These are about the number of atoms in aspirin, where a single PIPs was used. Clearly the sum of the number of atoms is almost twice the number of atoms in the molecule. This is a consequence of the overlapping basis, i.e., a number of Morse variables are in common in the three PIPs bases. (This can lead to duplication of PIPs in the final basis; however, these can be deleted using the software PESPIP. ) Some comments about the permutational symmetry of the F-PES and the MB-PES are worthwhile. The MB-PES is inherently fully permutationally symmetric. This should be clear by simply noting that the order of summation over the C and H atoms for each n-body term is arbitrary and so invariant with respect to permutation of indices. A reasonable question to ask is whether this complete permutational symmetry is needed, when in fact H and C atoms do not exchange, at least at the energies of our dataset. The answer is not straightforward for this highly atom-symmetric molecule. To see this, imagine a change in energy due to a small change in the bond distance between C14 and H44. If we were to instead perform a similar geometry change to the bond distance between C1 and H15, we should get the same change in energy. The permutational symmetry of the MB-PES ensures that this will be the case. However, the permutational symmetry of the F-PES is more nuanced. We know that the symmetry of the three H atoms in the two methyl groups is an essential symmetry, independent of the molecular configuration, as is the permutational symmetry of the pair of hydrogens on each carbon atom. Both of these symmetries are described in the F-PES. What is not explicitly described in the F-PES is the interchange symmetries of carbons; e.g., C1