Ab initioelectronic-structure computations with the recursion method

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Abstract
An accurate and efficient algorithm for using the recursion method in ab initio electronic-structure calculations with nonorthogonal real-space basis sets is presented. The matrix representation of the Hamiltonian operator in a localized basis is shown to possess a sparse represention, and is constructed from the Hamiltonian and overlap matrices, but without the full inverse of the overlap matrix. A method for calculating the change in the charge density due to a point defect is described. The mathematical structure of the recursion method is used to show that some local physical quantities, which are related to integrals over the local density of states, converge exponentially with the size of the cluster that surrounds the region of interest. The computation of these local properties scales independently of the number of atoms in the solid. As an illustration, the recursion method is used to compute the band-structure component of the cohesive energy of MgO.