Kohn-Sham regularizer in the bond-dissociation limit

With standard exchange-correlation (XC) approximations, Kohn-Sham density functional theory (KS-DFT) fails to correctly describe the breaking of a chemical bond. A nonlocal machine-learned XC can provide a good description of such strongly correlated systems when carefully embedded with prior knowledge and trained on accurate results. By training on just two separations, the Kohn-Sham regularizer (KSR) with a nonlocal neural network approximation to the XC energy density is shown to reproduce the entire binding energy curve of one-dimensional H₂ with chemical accuracy [1]. We analyze the ingredients of this nonlocal approximation and assess the importance of including prior knowledge in constructing machine-learned functionals. We further evaluate the generalizability of the performance of KSR local, semilocal and nonlocal neural XC approximations for one-dimensional strongly correlated molecules with limited training. We also analyze the machine-learned XC potentials, especially for stretched heteronuclear diatomic molecules where the exact XC potential has a characteristic localized upshift in the region around the more electronegative atom.

1] Li et al. Kohn-Sham equations as regularizer: Building prior knowledge into machine-learned physics. Phys. Rev. Lett. 126, 036401 (2021).