e i e j ij is a transformed pair distance between atoms ij of element type e i e j , O 2B is the user-defined two-body order for the polynomial series, and c e i e j ↵ are the Chebyshev polynomial coefficients that comprise the fitting parameters of the model. Note that we use the "/" symbol to indicate that smoothing and penalty functions have been excluded from these equations for simplicity. Many-body interactions are treated as the product of interactions for constituent atom pairs. For example, a three-body interaction is given by: