Periodic trends in the geometric structures of 13-atom metal clusters
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Bibliographic record
Abstract
We report structures of ${X}_{13}$ clusters for 26 metal elements found by global optimization of the energy calculated by density functional theory. The icosahedron is unstable in 19 of those cases. There are at least 11 truly distinct structures among the 26 global minima. Differences in geometries between elements are understood as resulting from competing structural principles. Periodic trends in structure relate to atomic properties. Cagelike features correlate with hardness, $(\mathrm{IE}\ensuremath{-}\mathrm{EA})∕2$, and the number of 90\ifmmode^\circ\else\textdegree\fi{} bond angles correlates with $p$- and $d$-type orbital participations in localized bonds.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it