Machine Learning a Highly Accurate Exchange and Correlation Functional of the Electronic Density

Sebastian Dick and Marivi Fernandez-Serra, Nat Commun 11, 3509 (2020)

Density functional theory (DFT) is the standard formalism to study the electronic structure of matter at the atomic scale. In Kohn–Sham DFT simulations, the balance between accuracy and computational cost depends on the choice of exchange and correlation functional, which only exists in approximate form. Here, we propose a framework to create density functionals using supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to lift the accuracy of baseline functionals towards that provided by more accurate methods while maintaining their efficiency. We show that the functionals learn a meaningful representation of the physical information contained in the training data, making them transferable across systems. A NeuralXC functional optimized for water outperforms other methods characterizing bond breaking and excels when comparing against experimental results. This work demonstrates that NeuralXC is a first step towards the design of a universal, highly accurate functional valid for both molecules and solids.