X2-GNN: A Physical Message Passing Neural Network with Natural Generalization Ability to Large and Complex Molecules

Neural network models excel in molecular property predictions but often struggle with generalizing from smaller to larger molecules due to increased structural diversity and complex interactions. To address this, we introduce an E(3) invariant (and equivariant capable) message passing graph neural network (GNN), namely, X2-GNN, that integrates physical insights via atomic orbital overlap integrals and core Hamiltonians. These features provide essential information about bond strength, electron delocalization, and many-body interactions, enhanced by an attention mechanism for improved learning efficiency. Benchmarked against mainstream GNNs on diverse data sets, X2-GNN trained solely on the QM9 data set (up to nine heavy atoms) effectively generalizes to larger molecules with tens of heavy atoms, achieving credible per-atom error rates. It also excels in potential energy surface modeling and accurately predicts the bond dissociation energy within subseconds. These results highlight X2-GNN's scalability and broad applicability, emphasizing the importance of integrating data-driven approaches with basic knowledge from electronic structure theory.