We construct hybrid functionals in a nonempirical way by fixing the fraction of Fock exchange through either the long-range screening or the generalized Koopmans' condition applied to defect charge-transition levels. These functionals not only give band gaps of solids as accurate as state-of-the-art GW calculations, but are also capable of describing polaronic distortions. The Koopmans' condition is found to be satisfied across a series of defects, to the point of achieving accurate band gaps through a hydrogen probe. Extension to range-separated functionals demonstrates the robustness of the present approach.

One of the big challenges of theoretical condensed-matter physics is the description, understanding, and prediction of the effects of the Coulomb interaction on materials properties. In electronic spectra, the Coulomb interaction causes a renormalization of energies and change of spectral weight. Most importantly, it can lead to new structures, often called satellites. These can be linked to the coupling of excitations, also termed dynamical effects. State-of-the-art methods in the framework of many-body perturbation theory, in particular, the widely used GW approximation, often fail to describe satellite spectra. Instead, approaches based on a picture of electron-boson coupling such as the cumulant expansion are promising for the description of plasmon satellites. In this work, we give a unified derivation of the GW approximation and the cumulant expansion for the one-body Green's function. Using the example of bulk sodium, we compare the resulting spectral functions both in the valence and in the core region, and we discuss the dispersion of quasi-particles and satellites. We show that self-consistency is crucial to obtain meaningful results, in particular, at large binding energies. Very good agreement with experiment is obtained when the intrinsic spectral function is corrected for extrinsic and interference effects. Finally, we sketch how one can approach the problem in the case of the two-body Green's function, and we discuss the cancellation of various dynamical effects that occur in that case.

We investigate the temporal evolution of the electronic states at the bismuth (111) surface by means of time- and angle-resolved photoelectron spectroscopy. The binding energy of bulklike bands oscillates with the frequency of the A(1g) phonon mode, whereas surface states are insensitive to the coherent displacement of the lattice. A strong dependence of the oscillation amplitude on the electronic wave vector is correctly reproduced by ab initio calculations of electron-phonon coupling. Besides these oscillations, all the electronic states also display a photoinduced shift towards higher binding energy whose dynamics follows the evolution of the electronic temperature.

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Copper vanadates have been proposed as promising photoanodes for water-splitting photoelectrochemical cells, but their performance has recently been shown to be severely limited. To understand this behavior, we study the electronic structure and the optical properties of β-CuVO both experimentally and computationally. The measured absorption spectrum shows an absorption peak at 1.5 eV followed by the onset of an apparent continuum at 2.26 eV, as generally found for this class of materials. We perform calculations within the framework of the QS GW̃ method and the Bethe-Salpeter equation while including effects of magnetic ordering, nuclear quantum motion, and thermal vibrations. We demonstrate the occurrence of two kinds of excitons with high binding energies upon optical excitation in β-CuVO, which account for the first absorption peak and the lower edge of the apparent continuum. The results are confirmed by photoluminescence measurements, where sub-band-gap emissions are found for both excitons. These results provide an explanation for the low photocatalytic efficiencies of copper vanadates, despite the favorable size of their optical band gaps.

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We present first-principles calculations of the electronic structure of BiVO 4 at various levels of theory. In the calculations, we take into account a series of effects that affect the band gap, i.e., spin-orbit coupling, electron-hole interaction, nuclear quantum motions, and thermal vibrations. All these effects lead to a significant renormalization of the band gap. After including the relevant corrections, the values achieved with the GW level of theory closely match the experiment. Additionally, by treating excitonic effects through the Bethe-Salpeter equation, we obtain an optical band gap and an absorption spectrum in good agreement with experimental data. Through the calculation of Tauc plots, we show that this technique gives the optical band gap within about 0.14 eV, but argue that it is unable to distinguish between direct and indirect bad gaps in the case of BiVO 4 .

The dynamic structure factor of materials is proportional to their linear electronic response and it displays their excitation spectra. Usually the response is measured on the same length scale as the perturbation. Here, we illustrate that much can be gained by studying also the mixed dynamic structure factor, which connects different spatial components of perturbation and response. We extend state-of-the-art ab initio calculations to access the mixed dynamic structure factor, including excitonic effects. Using bulk silicon and lithium fluoride as prototype examples, we show that these effects play a crucial role above and below the quasiparticle gap, and are needed in order to explain coherent inelastic x-ray scattering experiments. Our approach also yields important information concerning the microscopic structure of time-dependent density functional theory.