Bibliographic record
Abstract
This article reviews new methods for computing vibrational energy levels of small polyatomic molecules. The principal impediment to the calculation of energy levels is the size of the required basis set. If one uses a product basis the Hamiltonian matrix for a four-atom molecule is too large to store in core memory. We discuss iterative methods that enable one to use a product basis to compute energy levels (and spectra) without storing a Hamiltonian matrix. Despite the advantages of iterative methods it is not possible, using product basis functions, to calculate vibrational spectra of molecules with more than four atoms. A very recent method combining contracted basis functions and the Lanczos algorithm with which vibrational energy levels of methane have been computed is described. New ideas, based on exploiting preconditioning, for reducing the number of matrix-vector products required to converge energy levels of interest are also summarized.Key words: vibrational energy levels, kinetic energy operators, Lanczos algorithm, contracted basis functions, preconditioning.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.016 | 0.007 |
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 source (direct Gemma or distilled Codex), 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".