Next, we comment briefly on the connection of the present MB-PIPs approach to earlier work using MB-approaches for molecular potentials. The earliest work for atomic solids, notably Si, dates back to the mid 1980s. For chemical reactions a MB approach was applied for three and four-atom systems, by Murrell and co-workers. Our early work with PIPs used a 2-b and then full-body decomposition for H 5 O + 2 , 72 and we also noted the formal decomposition of a full PIPs basis into 2-b, 3-b, etc. PIPs terms. More recent and relevant, many-body, atom-centered ML methods have appeared, mainly for materials applications. The atomic cluster expansion (ACE) uses an atom-centered expansion, where interactions are 2-b, 3-b, etc. The basis for these n-body terms are given in terms of internuclear distances and angles and overall are more complex than the PIPs bases we use here, which are just functions of the transformed internuclear distances (Morse variables).