Fig. 2: Schematic structure of a 4G-HDNNP for a binary system.

For a binary system containing Na atoms of element a and Nb atoms of element b the total energy consists of a short-range energy Eshort, which is a sum of atomic energies Ei, and a long-range electrostatic energy Eelec computed from atomic charges Qi. The atomic charges are determined by a charge equilibration method using environment-dependent atomic electronegativies χi expressed by atomic neural networks (red). These charges are then used to calculate the electrostatic energy and in addition serve as non-local input for the short-range atomic neural networks (blue) yielding the Ei. The geometric atomic environments are described by atom-centered symmetry function vectors Gi, which depend on the Cartesian coordinates Ri of the atoms and serve as inputs for the atomic neural networks.