Considering interatomic potential U(q) where q=[q1β,q2β,β¦,qNβ]βR3N is a
vector describing positions, qiββR3, it is shown that
U can be defined as a function of the interatomic distance variables rijβ=β£qiββqjββ£, 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 rijβ, provided that
N>5, with the number of distance variables used scaling linearly with the
number of atoms, N