
Abstract
We review harmonic oscillator theory for closed, stable quantum systems. The H 2 potential energy curve (PEC) of Mexican hat-type, calculated with a confined Kratzer oscillator, is better than the Rydberg–Klein–Rees (RKR) H 2 PEC. Compared with QM, the theory of chemical bonding is simplified, since a confined Kratzer oscillator can also lead to the long sought for universal function, once called the Holy Grail of Molecular Spectroscopy. This is validated by reducing PECs for different bonds H 2 , HF, I 2 , N 2 and O 2 to a single one. The equal probability for H 2 , originating either from [Formula: see text] or [Formula: see text], is quantified with a Gauss probability density function. At the Bohr scale, a confined harmonic oscillator behaves properly at the extremes of bound two-nucleon quantum systems.
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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 | 0.000 | 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) | 0.000 | 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; a candidate call from one teacher head, 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".