Nonlocal Machine-Learned Density Functionals for Materials Chemistry

For many applications in materials chemistry, including semiconductor physics, battery chemistry, and heterogeneous catalysis, the reliability of computational studies is limited by the accuracy of density functional theory (DFT), specifically the exchange-correlation (XC) functional. This has motivated the use of machine learning (ML) to improve the accuracy of XC functionals. However, ML functionals have mostly not achieved widespread application, especially in materials chemistry, where good training data can be sparse. To overcome the limitations of existing models, we developed the "CIDER" framework for learning the XC energy. CIDER functionals use Gaussian process regression to tune model smoothness and account for training uncertainty, and the model inputs include nonlocal features that respect exact constraints on the XC energy. This combination of design choices yields data-efficient and transferable models. We also leverage Janak's theorem to directly train on DFT orbital energies, improving the description of band gaps and charge transfer processes. CIDER functionals are implemented in the CiderPress code package, which interfaces with the PySCF and GPAW codes to enable production-scale simulations in both atomic orbital and plane-wave basis sets. We demonstrate that CIDER functionals can accurately model complex systems including semiconductor point defects, localized polarons, and battery cathode materials using only a few hundred training data from isolated atoms, simple molecules, and bulk solids.