Δ² machine learning for reaction property prediction

The emergence of Δ-learning models, whereby machine learning (ML) is used to predict a correction to a low-level energy calculation, provides a versatile route to accelerate high-level energy evaluations at a given geometry. However, Δ-learning models are inapplicable to reaction properties like heats of reaction and activation energies that require both a high-level geometry and energy evaluation. Here, a Δ²-learning model is introduced that can predict high-level activation energies based on low-level critical-point geometries. The Δ² model uses an atom-wise featurization typical of contemporary ML interatomic potentials (MLIPs) and is trained on a dataset of ∼167 000 reactions, using the GFN2-xTB energy and critical-point geometry as a low-level input and the B3LYP-D3/TZVP energy calculated at the B3LYP-D3/TZVP critical point as a high-level target. The excellent performance of the Δ² model on unseen reactions demonstrates the surprising ease with which the model implicitly learns the geometric deviations between the low-level and high-level geometries that condition the activation energy prediction. The transferability of the Δ² model is validated on several external testing sets where it shows near chemical accuracy, illustrating the benefits of combining ML models with readily available physical-based information from semi-empirical quantum chemistry calculations. Fine-tuning of the Δ² model on a small number of Gaussian-4 calculations produced a 35% accuracy improvement over DFT activation energy predictions while retaining xTB-level cost. The Δ² model approach proves to be an efficient strategy for accelerating chemical reaction characterization with minimal sacrifice in prediction accuracy.