High-Dimensional Neural Network Potentials for Atomistic Simulations

High-dimensional neural network potentials, proposed by Behler and Parrinello in 2007, have become an established method to calculate potential energy surfaces with first-principles accuracy at a fraction of the computational costs. The method is general and can describe all types of chemical interactions (e.g., covalent, metallic, hydrogen bonding, and dispersion) for the entire periodic table, including chemical reactions, in which bonds break or form. Typically, many-body atom-centered symmetry functions, which incorporate the translational, rotational, and permutational invariances of the potential energy surface exactly, are used as descriptors for the atomic environments. This chapter describes how such symmetry functions and high-dimensional neural network potentials are constructed and validated.