Transferable equivariant graph neural networks for the Hamiltonians of molecules and solids

This work presents an E(3) equivariant graph neural network called HamGNN, which can fit the electronic Hamiltonian matrix of molecules and solids by a complete data-driven method. Unlike invariant models that achieve equivariance approximately through data augmentation, HamGNN employs E(3) equivariant convolutions to construct the Hamiltonian matrix, ensuring strict adherence to all equivariant constraints inherent in the physical system. In contrast to previous models with limited transferability, HamGNN demonstrates exceptional accuracy on various datasets, including QM9 molecular datasets, carbon allotropes, silicon allotropes, SiO2 isomers, and BixSey compounds. The trained HamGNN models exhibit accurate predictions of electronic structures for large crystals beyond the training set, including the Moiré twisted bilayer MoS2 and silicon supercells with dislocation defects, showcasing remarkable transferability and generalization capabilities. The HamGNN model, trained on small systems, can serve as an efficient alternative to density functional theory (DFT) for accurately computing the electronic structures of large systems.