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.

Various schemes for correcting the finite-size supercell errors in the case of charged defect calculations are analyzed and their performance for a series of defect systems is compared. We focus on the schemes proposed by Makov and Payne (MP), Freysoldt, Neugebauer, and Van de Walle (FNV), and Lany and Zunger (LZ). The role of the potential alignment is also assessed. We demonstrate a connection between the defect charge distribution and the potential alignment, which establishes a relation between the MP and FNV schemes. Calculations are performed using supercells of various sizes and the corrected formation energies are compared to the values obtained by extrapolation to infinitely large supercells. For defects with localized charge distributions, we generally find that the FNV scheme improves upon the LZ one, while the MP scheme tends to overcorrect except for point-charge-like defects. We also encountered a class of defects, for which all the correction schemes fail to produce results consistent with the extrapolated values. This behavior is found to be caused by partial delocalization of the defect charge. We associate this effect to hybridization between the defect state and the band-edge states of the host. The occurrence of defect charge delocalization also reflects in the evolution of the defect Kohn-Sham levels with increasing supercell size. We discuss the physical relevance of the latter class of defects.

We model a Kohn-Sham potential with the discontinuity at integer particle numbers starting from the approximation by (GLLB) Gritsenko et al. [Phys. Rev. A 51, 1944 (1995)]. 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 generalized gradient approximation (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.

We observe using ab initio methods that localized surface plasmon resonances in icosahedral silver nanoparticles enter the asymptotic region already between diameters of 1 and 2 nm, converging close to the classical quasistatic limit around 3.4 eV. We base the observation on time-dependent density-functional theory simulations of the icosahedral silver clusters ${\mathrm{Ag}}_{55}\left(1.06\mathrm{nm}\right)$, ${\mathrm{Ag}}_{147}\left(1.60\mathrm{nm}\right)$, ${\mathrm{Ag}}_{309}\left(2.14\mathrm{nm}\right)$, and ${\mathrm{Ag}}_{561}(2.68 \mathrm{nm})$. The simulation method combines the adiabatic GLLB–SC exchange-correlation functional with real time propagation in an atomic orbital basis set using the projector-augmented wave method. The method has been implemented for the electron structure code GPAW within the scope of this work. We obtain good agreement with experimental data and modeled results, including photoemission and plasmon resonance. Moreover, we can extrapolate the ab initio results to the classical quasistatically modeled icosahedral clusters.

Theoretical consideration of recently proposed ordered stoichiometric and oxygen-deficient (110) surfaces of ${\mathrm{SnO}}_2$ crystal with $1\times 1,$ $1\times 2,$ $2\times 1,$ and $1\times 4$ symmetries have been done. We use a first-principles density-functional method and plane-wave basis, combined with pseudopotentials to calculate surface electronic structures, surface geometries, and energetics. Calculated surface formation energies suggest that stability of the oxygen-deficient surfaces decrease with increasing oxygen deficiency. At oxygen-deficient $1\times 2$ and $1\times 4$ surfaces tin atoms similar to those in SnO crystal were found to appear. In all cases, the highest occupied orbitals were considerably localized at the sites of surface oxygen vacancies. The $2\times 1$ added row surface structures were found to be relatively stable and associated with the decrease of the band gap due to jagged surface. Also, ultraviolet optical absorption coefficients for different surface structures were determined by using the electric dipole approximation with a scissor correction.