Au<sub>21</sub> cage structures and their magic number tri‐cations
Bibliographic record
Abstract
Abstract We examine the stability and properties of three Au 21 cage structures, one with D 3 symmetry and denoted as Au 21 (D 3 ), which is novel, and the other two with C 2v symmetry. One, denoted as Au 21 (C 2v ‐1), has been previously reported but the other, denoted as Au 21 (C 2v ‐2), is novel. As reference Au 21 structures, we also examine a sheet isomer and a compact isomer, Au 21 (C s ‐Tetra), formed by adsorbing an Au atom on Au 20 (T d ). For all structures, we consider charge ranging from −1 to +4. For the Au 21 cage structures, a primary property of interest is their spherical aromaticity, as measured by their nucleus independent chemical shift. Our focus is on charge +3 since each gold atom is assumed to contribute one (6s) valence electron, and 18 is a magic number for shell closing. We find that, although Au 21 (D 3 ) +3 has the largest aromaticity, it is not the most stable cage species. Surprisingly, Au 21 (C 2v ‐2), which is not even stable as a neutral cage species, is the most stable tri‐cation cage species. We also examine the stability of (neutral) Au 21 X n cage structures relative to Au 21 X n structures derived from Au 21 (C s ‐Tetra) (with X = F, Cl, Br, I and n = 1, 3, 5). We find that, although Au 21 F 3 derived from Au 21 (D 3 ) has the largest aromaticity, it is not the most stable Au 21 F 3 cage structure. Nonetheless, all cage structures are stabilized relative to Au 21 (C s ‐Tetra) and, remarkably, for the trichlorinated, tribrominated, and triiodineated clusters, at least one cage structure is more stable than its Au 21 (C s ‐Tetra) counterpart.
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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 | 0.000 | 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 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".