Transferable E(3) equivariant parameterization for Hamiltonian of molecules and solids

Machine learning, especially deep learning, can build a direct mapping from structure to properties with its huge parameter space, making it possible to perform high-throughput screening for the desired properties of materials. However, since the electronic Hamiltonian transforms non-trivially under rotation operations, it is challenging to accurately predict the electronic Hamiltonian while strictly satisfying this constraint. There is currently a lack of transferable machine learning models that can bypass the computationally demanding density functional theory (DFT) to obtain the ab initio Hamiltonian of molecules and materials by complete data-driven methods. In this work, we point out the necessity of explicitly considering the parity symmetry of the electronic Hamiltonian in addition to rotational equivariance. We propose a parameterized Hamiltonian that strictly satisfies rotational equivariance and parity symmetry simultaneously, based on which we develop an E(3) equivariant neural network called HamNet to predict the ab initio tight-binding Hamiltonian of various molecules and solids. The tests show that this model has similar transferability to that of machine learning potentials and can be applied to a class of materials with different configurations using the same set of trained network weights. The proposed framework provides a general transferable model for accelerating electronic structure calculations.