Self-interaction in Green's-function theory of the hydrogen atom

Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation-theory (MBPT) in Hedin's GW approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the GW self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for GW and show that the self-interaction part of the GW self-energy, while non-zero, is small. The effect of calculating the GW self-energy from exact wavefunctions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating

Ultrathin oxides: bulk-oxide-like model surfaces or unique films?

To better understand the electronic and chemical properties of wide-gap oxide surfaces at the atomic scale, experimental work has focused on epitaxial films on metal substrates. Recent findings show that these films are considerably thinner than previously thought. This raises doubts about the transferability of the results to surface properties of thicker films and bulk crystals. By means of density-functional theory and approximate GW corrections for the electronic spectra we demonstrate for three characteristic wide-gap oxides (silica, alumina, and hafnia) the influence of the substrate and highlight critical differences between the ultrathin films and surfaces of bulk materials. Our results imply that monolayer-thin oxide films have rather unique properties.Comment: 5 pages, 3 figures, accepted by PR

Vertex corrections in localized and extended systems

Within many-body perturbation theory we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a DFT-LDA Green's function. The vertex appears in two places -- in the screened Coulomb interaction, W, and in the self-energy, \Sigma -- and we obtain a systematic discrimination of these two effects by turning the vertex in \Sigma on and off. We also make comparisons to standard GW results within the usual random-phase approximation (RPA), which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate only limited improvements over standard GW. For jellium we observe marked improvement in the quasiparticle band width when the vertex is included only in W, whereas turning on the vertex in \Sigma leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in \Sigma is unphysical, and points the way to development of improved vertices for ab initio electronic structure calculations.Comment: 8 Pages, 6 Figures. Updated with quasiparticle neon results, extended conclusions and references section. Minor changes: Updated references, minor improvement

Large-scale surface reconstruction energetics of Pt(100) and Au(100) by all-electron DFT

The low-index surfaces of Au and Pt all tend to reconstruct, a fact that is of key importance in many nanostructure, catalytic, and electrochemical applications. Remarkably, some significant questions regarding their structural energies remain even today, in particular for the large-scale quasihexagonal reconstructed (100) surfaces: Rather dissimilar reconstruction energies for Au and Pt in available experiments, and experiment and theory do not match for Pt. We here show by all-electron density-functional theory that only large enough "(5 x N)" approximant supercells capture the qualitative reconstruction energy trend between Au(100) and Pt(100), in contrast to what is often done in the theoretical literature. Their magnitudes are then in fact similar, and closer to the measured value for Pt(100); our calculations achieve excellent agreement with known geometric characteristics and provide direct evidence for the electronic reconstruction driving force.Comment: updated version - also includes EPAPS information as auxiliary file; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Image states in metal clusters

The existence of image states in small clusters is shown, using a quantum-mechanical many-body approach. We present image state energies and wave functions for spherical jellium clusters up to 186 atoms, calculated in the GW approximation, where G is the Green's function and W is the dynamically screened Coulomb interaction, which by construction contains the dynamic long-range correlation effects that give rise to image effects. In addition, we find that image states are also subject to quantum confinement. To extrapolate our investigations to clusters in the mesoscopic size range, we propose a semiclassical model potential, which we test against our full GW results

How Combining Terrorism, Muslim, and Refugee Topics Drives Emotional Tone in Online News: A Six-Country Cross-Cultural Sentiment Analysis

This study looks into how the combination of Islam, refugees, and terrorism topics leads to text-internal changes in the emotional tone of news articles and how these vary across countries and media outlets. Using a multilingual human-validated sentiment analysis, we compare fear and pity in more than 560,000 articles from the most important online news sources in six countries (U.S., Australia, Germany, Switzerland, Turkey, and Lebanon). We observe that fear and pity work antagonistically—that is, the more articles in a particular topical category contain fear, the less pity they will feature. The coverage of refugees without mentioning terrorists and Muslims/Islam featured the lowest fear and highest pity levels of all topical categories studied here. However, when refugees were covered in combination with terrorism and/or Islam, fear increased and pity decreased in Christian-majority countries, whereas no such pattern appeared in Muslim-majority countries (Lebanon, Turkey). Variations in emotions are generally driven more by country-level differences than by the political alignment of individual outlets

Defect Formation Energies without the Band-Gap Problem: Combining DFT and GW for the Silicon Self-Interstitial

We present an improved method to calculate defect formation energies that overcomes the band-gap problem of Kohn-Sham density-functional theory (DFT) and reduces the self-interaction error of the local-density approximation (LDA) to DFT. We demonstrate for the silicon self-interstitial that combining LDA with quasiparticle energy calculations in the G0W0 approach increases the defect formation energy of the neutral charge state by ~1.1 eV, which is in good agreement with diffusion Monte Carlo calculations (E. R. Batista et al. Phys. Rev. B 74, 121102(R) (2006), W.-K. Leung et al. Phys. Rev. Lett. 83, 2351 (1999)). Moreover, the G0W0-corrected charge transition levels agree well with recent measurements.Comment: 4 pages including 3 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Image resonance in the many-body density of states at a metal surface

The electronic properties of a semi-infinite metal surface without a bulk gap are studied by a formalism that is able to account for the continuous spectrum of the system. The density of states at the surface is calculated within the GW approximation of many-body perturbation theory. We demonstrate the presence of an unoccupied surface resonance peaked at the position of the first image state. The resonance encompasses the whole Rydberg series of image states and cannot be resolved into individual peaks. Its origin is the shift in spectral weight when many-body correlation effects are taken into account