where {p}, {p ′ }, and {p ′′ } are PIPs bases for the n th fragment, n = 1,2,3, {c}, {c ′ }, {c ′′ } are the corresponding linear coefficients, τ n represent the set of corresponding Morse variables, and m n indicate a set of monomials built from the Morse variables for fragment n. By choosing the atoms in each fragment judiciously, one can keep those Morse variables for atoms that are close to one another while neglecting those for atoms that are far apart.