Fig. 1: Schematic workflow and illustration of non-local nature in hybrid functionals.
From: A deep equivariant neural network approach for efficient hybrid density functional calculations
a Schematic workflow of the DeepH-hybrid method. Neural networks are used to learn the relationship between hybrid-functional Hamiltonian and material structure. The method applies ab initio calculations of small-size systems for training and makes inferences on large-size systems for predicting electronic structure and physical properties. b Non-local nature of the exact-exchange potential. Two non-overlapping atomic orbitals Ï•i and Ï•j with a finite cutoff radius RC can contribute non-zero hybrid-functional Hamiltonian matrix elements due to the presence of non-local potential \(v({{{\bf{r}}}},{{{{\bf{r}}}}}^{{\prime} })\). Other atomic orbitals Ï•k and Ï•l are involved in the non-local coupling.
