Tight-binding electronic-structure calculations and tight-binding molecular dynamics with localized orbitals

We describe in detail and extend our recent algorithm for tight-binding total-energy calculations and tight-binding molecular dynamics, which scales quadratically with the size of the system for small systems and linearly for big systems. It is intrinsically parallel and gives an excellent performance on parallel computers. The central quantity in this algorithm is the localized orbitals. We show in the context of various examples, that our localized-orbital algorithm is not only fast, but gives us also a better physical understanding than conventional extended orbitals and more flexibility in treating complicated geometries. The algorithm can also efficiently handle metallic systems and does not lead to unphysical distortions of the electronic density of states around the Fermi level.