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Linear scaling Krylov subspace method for large scale {\it ab initio} electronic structure calculations of metals

An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the 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 convergence for not only insulators but also metals. As an illustration of the method, we present a large scale calculation based on density functional theory for a palladium cluster with a single iron impurity.