Here, k q,A and k tot are element-wise and global parameters, respectively, and n at is the number of atoms. Note that the sum of the local charges does not necessarily conserve the overall molecular charge. Instead, it aims to reproduce only the relative magnitude of atomic charges in a local environment. While this is a crude approximation, its local nature has the benefit that no artificial charge transfer can occur, which plagues more sophisticated electronegativity-based charge equilibration models. With q loc , the standard expressions for the atom-resolved second-and onsite third-order tight-binding define the matrix elements of H 1 * :