Computing vibrational energy levels of CH4 with a Smolyak collocation method
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Bibliographic record
Abstract
In this paper, we demonstrate that it is possible to apply collocation to compute vibrational energy levels of a five-atom molecule using an exact kinetic energy operator (with cross terms and coordinate-dependent coefficients). This is made possible by using (1) a pruned basis of products of univariate functions; (2) a Smolyak grid made from nested sequences of grids for each coordinate; (3) a collocation method that obviates the need to solve a generalized eigenvalue problem; (4) an efficient sequential transformation between the (nondirect product) grid and the (nondirect product) basis representations; and (5) hierarchical univariate functions that make it possible to avoid storing large intermediate vectors. The accuracy of the method is confirmed by computing 500 vibrational energy levels of methane.
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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 | 0.001 | 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 it