Geometric and electronic structure of closed-shell bimetallic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:mrow></mml:math>clusters
Bibliographic record
Abstract
We studied, by density functional theory, a group of 16 clusters having the general formula ${A}_{4}{B}_{12}$, where ``$A$'' is divalent and ``$B$'' monovalent. Global optimization was done in each case followed by calculation of energy second derivatives and vibrational frequencies. The clusters have large highest occupied molecular orbital-lowest unoccupied molecular orbital gaps ranging from $1.2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and other features suggesting special stability. This is consistent with the jellium model and 20 electron count. A ${T}_{d}$ symmetry cage structure is found as the putative global minimum for ${\mathrm{Mg}}_{4}{\mathrm{Ag}}_{12}$, ${\mathrm{Mg}}_{4}{\mathrm{Au}}_{12}$, ${\mathrm{Cd}}_{4}{\mathrm{Au}}_{12}$, and ${\mathrm{Ca}}_{4}{\mathrm{Na}}_{12}$. It is also a low energy isomer (less than $0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ above the global minimum) for ${\mathrm{Zn}}_{4}{\mathrm{Au}}_{12}$, ${\mathrm{Be}}_{4}{\mathrm{Au}}_{12}$, and ${\mathrm{Be}}_{4}{\mathrm{Ag}}_{12}$. The ${T}_{d}$ cage structure has ions arranged in shells, with charge $+8$ and $+12$, that match two jellium electronic shell closings, $(1{s}^{2},1{p}^{6})$ and $(1{d}^{10},2{s}^{2})$ with 8 and 12 electrons, respectively. The importance of symmetry and ion shells is shown by the relative stability of homotops of ${\mathrm{Mg}}_{4}{\mathrm{Ag}}_{12}$.
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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 | 0.004 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.307 | 0.003 |
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; both teacher heads agree on what is shown here.
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".