Structural and electronic properties of 13-atom<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>4</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:math>transition-metal clusters
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Bibliographic record
Abstract
We performed global optimization and property calculations by density-functional theory for the series of $4d$ transition-metal clusters ${M}_{13}$, $M=\text{Y}\ensuremath{-}\text{Pd}$. Calculated Gibbs free energies suggest the coexistence of isomers, or spin states, other than the global minimum in all cases except maybe ${\text{Zr}}_{13}$ and ${\text{Pd}}_{13}$. The calculated infrared spectra of these isomers are typically very different. Calculated ionization energies and magnetic moments agree well with available experimental results but do not allow to assign the geometric structure. Analysis of relative isomer energies and their electronic density of states suggests that these clusters tend to follow a maximum hardness principle: the lowest energy states and geometric structures are often the ones with lowest density of states near the Fermi level and lowest spin magnetic moment. In going from left to right in the $4d$ series, the geometric structures evolve from icosahedral (Y, Zr), to distorted compact structures (Nb, Mo), to fcc or simple-cubic crystal fragments (Tc, Ru, Rh), and icosahedron again (Pd). We rationalize this trend on the basis of the increasingly localized nature of molecular orbitals in going from left to right and the importance of $d$-type orbital bonding in the middle of the series.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it