The vibrational spectra of carbon dioxide and nitrous oxide: A Lie algebraic study
Bibliographic record
Abstract
The infrared vibrational levels of nitrous oxide (N2O) and carbon dioxide (CO2) are studied in the framework of Lie algebra. The aim of this work is to compare the frequency obtained in two algebraic models: “the vibron model” and “the mean field approximation of the vibron model”. To compare the two models we choose two triatomic molecules: CO2 of symmetry type D∞h and N2O of symmetry type C∞v. To construct the energy levels in the vibron model, the vibron numbers N for the two molecules are estimated from the harmonic frequency and the anharmonicity constant. After the proper estimation of N, the algebraic interaction parameters for both the molecules are evaluated against a least square fit with the experimental values using MATLAB R2015. Using the algebraic interaction parameters, the vibrational frequencies for the two molecules are calculated. Because CO2 is a linear symmetric triatomic molecule, the higher vibrational levels are largely affected by the mode mixing due to accidental degeneracy. The accidental degeneracy is studied introducing the Majorana and Fermi interaction parameters and the rms deviations are observed. The effects of accidental degeneracy for each of the molecules are not equal. In the second part of this report, the harmonic frequencies of CO2 and N2O are calculated using the mean field approximation. It is found that the results show good agreement.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".