A comparison of linear scaling tight-binding methods

Four linear scaling tight-binding methods (the density matrix method, bond order potentials, the global density of states method, and the Fermi operator expansion) are described and compared to show relative computational efficiency for a given accuracy. Various example systems are explored: an insulator (carbon in the diamond structure), a semiconductor (silicon), a transition metal (titanium) and a molecule (benzene). The density matrix method proves to be most efficient for systems with narrow features in their energy gaps, while recursion-based moments methods prove to be most efficient for metallic systems.