where "S" is the operator that symmetrizes monomials, and M is the maximum polynomial order. Our general software to perform this symmetrization and also to generate higher-order polynomials recursively has been described in detail. Also, a short video describing this software is available for the interested reader. This software has been applied to develop PESs for many molecules and complexes and most recently to the 21-atom aspirin molecule. To apply PIPs to even larger molecules, we proposed and tested a fragmentation scheme. However, the new method has not been applied to a molecule with more than 15 atoms. The remainder of this section is devoted to a description of the fragmented-basis approach to constructing PIPs and a new many-body method to construct a PIPs potential specifically for large molecules.