A real-space grid implementation of the Projector Augmented Wave method

TL;DR

This paper introduces a grid-based real-space implementation of the PAW method for DFT, enabling flexible boundary conditions and efficient parallelization, with accuracy validated on molecules and bulk aluminum.

Contribution

It presents a novel real-space grid implementation of the PAW method, improving flexibility and parallelization in DFT calculations.

Findings

Accurate atomization energies for twenty small molecules.

Correct bulk modulus and lattice constants for aluminum.

Comparable computational efficiency to plane-wave methods.

Abstract

A grid-based real-space implementation of the Projector Augmented Wave (PAW) method of P. E. Blochl [Phys. Rev. B 50, 17953 (1994)] for Density Functional Theory (DFT) calculations is presented. The use of uniform 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 twenty 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.