Bond length and the electron density at the bond critical point: XX, ZZ, and CZ bonds (X = Li‐F, Z = Na‐Cl)
Bibliographic record
Abstract
The aim was to investigate the relationship between the bond length and the electron density at the bond critical point in homonuclear X--X and Z--Z and heteronuclear C--Z bonds (X = Li-F, Z = Na-Cl). The d,rho(c) pairs were obtained from 472 target bonds in DFT-optimized (B3LYP/6-311+G(d,p)) small molecular species. These species were selected arbitrarily but with a view to maximize the range widths WR for each atom combination. It was found that (i) with one clear exception, the d(A - A) means (A = X or Z) correlate linearly with the bond lengths d(A(2)) of the respective diatomic molecules; (ii) the d(A - A) means correlate parabolically with n, the formal number of valence electrons in the atoms of the bond; and (iii) with increasing sample size N the ratio WR(rho(c))/WR(d) appears to converge toward a representation f [WR(rho(c))/WR(d)](N-->infinity) characteristic of A. Detailed analysis of the d,rho(c) relationship has shown that by and large simple power regression accounts best for the DFT data. The regression coefficients of d = arho(c) (-b) and rho(c) = alphad(-beta) (b, beta > 0) vary with n in a seemingly irregular manner but one that is consistent with simple chemical notions. The d(A(2)) can be approximated in terms of multilinear MO electron occupancies.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".