Crystal binding (interatomic forces): Ionic bonding and crystals

We discuss in general terms the models that are appropriate for describing interatomic forces and performing atomistic simulations in ionic materials. In particular we show how the framework of density functional theory (DFT) and second-order perturbation theory provides a unified way of deriving ionic models, including the Born model and shell models, besides variable charge-transfer models, such as charge equilibration models, and the self-consistent tight-binding model. We also discuss progress in the direct numerical fitting of functions to calculated data, which has made significant progress in recent years with the development of machine learning interatomic potentials and other data-driven approaches.