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.

Small-angle X-ray scattering (SAXS) is used to demonstrate the presence of density fluctuations in ambient water on a physical length-scale of ≈1 nm; this is retained with decreasing temperature while the magnitude is enhanced. In contrast, the magnitude of fluctuations in a normal liquid, such as CCl ₄ , exhibits no enhancement with decreasing temperature, as is also the case for water from molecular dynamics simulations under ambient conditions. Based on X-ray emission spectroscopy and X-ray Raman scattering data we propose that the density difference contrast in SAXS is due to fluctuations between tetrahedral-like and hydrogen-bond distorted structures related to, respectively, low and high density water. We combine our experimental observations to propose a model of water as a temperature-dependent, fluctuating equilibrium between the two types of local structures driven by incommensurate requirements for minimizing enthalpy (strong near-tetrahedral hydrogen-bonds) and maximizing entropy (nondirectional H-bonds and disorder). The present results provide experimental evidence that the extreme differences anticipated in the hydrogen-bonding environment in the deeply supercooled regime surprisingly remain in bulk water even at conditions ranging from ambient up to close to the boiling point.

We present a scheme to construct model potentials, with parameters computed from first principles, for large-scale lattice-dynamical simulations of materials. We mimic the traditional solid-state approach to the investigation of vibrational spectra, i.e., we start from a suitably chosen reference configuration of the compound and describe its energy as a function of arbitrary atomic distortions by means of a Taylor series. Such a form of the potential-energy surface is general, trivial to formulate for any material, and physically transparent. Further, such models involve clear-cut approximations, their precision can be improved in a systematic fashion, and their simplicity allows for convenient and practical strategies to compute/fit the potential parameters. We illustrate our scheme with two challenging cases in which the model potential is strongly anharmonic, namely, the ferroic perovskite oxides PbTiO3 and SrTiO3. Studying these compounds allows us to better describe the connection between the so-called effective-Hamiltonian method and ours (which may be seen as an extension of the former), and to show the physical insight and predictive power provided by our approach-e.g., we present new results regarding the factors controlling phase-transition temperatures, novel phase transitions under elastic constraints, an improved treatment of thermal expansion, etc.

We use the reverse Monte Carlo modeling technique to fit two extreme structure models for water to available x-ray and neutron diffraction data in q space as well as to the electric field distribution as a representation of the OH stretch Raman spectrum of dilue HOD in D2O; the internal geometries were fitted to a quantum distribution. Forcing the fit to maximize the number of hydrogen (H) bonds results in a tetrahedral model with 74% double H-bond donors (DD) and 21% single donors (SD). Maximizing instead the number of SD species gives 81% SD and 18% DD, while still reproducing the experimental data and losing only 0.7–1.8 kJ/mole interaction energy. By decomposing the simulated Raman spectrum we can relate the models to the observed ultrafast frequency shifts in recent pump-probe measurements. Within the tetrahedral DD structure model the assumed connection between spectrum position and H-bonding indicates ultrafast dynamics in terms of breaking and reforming H bonds while in the strongly distorted model the observed frequency shifts do not necessarily imply H-bond changes. Both pictures are equally valid based on present diffraction and vibrational experimental data. There is thus no strict proof of tetrahedral water based on these data. We also note that the tetrahedral structure model must, to fit diffraction data, be less structured than most models obtained from molecular dynamics simulations.

X-ray photoelectron spectroscopy (XPS) is a widely used tool for studying the chemical composition of materials and it is a standard technique in surface science and technology. XPS is particularly useful for characterizing nanostructures such as carbon nanomaterials due to their reduced dimensionality. In order to assign the measured binding energies to specific bonding environments, reference energy values need to be known. Experimental measurements of the core level signals of the elements present in novel materials such as graphene have often been compared to values measured for molecules, or calculated for finite clusters. Here we have calculated core level binding energies for variously functionalized or defected graphene by delta Kohn–Sham total energy differences in the real-space grid-based projector-augmented wave density functional theory code (GPAW). To accurately model extended systems, we applied periodic boundary conditions in large unit cells to avoid computational artifacts. In select cases, we compared the results to all-electron calculations using an ab initio molecular simulations (FHI-aims) code. We calculated the carbon and oxygen 1s core level binding energies for oxygen and hydrogen functionalities such as graphane-like hydrogenation, and epoxide, hydroxide and carboxylic functional groups. In all cases, we considered binding energy contributions arising from carbon atoms up to the third nearest neighbor from the functional group, and plotted C 1s line shapes by using experimentally realistic broadenings. Furthermore, we simulated the simplest atomic defects, namely single and double vacancies and the Stone–Thrower–Wales defect. Finally, we studied modifications of a reactive single vacancy with O and H functionalities, and compared the calculated values to data found in the literature.