For two-body potentials this gradient reduces, thanks to the symmetry with respect to i j in the potential form, to straightforward differentiation with respect to the interatomic distances r i j . However, for many-body potentials (three-body, four-body, etc.) the differentiation becomes considerably more complex since the potential may not be any longer symmetric with respect to i j exchange. In other words, also the energy of atoms k that are not direct neighbours of i can depend on the position r → → i because of angular and other many-body terms, and hence contribute to the gradient ∇ ∇ r → → k .