Theoretical studies in the molecular Platonic solids: Pure and mixed carbon, nitrogen, phosphorus, and silicon tetrahedranes
Bibliographic record
Abstract
Calculations were conducted at the G4MP2 and G4 composite method levels of theory on the 35 potential carbon, nitrogen, silicon, and phosphorus tetrahedrane derivatives with the general form C~a~N~b~Si~c~P~d~H~(4-b-d)~ (where a+b+c+d=4). At both levels of theory, optimized electronic ground state neutral singlet gas phase (298.15 K, 1 atm) geometries were obtained for 24 of the 35 possible C/N/Si/P tetrahedrane derivatives. Corresponding enthalpies of formation were calculated using the atomization method. Triplet state neutral tetrahedron starting geometries for all compounds either resulted in cage opening or failed to converge. Only 9 cationic and 3 anionic forms converged to stable geometries that retained the tetrahedron cage and were absent imaginary frequencies, thereby allowing the calculation of adiabatic ionization energies and electron affinities.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".