Reaction Barrier Prediction from Reactants & Products

What this research found

Finding a reaction's transition state is the expensive part of computing how fast it will go, so the question here was how much of the activation barrier can be inferred from the reactants and products alone. Each of 11,961 elementary gas-phase reactions was encoded as the difference between product and reactant substructure-count fingerprints — no transition-state geometry ever entered the model — and regressed onto the forward barrier. A random forest reached a held-out mean absolute error of 10.16 kcal/mol and placed 40.4% of reactions within 5 kcal/mol, well ahead of a thermodynamics-only Bell–Evans–Polanyi baseline at 16.32 kcal/mol.

• The selected random forest reached a test mean absolute error of 10.16 kcal/mol, a root-mean-square error of 14.57 kcal/mol and R² = 0.590 on 2393 held-out reactions, predicting 967 of them (40.4%) within 5 kcal/mol of the reference barrier.
• Structural information beats thermodynamics decisively. Against a Bell–Evans–Polanyi baseline that regresses barrier on reaction enthalpy alone, the fingerprint model cuts mean absolute error from 16.32 to 10.16 kcal/mol, raises R² from 0.233 to 0.590, and more than doubles the within-5 kcal/mol hit rate from 16.0% to 40.4%.
• The relationship is genuinely non-linear: both tree ensembles beat Ridge regression on identical features (15.35 kcal/mol), though even a linear read-out of the structural difference still edges out the enthalpy-only baseline.
• Practical accuracy across thresholds: 22.2% of reactions land within 2.5 kcal/mol, 40.4% within 5, 63.2% within 10, 76.5% within 15 and 85.4% within 20 kcal/mol, with a median absolute error of 6.91 kcal/mol against a mean of 10.16 — a right-skewed distribution dominated by a minority of large misses.
• The model is unbiased in the data-dense core (mean signed error −0.03 kcal/mol, predicted-versus-reference correlation 0.776) but cannot extrapolate: predictions span only 44.8 to 141.1 kcal/mol against a reference range of 19.9 to 192.3, so low barriers are over-predicted and high ones under-predicted. The worst single case is a 192.3 kcal/mol reaction predicted at 100.1.
• Reaction enthalpy alone is a weak signal on this chemically diverse set: barrier and enthalpy correlate at Pearson r = 0.464, which caps what any single global Bell–Evans–Polanyi line can achieve.

How it was done

The higher-accuracy ωB97X-D3/def2-TZVP subset of the Grambow–Pattanaik–Green reaction dataset supplied 11,961 elementary gas-phase reactions of small organic molecules with forward barriers averaging 83.4 kcal/mol (range 10.7 to 204.7). Every molecule was encoded as a 2048-bit Morgan count fingerprint of radius 2, with the components of multi-fragment sides summed, and the reaction represented as the signed difference between product and reactant vectors so that positive entries mark substructures created and negative entries substructures destroyed. Counts rather than binary bits were used deliberately, since a barrier depends on how many bonds of a given type change. Featurization succeeded for all reactions, giving roughly 23 non-zero difference entries each. After an 80/20 split, Ridge regression, a random forest and histogram-based gradient boosting were tuned by five-fold cross-validation, and the best model was scored once on the untouched test set alongside a least-squares Bell–Evans–Polanyi baseline. Errors were then stratified by reference barrier height.

Data sources

• Grambow, Pattanaik & Green, Scientific Data 7:137 (2020), Zenodo record 3715478 — ωB97X-D3/def2-TZVP subset, 11,961 elementary reactions with atom-mapped reactants, products and barriers
• Morgan count fingerprints via RDKit 2026.03; reaction difference fingerprint construction after Schneider et al. (2015)
• scikit-learn for the random forest, gradient boosting, Ridge baseline and cross-validation