Injecting Domain Knowledge from Empirical Interatomic Potentials to Neural Networks for Predicting Material Properties

A.1 Periodic Boundary Conditions Under periodic boundary conditions (PBCs), the positions of atoms outside the simulation cell are obtained by generating periodic images of those within the cell through translations commensurate with its periodicity. This methodology is capable of modeling infinite systems because the interactions between atoms separated by more than a modest cutoff distance are very small and thus ignored when defining empirical models. This limited range of interaction gives rise to the concept of an atomic environment. The environment of a given atom consists of itself and all other atoms, including periodic images, that fall within a prescribed cutoff distance of it. The consequence of this locality is that an infinite system can be modeled exactly using a finite periodic cell so long as a sufficient number of periodic images surrounding it are explicitly accounted for. An example of PBCs for a two-dimensional square cell and a local atomic environment is illustrated in Figure 1.