Symmetries of many-body systems imply distance-dependent potentials - Utterson, J; Erban, R (American Physical Society, 2023)
Considering interatomic potential U(q) where q = [q1, q2, . . . , qN ] ∈ R 3N is a vector describing positions, qi ∈ R 3 , it is shown that U can be defined as a function of the interatomic distance variables rij = |qi − qj |, 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 rij , provided that N > 5, with the number of distance variables used scaling linearly with the number of atoms, N.