Electronic structure calculations with GPAW: a real-space implementation of the projectoraugmented-wave method

Abstract

Electronic structure calculations have become an indispensable tool in many areas ofmaterials science and quantum chemistry. Even though the Kohn–Sham formulation of thedensity-functional theory (DFT) simplifies the many-body problem significantly, one is stillconfronted with several numerical challenges. In this article we present the projectoraugmented-wave (PAW) method as implemented in the GPAW program package(https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representationof the electronic wavefunctions. Compared to more traditional plane wave orlocalized basis set approaches, real-space grids offer several advantages, mostnotably good computational scalability and systematic convergence properties.However, as a unique feature GPAW also facilitates a localized atomic-orbitalbasis set in addition to the grid. The efficient atomic basis set is complementaryto the more accurate grid, and the possibility to seamlessly switch between thetwo representations provides great flexibility. While DFT allows one to studyground state properties, time-dependent density-functional theory (TDDFT)provides access to the excited states. We have implemented the two commonformulations of TDDFT, namely the linear-response and the time propagation schemes.Electron transport calculations under finite-bias conditions can be performed withGPAW using non-equilibrium Green functions and the localized basis set. Inaddition to the basic features of the real-space PAW method, we also describe theimplementation of selected exchange–correlation functionals, parallelization schemes,ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.