<i>K</i>-independent vibrational bases for systems with large amplitude motion
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
For J > 0 calculations it would be advantageous to have a vibrational basis independent of rotational quantum numbers, but which can be applied to molecules or systems with large amplitude motion. Several authors have explored the possibility of using as bend functions (m = 0) Legendre polynomials. Their most obvious disadvantage is the existence of infinite matrix elements. Their behaviour near the θ = 0 and π singularities will also be inappropriate for some wavefunctions. In this paper, we test and analyse several rotational-index-independent vibrational bases and compare them to the standard basis of associated Legendre polynomials, , where m depends on K, the quantum number for the molecule-fixed z component of the angular momentum. We find that for three-atom systems with wavefunctions having both significant amplitude at linearity and important Θ m=odd components a Legendre basis is poor, despite the repulsive singularity at linear geometries. Similar problems occur for systems with more than three atoms.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 it