Empirical Determination of the Harmonic Force Constants in Benzene. 3. The Harmonic Frequencies
Bibliographic record
Abstract
The aim of this work is to present a full set of 34 empirically determined harmonic force constants F i,k for benzene (in symmetrized Whiffen's coordinates), as well as the corresponding set of 20 harmonic normal mode (NM) frequencies for all four D 6 h isotopomers: C 6 H 6, C 6 D 6, 13 C 6 H 6, 13 C 6 D 6 . The reliability of the obtained harmonic force constant values is reinforced by their ability to reproduce satisfactorily the experimentally measured fundamental vibrational frequencies of the four D 6 h benzene isotopomers. A specific combined LM (local mode)/SM (symmetrized modes) complex symmetrized nonperturbative vibrational model, developed in our previous work, has been employed for calculations on the vibrational energy levels in benzene, using the harmonic force constants F i,k and a few diagonal anharmonic parameters, as input data. A set of local (valence) harmonic force constants has also been derived from the empirically determined symmetrized force constants F i,k, and their physical meaning was discussed. The set of 20 harmonic NM frequencies ω k for all four D 6 h benzene isotopomers, calculated in the present work using the empirically determined set of F i,k values, have been analyzed and compared to previous empirical and ab initio determinations by other authors.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".