Machine Learning Accurate Exchange-Correlation Potentials for Reducing Delocalization Error in Density Functional Theory.

We propose a machine learning approach to generate accurate exchange-correlation potentials that reduce delocalization errors in density functional theory. By solving the Kohn-Sham equations using a deep neural network, electron densities and molecular properties can be calculated self-consistently. We demonstrate that for stretched molecular systems, where restricted calculations are employed to ensure the spin symmetry and density-driven delocalization errors become dominant, both traditional functionals and recent machine-learned functionals fail dramatically, leading to unphysical electronic charge distributions and electric dipole moments that diverge. Our trained functional, however, accurately captures the correct dissociation limit, providing electron densities, electric dipole moments, and atomic forces in excellent agreement with the reference CCSD data. By addressing delocalization errors from electron density to energy gradient calculations, our approach proves to be a potential tool for predicting molecular properties across a broad range of chemical species.