Efficient real-space multigrid method and applications to clusters and defects in SiO2

Abstract

We present all efficient real-space multigrid for first-priniciples electronic structure calculations in the framework of the local-density-functional approximation and the generalized gradient approximation. The Laplacian and gradient operations are discretized on mesh in real space by using a higher-order finite difference method. The Poisson and Kohm-Sham equations are Solved by a multigrid method that uses different relaxations on several grid levels. Testing various systems. we find the convergence rates to be nearly independent of the number of real-space grids. For charged Si clusters. the real-space method using a nonperiodic boundary conditions gives exact total energies, as compared to plane-wave supercell calculations. The error caused by the use of supercell are enlarged as excess or deficit charges from neutral clusters increase. In bulk materials where periodic boundary conditions are employed, the Slater-Janak transition-state theorem is used to calculate the total energies of the charged defects. Including spin polarization effects, we extend the test of our real-space calculations to oxygen the test of, our real-space calculations to oxygen-related defects such as oxygen vacancies. oxygen interstitials and oxygen molecules in SiO2.