Computing rovibrational levels of polyatomic molecules with polyspherical coordinates and a contracted basis built with a <i>K</i>-independent vibrational primitive basis
Bibliographic record
Abstract
To compute the rovibrational spectrum of a molecule undergoing large amplitude motion it is important to use geometrically defined internal coordinates. In this paper, we use polar-type coordinates and a contracted basis of products of vibrational wavefunctions and symmetric top functions: |v〉|JKM〉. To facilitate computing matrix elements of the kinetic energy operator obtained when the molecule-fixed axes are attached to two of the vectors used to define the coordinates, it is common to use vibrational basis functions that depend on K, the quantum number for the molecule-fixed z component of the angular momentum. In this paper, we show that it is possible to use a |v〉|JKM〉 basis and forgo the K-dependent primitive vibrational functions. Instead, we use a K-independent primitive basis that is an extension of the one employed in Mol. Phys. 110, 825, (2012) for triatomics. Using a K-independent primitive basis obviates the need to compute and store contracted vibrational bases for each K. First, we demonstrate that rovibrational levels of H2O2 computed with the primitive basis, and no contraction, are accurate. Second, using the contracted |v〉|JKM〉 basis we compute J > 0 levels of CH3D. In both cases, we compute rovibrational levels with J values higher than those of levels calculated heretofore and for lower J there is satisfying agreement with previous calculations using K-dependent vibrational basis functions.
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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".