Considering interatomic potential $U({ \mathbf q})$ where ${ \mathbf q} = [{ \mathbf q}_1, { \mathbf q}_2, \dots, { \mathbf q}_N] \in { \mathbb R}^{ 3N}$ is a vector describing positions, $\mathbf{ q}_i \in { \mathbb R}^3$, it is shown that $U$ can be defined as a function of the interatomic distance variables $r_{ ij} = |{ \mathbf q}_i - { \mathbf q}_j |$, provided that the potential $U$ satisfies some symmetry assumptions. Moreover, the potential $U$ can be defined as a function of a proper subset of the distance variables $r_{ ij}$, provided that $N > 5$, with the number of distance variables used scaling linearly with the number of atoms, $N$.
Categories: physics.class-ph physics.chem-ph