Deep-learning density functional theory Hamiltonian for efficient ab initio electronic-structure calculation

The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent DFT Hamiltonian (DeepH) of crystalline materials, aiming to bypass the computationally demanding self-consistent field iterations of DFT and substantially improve the efficiency of ab initio electronic-structure calculations. A general framework is proposed to deal with the large dimensionality and gauge (or rotation) covariance of DFT Hamiltonian matrix by virtue of locality and is realized by the message passing neural network for deep learning. High accuracy, high efficiency and good transferability of the DeepH method are generally demonstrated for various kinds of material systems and physical properties. The method provides a solution to the accuracy-efficiency dilemma of DFT and opens opportunities to explore large-scale material systems, as evidenced by a promising application to study twisted van der Waals materials.