Linear scaling algorithm for tight-binding molecular dynamics simulations

The linear scaling or O(N) methods, which exhibit linear scaling with respect to the size of system, are a powerful tool for theoretically treating a huge system containing many atoms. We present a new linear scaling algorithm for large-scale tight-binding molecular dynamics simulations based on the divide-and-conquer approach, in which a system is divided into subsystems and each subsystem is calculated separately. Different from the common realization of the divide-and-conquer approach, our proposed method avoids building the density matrix or electronic density and gives a new strategy to access the physical properties of a large system. We apply this method to the tungsten metallic system and show that this method very effectively yields the same results including the atomic structures, the melting point, the formation energy of defects, and the electronic properties as those obtained from the exact diagonalization of tight-binding Hamiltonian matrix of a whole system. This method has the advantages of linear scaling complexity, less memory consumption, and high parallel efficiency, which make it to be used for the large-scale simulations.