An electron-preceding perspective on the deformation of materials
Bibliographic record
Abstract
Elements of Bader's theory of atoms in molecules are combined with density-functional theory to provide an electron-preceding perspective on the deformation of materials. From this perspective, a network of atoms is changed by moving the bonds that connect them; the nuclei then follow. The electronic stress tensor is the key to understanding this process. Eigenvectors of the electronic stress tensor at critical points of the electron density provide insight into the "normal electronic modes" that accompany structural dynamics and rearrangements. Eigenvectors of the second-derivative matrix of the electron density emerge as effective approximations to the eigenvectors of the stress tensor; this makes it possible to apply our results to experimentally and computationally determined electron densities. To demonstrate the usefulness of our analysis, we show that (a) the low-frequency modes of ice Ic can be predicted from the eigenvectors of the second-derivative matrix and (b) the eigenvectors of the second-derivative matrix are associated with the direction of structural change during the pressure-induced phase transition from ice XI to a ferroelectric ice VIII-like structure. We conclude that the eigenvectors of the second-derivative matrix of the electron density are the key ingredient for constructing a dynamical theory of atoms in molecules.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.001 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".