Estimation of Hammett sigma constants of substituted benzenes through accurate density‐functional calculation of core‐electron binding energy shifts
Bibliographic record
Abstract
Abstract For substituted benzenes such as (p‐F‐C 6 H 4 ‐Z), Linderberg et al. 1 demonstrated the validity of an equation similar to: ΔCEBE ≈ κσ, where ΔCEBE is the difference in core‐electron binding energies (CEBEs) of the fluorinated carbon in p‐F‐C 6 H 4 ‐Z and that in FC 6 H 5 , the parameter κ is a function of the type of reaction, and σ is the Hammett substituent (σ) constant. In this work, CEBEs of ring carbon atoms for a series of para disubstituted molecules p‐F‐C 6 H 4 ‐Z were first calculated using Density Functional Theory (DFT) with the scheme Δ E KS (PW86‐PW91)/TZP+C rel //HF/6‐31G*. An average absolute deviation of 0.13 eV from experiment was obtained for the CEBEs. Then we performed a linear regression analysis in the form of Y = A+B*X for a plot of Hammett σ p constants against calculated shifts ΔCEBEs (in eV) for the fluorinated carbon. The results were: A = –0.08 and B = 1.01, with correlation coefficient R = 0.973, standard deviation = 0.12, and P < 0.0001. The intercept A of the fitted line, close to zero, shows that the Hammett σ p constant is proportional to the calculated ΔCEBEs. On the other hand, the slope B of the straight line gives an estimate of the parameter κ. Similar statistical correlations were obtained for the carbon atoms ortho and meta to the substituent Z. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".