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

We model a Kohn-Sham potential with a discontinuity at integer particle numbers derived from the GLLB approximation of Gritsenko et al. We evaluate the Kohn-Sham gap and the discontinuity to obtain the quasiparticle gap. This allows us to compare the Kohn-Sham gaps to those obtained by accurate many-body perturbation theory based optimized potential methods. In addition, the resulting quasiparticle band gap is compared to experimental gaps. In the GLLB model potential, the exchange-correlation hole is modeled using a GGA energy density and the response of the hole to density variations is evaluated by using the common-denominator approximation and homogeneous electron gas based assumptions. In our modification, we have chosen the PBEsol potential as the GGA to model the exchange hole, and add a consistent correlation potential. The method is implemented in the GPAW code, which allows efficient parallelization to study large systems. A fair agreement for Kohn-Sham and the quasiparticle band gaps with semiconductors and other band gap materials is obtained with a potential which is as fast as GGA to calculate.

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An azobenzene molecule Disperse Red 1 with strongly delocalised frontier orbitals has been studied with a number of density-functional theory (DFT) related approaches. The purpose is twofold: to interpret observed photoabsorption and to compare the performance of various DFT-based approximations. The planarity of the vacuum conformation of the lower energy trans conformation is found to be significantly distorted when transformed to the higher energy cis conformation, and both isomers are found to absorb in the experimentally observed wavelengths in solutions. A common feature in both is essentially forbidden lowest energy absorption because of a negligible overlap of HOMO and LUMO due to symmetry unmatch. We find the time-dependent DFT to be the best approach for quantitative evaluation of photoabsorption energies and intensities, whereas Kohn-Sham eigenenergies and orbitals give good description only qualitatively. Isomerisation and dimerisation energetics have also been evaluated, and trans dimers have found to be up to 1 eV per molecule more stable than single molecules.

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