Convergence of the many-body expansion of interaction potentials: From van der Waals to covalent and metallic systems
Bibliographic record
Abstract
The many-body expansion of the interaction potential between atoms and molecules is analyzed in detail for different types of interactions involving up to seven atoms. Elementary clusters of Ar, Na, Si, and, in particular, Au are studied, using first-principles wave-function- and density-functional-based methods to obtain the individual $n$-body contributions to the interaction energies. With increasing atom number the many-body expansion converges rapidly only for long-range weak interactions. Large oscillatory behavior is observed for other types of interactions. This is consistent with the fact that Au clusters up to a certain size prefer planar structures over the more compact three-dimensional Lennard-Jones-type structures. Several Au model potentials and semiempirical PM6 theory are investigated for their ability to reproduce the quantum results. We further investigate small water clusters as prototypes of hydrogen-bonded systems. Here, the many-body expansion converges rapidly, reflecting the localized nature of the hydrogen bond and justifying the use of two-body potentials to describe water-water interactions. The question of whether electron correlation contributions can be successfully modeled by a many-body interaction potential is also addressed.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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 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".