Real-space grid implementation of the projector augmented wave method

TLDR

The projector augmented wave (PAW) method, originally developed by Blöchl, is a widely used approach in density functional theory that can be implemented on real‑space grids. This work presents a grid‑based real‑space implementation of the PAW method for density functional theory calculations. The implementation employs uniform three‑dimensional real‑space grids to represent wave functions, densities, and potentials, enabling flexible boundary conditions, efficient multigrid solutions of Poisson and Kohn‑Sham equations, and simple domain‑decomposition parallelization, while using the PAW frozen‑core approximation with smooth valence wave functions on relatively coarse grids. The method accurately reproduces atomization energies of 20 small molecules and bulk properties of aluminum, and its computational efficiency is comparable to plane‑wave approaches, though it requires more memory.

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.