Machine Learning Accurate Exchange and Correlation Functionals of the Electronic Density

Density Functional Theory (DFT) is the standard formalism to study the electronic structure of matter
at the atomic scale. The balance between accuracy and computational cost that
DFT-based simulations provide allows researchers to understand the structural and dynamical properties of increasingly large and complex systems at the quantum mechanical level.
In Kohn-Sham DFT, this balance depends on the choice of exchange and correlation functional, which only exists
in approximate form. Increasing the non-locality of this functional and climbing the figurative Jacob's ladder of DFT, one can systematically reduce the amount of approximation involved and thus approach the exact functional. Doing this, however, comes at the price of increased computational cost, and so, for extensive systems, the predominant methods of choice can still be found within the lower-rung approximations.
Here we propose a framework to create highly accurate density functionals by using supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to lift the accuracy of local and semilocal functionals to 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. We further demonstrate how a functional optimized on water can reproduce experimental results when used in molecular dynamics simulations. Finally, we discuss the effects that our method has on self-consistent electron densities by comparing these densities to benchmark coupled-cluster results.