Part I: Calculating E(r)

For any arrangement of atoms, there is an associated energy. This mapping — configuration to energy — is the potential energy surface, and calculating it is the foundation of computational materials science. This part covers the potential energy surface itself and three approaches to calculating \(E(\mathbf{r})\): classical potentials, which are fast but limited by their functional form; density functional theory, which is transferable but computationally expensive; and machine-learned interatomic potentials, which learn from quantum mechanical data to approach first-principles accuracy at reduced cost. These methods differ in their tradeoffs, but any of them can be combined with the techniques covered in Parts II and III.