Large-scale electronic structure calculation theory and applications to nanostructure materials

We review our recently developed methods in large-scale electronic structure calculations. The calculation is based on the tight-binding formalism of the Hamiltonian. First, the mathematical foundation of Krylov subspace method is focused. The density matrix can be calculated exactly and the numerical accuracy can be monitored during the iterative calculation. The key technique of the shifted-COCG (conjugate orthogonal conjugate gradient) method, collinear residual and seed switching, is explained in details. Second, several applications to nanostructure of semiconductors and metals, fracture propagation and surface reconstruction and formation process of gold nanowire, are explained.