Fig. 1. The NewtonNet model and its performance on the ANI-1 and T1x data sets.

a The equivariant message-passing neural network designed for 3D molecular graphs with nodes {Z_i} and edges {R_ij} to predict molecular energies E and atomic forces F_i³². In this work, we further differentiate the network to derive H_ij for TS optimization tasks. b The distribution of atomic pairwise distances, R, relative to equilibrium bond distances, R₀, among datasets we used for training, where the T1x data set provides more data in the TS region, and further augmented with the ANI-1x data to add data corresponding to bond compression. The predicted (c) potential energies and (d) forces along the reaction coordinate for an unseen reaction for the pre-trained and fine-tuned model. A comprehensive statistical analysis of energy and force prediction errors along the reaction coordinates for 1248 unseen test reactions is summarized in Supplementary Fig. S1 for the pre-trained and fine-tuned models. Details of the training protocols are described in Methods and Supplementary Fig. S2 and S3. TS: transition state. Source data for this figure are provided with this paper.