How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?

Kohn-Sham regularizer (KSR) is a differentiable machine learning approachtofinding the exchange-correlation functional in Kohn-Sham density functional theory thatworks for strongly correlated systems. Here we test KSR for a weak correlation. We proposespin-adapted KSR (sKSR) with trainable local, semilocal, and nonlocal approximations foundby minimizing density and total energy loss. We assess the atoms-to-molecules generalizabilityby training on one-dimensional (1D) H, He, Li, Be, and Be2+and testing on 1D hydrogenchains, LiH, BeH2, and helium hydride complexes. The generalization error from oursemilocal approximation is comparable to other differentiable approaches, but our nonlocalfunctional outperforms any existing machine learning functionals, predicting ground-stateenergies of test systems with a mean absolute error of 2.7 mH.

Automated summary

The study tests the application of KSR in weakly correlated systems and introduces spin-adapted KSR with trainable local, semilocal, and nonlocal approximations. The results show that the generalization error of the semilocal approximation is comparable to other methods, while the nonlocal functional outperforms any existing machine learning functionals in predicting the ground-state energies of test systems.