Tracing the minimum-energy path on the free-energy surface
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Bibliographic record
Abstract
The free-energy profile of a reaction can be estimated in a molecular-dynamics approach by imposing a mechanical constraint along a reaction coordinate (RC). Many recent studies have shown that the temperature can greatly influence the path followed by the reactants. Here, we propose a practical way to construct the minimum-energy path directly on the free-energy surface at a given temperature. First, we follow the blue-moon ensemble method to derive the expression of the free-energy gradient for a given RC. These derivatives are then used to find the actual minimum-energy reaction path at finite temperature, in a way similar to the intrinsic reaction path of Fukui on the potential-energy surface. [K. Fukui, J. Phys. Chem. 74, 4161 (1970)]. Once the path is known, one can calculate the free-energy profile using thermodynamic integration. We also show that the mass-metric correction cancels for many types of constraints, making the procedure easy to use. Finally, the minimum-free-energy path at 300 K for the addition of CCl2 to ethylene is compared with a path based on a simple one-dimensional reaction coordinate. A comparison is also given with the reaction path at 0 K.
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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 | 0.000 | 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 | 0.001 | 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 it