Δ(2) 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 Δ(2)-learning model is introduced that can predict high-level activation energies based on low-level critical-point geometries. The Δ(2) 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 Δ(2) 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 Δ(2) 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 Δ(2) 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 Δ(2) model approach proves to be an efficient strategy for accelerating chemical reaction characterization with minimal sacrifice in prediction accuracy.