Truhlar and co-workers suggested a simple solution to this issue, namely to just eliminate these polynomials. This is done in that group's software PIPFIT which is limited to 3 and 4-atom systems. This is what we term "purifying" and the resulting basis is thus "pruned" in size as well. Doing this for large PIP bases that are recursively obtained is non-trivial; however this achieved with Mathematica scripts as described in detail in ref. 32.