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 ($\rho$) 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 from both practical and fundamental standpoints. Herein, a machine learning strategy DeepSCF is presented in which the map between the SCF $\rho$ and the initial guess density ($\rho_0$) 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 expanding the input features to include atomic fingerprints beyond $\rho_0$ and encoding them on a 3D grid. The prediction of the residual density ($\delta\rho$) rather than $\rho$ itself is targeted, and, since $\delta\rho$ corresponds to chemical bonding information, a dataset of small-sized organic molecules featuring diverse bonding characters is adopted. After enhancing the fidelity of the method by subjecting the atomic geometries in the dataset to random strains and rotations, the effectiveness of DeepSCF is finally demonstrated using a complex large carbon nanotube-based DNA sequencer model. This work evidences that the nearsightedness in electronic structures can be optimally represented via the local connectivity in CNNs.