Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator. An Undergraduate Vibrational Spectroscopy Laboratory Exercise
Bibliographic record
Abstract
An undergraduate exercise in vibrational spectroscopy is described, involving the prediction of wavenumber positions for absorptions associated with stretching vibrational modes of common organic molecules. This is done by modeling the portion of the molecule undergoing the bulk of the normal mode motion with a pseudodiatomic molecule, for which the known solution to the quantum-mechanical harmonic oscillator is approximately valid. Student-generated stretching vibrational mode data are used to determine an effective single-bond force constant for stretching modes of any typical covalently bound molecule composed of C, H, O, and N. Double- and triple-bond stretching modes are treated as having a force constant equal to twice or three times the single-bond value. The effective single-bond force constant is then refined to obtain the best possible value for stretching modes of organic molecules, 556 N m -1 for our data set. The exercise demonstrates that, for a well-behaved class of molecules, the major causes for the variation in the position of infrared spectroscopic absorptions due to stretching modes are (i) changes in the mass of the nuclei involved and (ii) changes in the order of the bond. The basic approach to refining a model is illustrated as well.
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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 | 0.001 |
| 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 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".