Density-functional-theory study of 13-atom metal clusters<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mtext>Ta</mml:mtext><mml:mo>–</mml:mo><mml:mtext>Pt</mml:mtext></mml:mrow></mml:math>
Bibliographic record
Abstract
We report on the structures of six proposed global minima (GMs) of ${M}_{13}$ clusters ($M=\text{Ta}$, W, Re, Os, Ir, and Pt) and 62 isomers that are within roughly 1 eV of the GM. The GM and isomers were obtained after several global optimization runs using a first-principles (Perdew-Burke-Enzerhof exchange-correlation) method to evaluate the energy. The GM and lowest-energy isomers can be described qualitatively as amorphous and compact for Ta, W, and Pt; quasicrystalline for Re; and cubic-prismatic for Os and Ir. The icosahedron is more than 1 eV above the GM in all cases, except 0.56 eV for ${\text{Ta}}_{13}$. The ground-state electronic configuration of the atoms is essential to understand structural trends in the clusters. Elements with a nearly closed-shell ground-state atom (W and Pt) produce many more low-energy cluster isomers than elements with partially filled $d$ shells, and those isomers are generally compact and amorphous. Partially filled $d$ shells in Os and Ir lead to strong directional bonding and many $90\ifmmode^\circ\else\textdegree\fi{}$ angles between nearest neighbors. The predicted spin multiplicity of the GM is 2 $({\text{Ta}}_{13})$, 1 $({\text{W}}_{13})$, 6 $({\text{Re}}_{13})$, 5 $({\text{Os}}_{13})$, 4 $({\text{Ir}}_{13})$, and 3 $({\text{Pt}}_{13})$, and the spin multiplicity of all isomers within 0.5 eV of the GM is within $\ifmmode\pm\else\textpm\fi{}2$ of these values and is smaller than 6.
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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) | 0.003 | 0.006 |
| Meta-epidemiology (broad) | 0.002 | 0.007 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.004 | 0.005 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.006 | 0.006 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.102 | 0.008 |
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".