O(N) Krylov-subspace method for large-scale ab initio electronic structure calculations

An efficient and robust $O(N)$ method is presented for fully self-consistent large-scale ab initio electronic structure calculations. Detailed short range and effective long range contributions to the electronic structure are taken into account by solving an embedded cluster defined in a Krylov subspace, which provides rapid convergent results for not only insulators but also metals. As illustrations of the capability of the method, we present three large-scale calculations based on the density functional theory: (i) calculation of full wave function of DNA, (ii) interaction between a carbon nanotube and metal surface, and (iii) geometry optimization of a boron doped diamond, which clearly show that the method is a promising approach for realization of large-scale ab initio calculations for a wide variety of materials including metals.