where E is the total ChIMES energy for a system of n a atoms, E i is the energy for a single atom, i, E ij , and E ijk are the energy for a cluster of two or three atoms (i.e., ij or ijk), respectively. This expansion can extend to arbitrary bodiedness, though all models produced to date contain a maximum of 4-body terms. Interactions between pairs of atoms are described through Chebyshev polynomial series that take as input interatomic pair distances, i.e., for a pair of two atoms ij: