Recently, we proposed a way to directly fragment the PIP basis. This is done by partitioning the molecule into fragments, generating the PIP basis of each fragment and then making the the entire PIP basis as the union of these fragment bases. It is worth noting that this approach is not the same as the fragment approach to obtain the energy of large molecules, developed by several groups. Here we are generating a single PIP basis for fitting the energies (and gradients) of a large molecule. In this approach the "user" fragments a molecule in a completely arbitrary way such that ideally the fragments are isolated from each other. Clearly, by fragmenting a parent molecule into groups of smaller molecular moieties the basis for each smaller moiety can be calculated rapidly and then combined with those of other fragments to provide a compact and hopefully precise representation of the potential energy. To be specific, consider a 3-fragment scheme for 12-atom N -methyl acetamide for which the potential is given schematically by