Before we describe our recent work using PIPs for molecules with 12, 15, 21 atoms and beyond, we make some remarks about the flexibility in choosing the PIP basis. As noted in the flow chart above describing the MSA workflow, the user is asked to input the molecule symmetry. This is a string of numbers, i.e., lmn...which represents a molecule with the symbolic formula A l B m C n ... This indicates the permutational symmetry and associated atoms that are treated as identical. For the H 3 O - 2 example in the video mentioned above, the input is 32. This describes the full permutational symmetry for this molecule and the PIP basis generated (for the maximum total polynomial order indicated in the input) describes this full symmetry. For larger molecules, such as 15-atom acetylacetone, the full permutational symmetry may or may not be used and thus the PIP approach is flexible in this respect. While in principle a PIPs basis can be obtained for any size molecule, there are computational trade-offs that must be considered. In general, the PIP basis is smallest for the largest symmetry type (for a given total polynomial order). And the computational effort is generally the largest for this case. (The detailed dependence is complex and the interested reader is referred to literature. ) As the symmetry is reduced the basis size increases and in general the computational effort in MSA decreases. Also, and perhaps more important, is the concomitant number of linear coefficients to be optimized in the fitting of a given dataset. In our experience, a larger number of coefficients generally leads to more precise fitting. However, in order to avoid overfitting we always keep this number much less than the datasize. Also, we always include the "minimum" symmetry, for example three equivalent H atoms on each methyl group. So in practical applications some experimentation with the symmetry choice and the maximum polynomial order is done to determine a reasonable basis for a given datasize. Using a reduced permutational symmetry for the PIP basis has been used successfully for 12-atom N -methyl acetaminde, 45, 15-atom acetylacetone,, 15-atom tropolone and 21-atom aspirin, which we discuss in more detail below.