Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques

Abstract

We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent equations are solved on a heirarchy of grids of increasing resolution with a nonlinear Full Approximation Scheme, Full Multigrid algorithm. The self consistency is effected by updates of the Poisson equation and the exchange correlation potential at the end of each eigenfunction correction cycle. The algorithm leads to highly efficient solution of the equations, whereby the ground state electron distribution is obtained in only two or three self consistency iterations on the finest scale.

13 pages, 2 figures

References in corpus (3)

• Real-Space Adaptive-Coordinate Electronic Structure Calculations
• Application of A Distributed Nucleus Approximation In Grid Based Minimization of the Kohn-Sham Energy Functional
• A Real-Space Full Multigrid study of the fragmentation of Li11+ clusters

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• A novel multigrid method for electronic structure calculations
• Three real-space discretization techniques in electronic structure calculations
• A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules
• MIKA: a multigrid-based program package for electronic structure calculations