Flexible transition state theory for a variable reaction coordinate: Derivation of canonical and microcanonical forms
Bibliographic record
Abstract
A completely general canonical and microcanonical (energy-resolved) flexible transition state theory (FTST) expression for the rate constant is derived for an arbitrary choice of reaction coordinate. The derivation is thorough and rigorous within the framework of FTST and replaces our previous treatments [Robertson et al., J. Chem. Phys. 103, 2917 (1995); Robertson et al., Faraday Discuss. Chem. Soc. 102, 65 (1995)] which implicitly involved some significant assumptions. The canonical rate expressions obtained here agree with our earlier results. The corresponding microcanonical results are new. The rate expressions apply to any definition of the separation distance between fragments in a barrierless recombination (or dissociation) that is held fixed during hindered rotations at the transition state, and to any combination of fragment structure (atom, linear top, nonlinear top). The minimization of the rate constant with respect to this definition can be regarded as optimizing the reaction coordinate within a canonical or microcanonical framework. The expression is analytic except for a configuration integral whose evaluation generally requires numerical integration over internal angles (from one to five depending on the fragment structures). The form of the integrand in this integral has important conceptual and computational implications. The primary component of the integrand is the determinant of the inverse G-matrix associated with the external rotations and the relative internal motion of the fragments.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".