Properties of atoms in molecules: Construction of one-density matrix from functional group densities
Bibliographic record
Abstract
The demonstrated transferability of functional groups defined as proper open systems within the theory of atoms in molecules is used to iteratively construct a one-electron density matrix P and its derived electron density distribution. The initial guess at the density used in the fitting procedure is obtained from the addition of the density distributions of groups defined in parent molecules by the maximal matching of their interatomic surfaces. The method thus takes advantage of the observation that the “zero-flux” boundary condition defining a proper open system maximizes the transferability of the density distribution of a given group between molecules, one that is accompanied by a paralleling transferability in all of its properties. The construction is subject to the constraints that P be idempotent and normalized. The method is applied to the construction of P for the molecules HCH2|CH2X, with X=CH3, NH2, OH, and F, where the vertical bar denotes the new C–C interatomic surface, the new zero-flux boundary. The densities for the groups HCH2| and |CH2X are defined in their dimer molecules, HCH2|CH2H and XCH2|CH2X.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.003 | 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".