where "S" is the operator that symmetrizes monomials. To implement the symmetrization all that is needed is the mapping of atom permutations to internuclear distances. This is straightforward to do as illustrated for A 3 molecules. Let 1, 2, 3 denote the initial arrangement of the three atoms. Consider the permutation 2, 3, 1. Initial internuclear distances r 12 , r 13 , r 23 map onto r 23 , r 21 , r 31 , which we re-write in normal order as r 23 , r 12 , r 13 . Thus, the monomial r a 12 r b 13 r c 14 maps onto r a 23 r b 12 r c 13 which can be re-written as the original monomial with permuted powers as r b 12 r c 13 r a 23 . Adding to these two monomials the four other ones corresponding to the four additional permutations gives a fully symmetrized sum of monomials.