A deep learning framework to emulate density functional theory

Density functional theory(DFT)has been a critical component of computational materials research and discovery for decades.However,the computational cost of solving the central Kohn–Sham equation remains a major obstacle for dynamical studies of complex phenomena at-scale.Here,we propose an end-to-end machine learning(ML)model that emulates the essence of DFT by mapping the atomic structure of the system to its electronic charge density,followed by the prediction of other properties such as density of states,potential energy,atomic forces,and stress tensor,by using the atomic structure and charge density as input.Our deep learning model successfully bypasses the explicit solution of the Kohn-Sham equation with orders of magnitude speedup(linear scaling with system size with a small prefactor),while maintaining chemical accuracy.We demonstrate the capability of this ML-DFT concept for an extensive database of organic molecules,polymer chains,and polymer crystals.