Phys. Rev. B 73, 165108 (2006) [9 pages]Linear algebraic calculation of the Green’s function for large-scale electronic structure theoryReceived 23 March 2005; revised 14 December 2005; published 7 April 2006 A linear algebraic method named the shifted conjugate-orthogonal conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green’s function and the density matrix without calculating eigenstates. The problem is reduced to independent linear equations at many energy points and the calculation is actually carried out only for a single energy point. The method is robust against the round-off error and the calculation can reach the machine accuracy. With the observation of residual vectors, the accuracy can be controlled, microscopically, independently for each element of the Green’s function, and dynamically, at each step in dynamical simulations. The method is applied to both a semiconductor and a metal. © 2006 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevB.73.165108
DOI:
10.1103/PhysRevB.73.165108
PACS:
71.15.−m, 71.15.Nc, 71.15.Pd
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