This logic can be extended for construction of higher-body interactions. Notably, pure component terms (and thus, parameters) for C and N interactions are confined to the first two terms of equations 7 and 8, and are non-interacting. Two-atom-type cross-interactions are contained in the remaining terms. This point is illustrated in Figure . For a C, H, O, and N ChIMES model, all terms for interactions between only C atoms and between only N atoms are contained in the orange C and N blocks, respectively, while all C/N crossinteraction terms are contained within the yellow CN block. Critically, this means parameters for a given block in the same column can be fit in parallel, completely independently of one another. For example, a ChIMES model containing up to four body interactions for a C/N system is comprised of two "building blocks" containing {C, CC, CCC, CCCC} and {N, NN, NNN, NNNN} parameters, and a CN cross-term building block containing {CN, CCN, CNN, CCCN, CCNN, CNNN}.