The Ehrenfest force topology: a physically intuitive approach for analyzing chemical interactions
Bibliographic record
Abstract
Modified ANO-RCC basis sets are used to determine twelve molecular graphs of the Ehrenfest force for H2, CH4, CH2O, CH3NO, C2H2, C2H4, C3H3NO, N4H4, H2O, (H2O)2, (H2O)4 and (H2O)6. The molecular graphs include all types of topological critical points and a mix of bonding types is chosen to include sigma-, π- and hydrogen-bonding. We then compare a wide range of point properties: charge density, trace of the Hessian, eigenvalues, ellipticity, stiffness, total local energy and the eigenvectors are calculated at the bond critical points (BCPs) and compared for the Ehrenfest, QTAIM and stress tensor schemes. QTAIM is found to be the only partitioning scheme that can differentiate between shared- and closed-shell chemical bond types. Only the results from the Ehrenfest force partitioning, however, are demonstrated to be physically intuitive. This is demonstrated for the water molecule, the water-dimer and the water clusters (H2O)4 and (H2O)6. In particular, both the stiffness and the trace of the Hessians of the appropriate quantities of the sigma-bond BCPs for the water clusters are found to depend on the quantum topology dimension of the molecular graph. The behavior of all the stress tensor point properties is found to be erratic. This is explained by the ambiguity in the theoretical definition of the stress tensor. As a complementary approach the Ehrenfest force provides a new indicator of the mixed chemical character of the hydrogen-bond BCP, which arises from the collinear donor sigma-bond donating a degree of covalent character to the hydrogen-bond. This indicator takes the form of the relative orientation of the shallowest direction of the Ehrenfest potential of the hydrogen-bond BCPs and the corresponding direction for the collinear sigma-bond BCP.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".