Theoretical study of the structure of lithium clusters
Bibliographic record
Abstract
Lithium clusters Lin (n=5 to 20) were studied by Kohn–Sham theory with local spin density and gradient-corrected energy functionals. We used a Tabu Search algorithm for structure optimization. The lowest energy Lin isomers that we found fall in two categories: (i) the pentagonal bipyramid, icosahedron, and related structures which are typical of most pair potentials, and (ii) structures containing centered square antiprisms which are reminiscent of the bulk bcc structure and have two characteristic peaks in the pair distribution function, one near 2.60 Å and the other near 3.05 Å. Calculated isomer energies and vibrational frequencies suggest that, at room temperature, many cluster sizes should show liquidlike behavior or coexistence of multiple isomers. The number of unpaired electrons “M” as a function of cluster size “n” generally alternates between 0 (singlet) and 1 (doublet), but some cluster sizes display anomalous spin magnetic moments M(n); they are M(13)=5, M(16)=2, M(17)=3, and M(18)=2. The Li7, Li8, Li19, and Li20 clusters are particularly stable: they each have a very compact structure and a shape consistent with the ellipsoidal jellium model.
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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 | 0.001 | 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".