Interatomic potentials: achievements and challenges

Interatomic potentials approximate the potential energy of atoms as a function their coordinates. Their main application is effective simulation many-atom systems. Here, we review empirical interatomic designed to reproduce elastic properties, defect energies, bond breaking, formation, and even redox reactions. We discuss popular two-body potentials, embedded-atom models for metals, bond-order covalently bonded systems, polarizable including charge-transfer approaches ionic systems quantum-Drude oscillator mimicking higher-order many-body dispersion. Particular emphasis laid on question what constraints ensue from functional form potential, e.g., in way Cauchy relations tensor elements can be violated this entails ratio cohesive or why boiling melting temperature tends large describing metals but small short-ranged pair potentials. The meant pedagogical rather than encyclopedic. This highlight with forms sufficiently simple remain amenable analytical treatments. Our objective provide stimulus how existing advanced meaningfully combined extent scope simulations based