Generalizing deep learning electronic structure calculation to the plane-wave basis

Deep neural networks capable of representing the density functional theory (DFT) Hamiltonian as a function of material structure hold great promise for revolutionizing future electronic structure calculations. However, a notable limitation of previous neural networks is their compatibility solely with the atomic-orbital (AO) basis, excluding the widely used plane-wave (PW) basis. Here we overcome this critical limitation by proposing an accurate and efficient real-space reconstruction method for directly computing AO Hamiltonian matrices from PW DFT results. The reconstruction method is orders of magnitude faster than traditional projection-based methods to convert PW results to the AO basis, and the reconstructed Hamiltonian matrices can faithfully reproduce the PW electronic structure, thus bridging the longstanding gap between the AO basis deep learning electronic structure approach and PW DFT. Advantages of the PW methods, such as high accuracy, high flexibility and wide applicability, thus can be all integrated into deep learning electronic structure methods without sacrificing these methods' inherent benefits. This allows for the construction of large-scale and high-fidelity training datasets with the help of PW DFT results towards the development of precise and broadly applicable deep learning electronic structure models. Deep learning electronic structure calculations are generalized from the atomic-orbital basis to the plane-wave basis, resulting in higher accuracy, improved transferability and the capability to utilize existing electronic structure big data.