In principle (and indeed in practice), Eq. 9 can be used to represent the potential of a covalently bonded molecule, where the "monomers" are atoms. These interactions are enumerated for all atoms in the molecule. For an n-body interaction among N atoms there are a total of ( N n ) interactions. To limit the number of interactions, physical range cutoffs are used for each n-body interaction and details can be found in reference 62 which reports our first application to the 44-atom alkane C 14 H 30 . In this example (and also for other twoelement molecules, clusters, materials, etc.,) there are three types of 2-b interactions, i.e., CC, HH, and CH interactions, four types of 3-b and five types of 4-b interactions. (We do not consider 5-b interactions.) For each interaction beyond 2-b, an appropriate PIP basis is used and there are fewer of these than the types of interactions. To see this, consider the 3-b CCC and HHH interactions. While these are different, the PIP basis is the same, namely the basis for A 3 but the corresponding sets of linear coefficients are different. To be specific, consider V 3-b ; it is given by This approach, as well as a fragmented basis, has been used recently to obtain a MB-PIP potential for C 14 H 30 . Full details of the PIP bases are given in ref. 62 along with details of extensive dataset of DFT energies using for the fitting. This is the largest molecule we have considered using the PIP approach. Properties related to the flexibilty and the vibrational power spectrum of this molecule were reported in ref. 63. Figure is based on a table in ref.