A “modified Lennard-Jones oscillator” model for diatom potential functions
Bibliographic record
Abstract
A flexible new analytical representation for the internuclear potential energy of a diatomic molecule is proposed and tested. The new model may be thought of as a generalization of the prototypical Lennard-Jones (2n,n) function, with the form V(R)=De[1−(Re/R)ne−β(z)z]2, where z=(R−Re)/(R+Re) is a dimensionless radial distance variable which approaches 1 as R→∞. This form explicitly incorporates the theoretically predicted attractive inverse-power asymptotic behavior V(R)=D−Cn/Rn associated with most potential energy curves. This “modified Lennard-Jones” (MLJ) function is tested against other flexible forms for the potential energy by performing nonlinear least-squares fits both to known numerical potential curves and to spectroscopic line positions.
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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".