where E BS corresponds to the band structure energy, E Coul is the charge fluctuation term, and E rep is the repulsive energy. E BS is calculated as a sum over occupied electronic states from the DFTB Hamiltonian. In practice, DFTB Hamiltonian matrix elements are computed from pre-tabulated Slater-Koster tables derived from reference calculations with a minimal basis set. The repulsive energy, E rep , corresponds to ion-ion repulsions, as well as Hartree and exchange-correlation double counting terms. This term can be expressed as an empirical function where parameters are fit to reproduce high-level quantum or experimental reference data. A pairwise potential energy function is often used for the repulsive energy term, though many-body interaction terms are required in some cases. DFTB is approximately three orders of magnitude more efficient than DFT calculations and exhibits O(N 3 ) scaling.