An Efficient Deep Learning Scheme To Predict the Electronic Structure of Materials and Molecules: The Example of Graphene-Derived Allotropes

Computations based on density functional theory (DFT) are transforming various aspects of materials research and discovery. However, the effort required to solve the central equation of DFT, namely the Kohn–Sham equation, which remains a major obstacle for studying large systems with hundreds of atoms in a practical amount of time with routine computational resources. Here, we propose a deep learning architecture that systematically learns the input–output behavior of the Kohn–Sham equation and predicts the electronic density of states, a primary output of DFT calculations, with unprecedented speed and chemical accuracy. The algorithm also adapts and progressively improves in predictive power and versatility as it is exposed to new diverse atomic configurations. We demonstrate this capability for a diverse set of carbon allotropes spanning a large configurational and phase space. The electronic density of states, along with the electronic charge density, may be used downstream to predict a variety of materials properties, bypassing the Kohn–Sham equation, leading to an ultrafast and high-fidelity DFT emulator.