The Utility of Constraining Basis Function Indices When Using the Lanczos Algorithm to Calculate Vibrational Energy Levels
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
Direct product basis sets are frequently used to calculate vibrational energy levels of small polyatomic molecules. They have the important advantage of simplicity. However, they have the important disadvantage that a very large number of direct product functions is necessary to obtain converged energy levels. By using an iterative, rather than an explicit, method to calculate eigenvalues of the Hamiltonian matrix, it is possible to calculate energy levels despite the huge size of the direct product basis. Nonetheless, it is natural to attempt to reduce the size of the direct product basis by excluding functions that do not contribute to the wave functions associated with the energy levels of interest. In this paper we present a variational basis representation (VBR) example and a discrete variable representation (DVR) example demonstrating that it is possible to use the Lanczos method and exclude direct product basis functions by restricting basis function indices while maintaining the favorable n f +1 scaling relation for the cost of direct product basis matrix-vector products.
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