where for simplicity the Morse variables are indexed by a single integer. For extended molecules many of the internuclear distances are large and so the corresponding Morse variables and corresponding monomials are nearly zero and can be pruned, i.e., discarded from the basis. This observation is the major motivation for the fragment-basis PIPs approach we proposed for large molecules. We do note that the straightforward way to prune the PIPs basis is to start with the full basis and then remove polynomials that are small. Of course a definition of "small" needs to be given and it must apply across the range of all Morse variables then compared to a threshold. Another approach, which is described in detail elsewhere, is to rank order the polynomials in magnitude over that range of Morse variables. Then the user can determine a cutoff based on desired size of the basis. However, this approach requires having the full PIPs basis, and this could be prohibitive for large molecules. To circumvent this problem, we proposed and tested a fragmented-basis method to obtain a PIPs basis without the full basis. This test was done for 12-atom N -methyl acetamide, where a full PIPs basis was feasible and provided benchmark results. It was shown that the "conservative" choice of making the smallest number of fragments worked well. And of course there had to be substantial overlap of fragments. We will illustrate this in detail below for the present application. Then the final PIPs basis is just the union of these fragment bases. Finally, we stress that this approach is not the same as fragmenting the molecule and obtaining the energy as the union of energies of the fragments.