Revisiting the Maximum Hardness Principle: A Quantitative Analysis on Reaction Datasets
Bibliographic record
Abstract
Chemical hardness is one of the fundamental concepts in chemical reactivity theory, rigorously defined within the framework of Conceptual Density Functional Theory (CDFT). The associated maximum hardness principle (MHP), which postulates that a favorable direction of reaction is toward the state of maximum hardness, has been widely applied as a guiding rule to govern the direction of chemical reactions. However, several studies have questioned its validity. In this work, we investigated the quantitative applicability of the MHP using two reaction datasets, viz, a dipolar cycloaddition dataset of 5269 reaction profiles and the more comprehensive BH9 dataset of 449 reactions. We adopted different approximations to compute the hardness, including Kohn-Sham orbital based frontier molecular orbital (FMO) and the finite difference approximation (FDA). The effect of using different definitions to compute the average hardness of bimolecular reactions is analyzed on the validity of MHP. Our analysis revealed dependence of hardness values on the level of theory, definitions and approximations used which should be kept in mind before criticizing the MHP. Among 5269 cycloaddition reactions, approximately 80% of the reactions are found to obey the MHP. For BH9 dataset, MHP is found to better supported for unimolecular reactions, while remaining strongly dependent on the definition used to compute the average hardness for bimolecular reactions. Reactions in which the individual hardness of the reactants differs significantly are more likely to disobey MHP. Nonetheless, since these electronic structure principles are qualitative in nature, their validity cannot be expected to be universal.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.000 | 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".