On the relationship between free energy difference calculations by thermodynamic integration and harmonic frequency analysis
Bibliographic record
Abstract
Harmonic frequency analysis (HFA), based on statistical mechanics, is a widely used and powerful tool for evaluating free energy changes between molecular states. It has, as such, been employed extensively to evaluate the free energy of reaction and activation for chemical processes. Alternatively, free energy differences can be calculated using thermodynamic integration (TI). In TI, the force on a constrained reaction coordinate is calculated, and this force from a to b is integrated to obtain the Helmholtz free energy change ΔA ab . Although HFA and TI clearly are related from a fundamental statistical mechanics point-of-view, the relationship is not immediately obvious when one considers the quite different procedures applied in the two methods. This article provides a detailed analysis and proof of the relation between HFA and TI.
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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 | 0.006 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.001 | 0.005 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".