As noted above, the fragmented basis does not manifestly describe the permutational symmetry with respect to the interchange of all C and H atoms. Specifically, this symmetry exchanges the coordinates between C1 and C14, C2 and C13, ..., C7 and C8, as well as between H15 and H44, H16 and H43, ..., H29 and H30. However, the F-PES can "learn" this symmetry from the dataset. To examine this, we took 2,000 geometries at random from the data set, changed the geometries by replacing the order in the xyz data with the interchanged order. We then calculated the energies for both the original and interchanged structures and compared them, as shown as a correlation plot in Figure SI-6. There is an excellent correlation despite the fact that the interchanged structures were not included in the original data set. The eRMSE is 282 cm -1 , the MAE is 129 cm -1 /bohr, and the R 2 coefficient is 0.999112. The reason that the correlation is so good appears to be due to the fact that the data set is so large. While exact interchange symmetry is not a feature of the structures in the data set, enough similar structures are included so that the fit basically maintains this symmetry.