A symmetry-preserving and transferable representation for learning the Kohn-Sham density matrix

The Kohn-Sham (KS) density matrix is one of the most essential properties in KS density functional theory (DFT), from which many other physical properties of interest can be derived. In this work, we present a parameterized representation for learning the mapping from a molecular configuration to its corresponding density matrix using the Atomic Cluster Expansion (ACE) framework, which preserves the physical symmetries of the mapping, including isometric equivariance and Grassmannianity. Trained on several typical molecules, the proposed representation is shown to be systematically improvable with the increase of the model parameters and is transferable to molecules that are not part of and even more complex than those in the training set. The models generated by the proposed approach are illustrated as being able to generate reasonable predictions of the density matrix to either accelerate the DFT calculations or to provide approximations to some properties of the molecules.