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 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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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".