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 experimental methods based on positron annihilation have evolved into important tools for researching the structure and properties of condensed matter. In particular, positron techniques are useful for the investigation of defects in solids and for the investigation of solid surfaces. Experimental methods need a comprehensive theory for a deep, quantitative understanding of the results. In the case of positron annihilation, the relevant theory includes models needed to describe the positron states as well as the different interaction processes in matter. In this review the present status of the theory of positrons in solids and on solid surfaces is given. The review consists of three main parts describing (a) the interaction processes, {b) the theory and methods for calculating positron states, and {c)selected recent results of positron studies of condensed matter. CONTENTS

An expression is derived for the total energy of a system of interacting atoms based on an ansatz for the total electron density of the system as a superposition of atom densities taken from calculations for the atoms embedded in a homogeneous electron gas. This leads to an expression for the interaction energy in terms of the embedding energy of the atoms in a homogeneous electron gas, and corrections accounting, for instance, for the d-d hybridization in the transition metals. The density of the homogeneous electron gas is chosen as the average of the density from the surrounding atoms. Due to the variational property of the total-energy functional, the errors in the interaction energy are second order in the deviation of the ansatz density from the true ground-state value. The applicability of the approach is illustrated by calculations of the cohesive properties of some simple metals and all the 3d transition metals. The interaction energy can be expressed in a form simple enough to allow calculations for low-symmetry systems and is very well suited for simulations of time-dependent and finite-temperature problems. Preliminary results for the phonon-dispersion relations and the surface energies and relaxations for Al are used to illustrate the versatility of the approach. The division of the total energy into a density-dependent part, an electrostatic "pairpotential" part, and a hybridization part provides a very simple way of understanding a number of these phenomena.

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A theory for calculating the momentum distribution of annihilating positron-electron pairs in solids is presented. To test the theory, momentum distributions are measured by the Doppler broadening of the annihilation radiation for several bulk metals and semiconductors, as well as for semiconductor alloys and for positrons trapped at vacancies in semiconductors. The theory is based on a two-particle description of the annihilating electron-positron pair. Then, the electron-positron correlation effects, i.e., the enhancement of the electron density at the positron, depend on the electronic state in question. The theory is suited for calculating the high-momentum part of the annihilation spectrum that arises from the core electrons and which can be measured by the Doppler broadening using coincidence techniques. The ideas of the theory are justified by a good agreement between theory and experiment in the case of positron annihilation in undefected bulk lattices. Moreover, the comparison of the theoretical and experimental spectra for alloys and vacancy defects tests the theoretical description for the positron distribution in delocalized and localized states, respectively. ͓S0163-1829͑96͒04327-5͔

Articles you may be interested inMixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry J. Chem. Phys. 129, 124108 (2008) We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born-Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method.

The efficiency of Cu­(In,Ga)­Se2 (CIGS)-based solar cells can be markedly improved by controlled introduction of alkali metal (AM) atoms using post-deposition treatment (PDT) after CIGS growth. Previous studies have indicated that AM atoms may act as impurities or agglomerate into secondary phases. To enable further progress, understanding of atomic level processes responsible for these improvements is required. To this end, we have investigated theoretically the effects of the AM elements Li, Na, K, Rb, and Cs on the properties of the parent material CuInSe2. First, the effects of the AM impurities in CuInSe2 have been investigated in terms of formation energies, charge transition levels, and migration energy barriers. We found that AM atoms preferentially substitute for Cu atoms at the neutral charge state. Under In-poor conditions, AM atoms at the In site also show low formation energies and are acceptors. The migration energy barriers show that the interstitial diffusion mechanism may be relevant only for Li, Na, and K, whereas all the AM atoms can diffuse with the help of Cu vacancies. The competition between these two mechanisms strongly depends on the concentration of Cu vacancies. We also discuss how AM atoms can contribute to increasing Cu-depleted regions. Second, AM atoms can form secondary phases with Se and In atoms. We suggest a mechanism for the secondary phase formation following the PDT process. On the basis of the calculated reaction enthalpies and migration considerations, we find that mixed phases are more likely in the case of LiInSe2 and NaInSe2, whereas formation of secondary phases is expected for KInSe2, RbInSe2, and CsInSe2. We discuss our findings in the light of experimental results obtained for AM treatments. The secondary phases have large energy band gaps and improve the morphology of the buffer surface by enabling a favorable band alignment, which can improve the electrical properties of the device. Moreover, they can also passivate the surface by forming a diffusion barrier. Overall, our work points to different roles played by the light and heavy AM atoms and suggests that both types may be needed to maximize their benefits on the solar cell performance.

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