where n a is the number of atoms in the system. The atomic energies E i are constants used to match energies from reference data, and two-body (pairwise) energies are expressed as linear combinations of Chebyshev polynomials of the first kind. Higher-bodied interactions are determined through products of a cluster's constituent pair-wise polynomials. ChIMES parameters are determined by fitting to the difference between the reference energies and atomic forces and those computed from DFTB alone using the following objective function: