Real-space grid implementation of the projector augmented wave method

2004/11/09 by Jens Jørgen Mortensen, J. J. Mortensen, L. B. Hansen +3 · 2,148 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Computer science #Density functional theory #Domain decomposition methods #Finite element method #Geometry #Grid #Mathematical analysis #Mathematics #Multigrid method #Optics #Partial differential equation #Physics #Physics of Superconductivity and Magnetism #Plane wave #Poisson's equation #Projector #Quantum mechanics #Wave function #cond-mat.mtrl-sci #nanoparticles nucleation surface interactions

paper · pdf · doi:10.1103/physrevb.71.035109

published in Physical Review B 71(3) (American Physical Society) · 13 pages, 3 figures, accepted for publication in Physical Review B

arxiv created 2004/11/09 · openalex publication_date 2005/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

A grid-based real-space implementation of the projector augmented wave (PAW) method of Bl"ochl [Phys. Rev. B 50, 17953 (1994)] for density functional theory (DFT) calculations is presented. The use of uniform three-dimensional (3D) real-space grids for representing wave functions, densities, and potentials allows for flexible boundary conditions, efficient multigrid algorithms for solving Poisson and Kohn-Sham equations, and efficient parallelization using simple real-space domain-decomposition. We use the PAW method to perform all-electron calculations in the frozen core approximation, with smooth valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of 20 small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency is comparable to standard plane-wave methods, but the memory requirements are higher.

Citations

• Projector augmented-wave method
• From ultrasoft pseudopotentials to the projector augmented-wave method
• Generalized Gradient Approximation Made Simple
• Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals
• Real-space full-multigrid study of the fragmentation ofLi11+clusters
• Efficient iterative schemes forab initiototal-energy calculations using a plane-wave basis set
• Soft self-consistent pseudopotentials in a generalized eigenvalue formalism
• Iterative minimization techniques forab initiototal-energy calculations: molecular dynamics and conjugate gradients
• Self-Consistent Equations Including Exchange and Correlation Effects

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