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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".