A novel multigrid method for electronic structure calculations

Abstract

A general real-space multigrid algorithm for the self-consistent solution of the Kohn-Sham equations appearing in the state-of-the-art electronic-structure calculations is described. The most important part of the method is the multigrid solver for the Schroedinger equation. Our choice is the Rayleigh quotient multigrid method (RQMG), which applies directly to the minimization of the Rayleigh quotient on the finest level. Very coarse correction grids can be used, because there is no need to be able to represent the states on the coarse levels. The RQMG method is generalized for the simultaneous solution of all the states of the system using a penalty functional to keep the states orthogonal. The performance of the scheme is demonstrated by applying it in a few molecular and solid-state systems described by non-local norm-conserving pseudopotentials.

9 pages, 3 figures

References in corpus (6)

• Real-Space Mesh Techniques in Density Functional Theory
• Multiresolution analysis of electronic structure: semicardinal and wavelet bases
• Real-Space Adaptive-Coordinate Electronic Structure Calculations
• Large Scale Electronic Structure Calculations with Multigrid Acceleration
• Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques
• A Real-Space Full Multigrid study of the fragmentation of Li11+ clusters

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