Density functional theory and global optimization study of Sn<i>m</i>Pb<i>n</i> clusters (7 ⩽ <i>m</i> + <i>n</i> ⩽ 12, 0 ⩽ <i>m</i>/(<i>m</i> + <i>n</i>) ⩽ 1)
Bibliographic record
Abstract
The global minima of the neutral binary Sn(m)Pb(n) atomic clusters, 7 ≤ m + n ≤ 12, of all the possible stoichiometric ratios have been found using tabu search in descriptor space and density functional theory. The effects of spin-orbit coupling on optimized geometries and energies are important. All of the binary clusters form substitution alloys. Apart from the 11-atom case, the pure clusters of the same size have the same ground state geometry. The relative energies of the isomers of a cluster depend on, in order of decreasing importance: the overall geometry; the specific sites occupied by the two atom types; and the degree of segregation. The total cohesive energy difference between the lowest energy homotops is typically on the order of 0.02 eV. The mixing/segregation trends are found to be very different depending on the size of the basis set. Calculations generally overestimate the dipole moments. The trends in calculated dipole moments agree with experiment for the lead-rich clusters, and to a lesser degree, the tin-rich clusters.
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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) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".