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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".