Convolutional network learning of self-consistent electron density via grid-projected atomic fingerprints

The self-consistent field (SCF) generation of the three-dimensional (3D) electron density distribution (ρ) represents a fundamental aspect of density functional theory (DFT) and related first-principles calculations, and how one can shorten or bypass the SCF loop represents a critical question in electronic structure theory from both practical and fundamental standpoints. Herein, a machine learning strategy, DeepSCF, is presented in which the map between the SCF ρ and the initial guess density (ρ0) constructed by the summation of neutral atomic densities is learned using 3D convolutional neural networks (CNNs). High accuracy and transferability of DeepSCF are achieved by first encoding ρ0 on a 3D grid and then expanding the input features to include atomic fingerprints beyond ρ0. The prediction of the residual density (δρ) rather than ρ itself is targeted, and given that δρ is indicative of chemical bonding information, a dataset of small-sized organic molecules featuring diverse bonding characters is adopted. The fidelity of DeepSCF is finally enhanced by subjecting the atomic geometries of the dataset to random rotations and strains. The effectiveness of DeepSCF is demonstrated using a complex carbon nanotube-based DNA sequencer model. This work evidences that the nearsightedness in electronic structure can be optimally represented via the spatial locality in CNNs, offering insight into the success of various machine learning-based atomistic materials simulations.