Abstract
Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, attaining general purpose chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functional by using the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN)–based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies and densities. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA on various thermochemistry datasets. These results underscore the promise of using the XC potential in modeling XC functionals and can pave the way for systematic learning of increasingly accurate XC functionals.
*We acknowledge the support of Department of Energy, Office of Science, through grant no. DE-SC0022241, under the auspices of which this study is conducted. B.K. and V.G. also acknowledge the support from AFOSR grant FA9550-21-1-0302 that supported development of certain aspects of inverse DFT framework for degenerate problems used in this study. This study used resources of the NERSC Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under contract no. DE-AC02-05CH11231. This study also used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725, via ASCR Leadership Computing Challenge (ALCC) award.
