Limit Theorems and Governing Equations for Levy Walks

The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit theorems and derive governing pseudo-differential equations for the law of the walker's position. Both Levy Walk and its limit process are continuous and ballistic in the case beta in (0,1). In the case beta in (1,2), the scaling limit of the process is beta-stable and hence discontinuous. This case exhibits an interesting situation in which scaling exponent 1/beta on the process level is seemingly unrelated to the scaling exponent 3-beta of the second moment. For beta = 2, the scaling limit is Brownian motion

First-principles, atomistic thermodynamics for oxidation catalysis

Present knowledge of the function of materials is largely based on studies (experimental and theoretical) that are performed at low temperatures and ultra-low pressures. However, the majority of everyday applications, like e.g. catalysis, operate at atmospheric pressures and temperatures at or higher than 300 K. Here we employ ab initio, atomistic thermodynamics to construct a phase diagram of surface structures in the (T,p)-space from ultra-high vacuum to technically-relevant pressures and temperatures. We emphasize the value of such phase diagrams as well as the importance of the reaction kinetics that may be crucial e.g. close to phase boundaries.Comment: 4 pages including 2 figure files. Submitted to Phys. Rev. Lett. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

The steady-state of heterogeneous catalysis, studied by first-principles statistical mechanics

The turn-over frequency of the catalytic oxidation of CO at RuO2(110) was calculated as function of temperature and partial pressures using ab initio statistical mechanics. The underlying energetics of the gas-phase molecules, dissociation, adsorption, surface diffusion, surface chemical reactions, and desorption were obtained by all-electron density-functional theory. The resulting CO2 formation rate [in the full (T, p_CO, p_O2)-space], the movies displaying the atomic motion and reactions over times scales from picoseconds to seconds, and the statistical analyses provide insights into the concerted actions ruling heterogeneous catalysis and open thermodynamic systems in general.Comment: 4 pages including 3 figures, Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Electronic properties of lanthanide oxides from the GW perspective

A first-principles understanding of the electronic properties of f -electron systems is currently regarded as a great challenge in condensed-matter physics because of the difficulty in treating both localized and itinerant states on the same footing by the current theoretical approaches, most notably density-functional theory (DFT) in the local-density or generalized gradient approximation (LDA/GGA). Lanthanide sesquioxides (Ln2O3) are typical f -electron systems for which the highly localized f states play an important role in determining their chemical and physical properties. In this paper, we present a systematic investigation of the performance of many-body perturbation theory in the GW approach for the electronic structure of the whole Ln2O3 series. To overcome the major failure of LDA/GGA, the traditional starting point for GW, for f -electron systems, we base our GW calculations on Hubbard U corrected LDA calculations (LDA+U). The influence of the crystal structure, the magnetic ordering, and the existence of metastable states on the electronic band structures are studied at both the LDA+U and the GW level. The evolution of the band structure with increasing number of f electrons is shown to be the origin for the characteristic structure of the band gap across the lanthanide sesquioxide series. A comparison is then made to dynamical mean-field theory (DMFT) combined with LDA or hybrid functionals to elucidate the pros and cons of these different approaches

Strain-Dependence of Surface Diffusion: Ag on Ag(111) and Pt(111)

Using density-functional theory with the local-density approximation and the generalized gradient approximation we compute the energy barriers for surface diffusion for Ag on Pt(111), Ag on one monolayer of Ag on Pt(111), and Ag on Ag(111). The diffusion barrier for Ag on Ag(111) is found to increase linearly with increasing lattice constant. We also discuss the reconstruction that has been found experimentally when two Ag layers are deposited on Pt(111). Our calculations explain why this strain driven reconstruction occurs only after two Ag layers have been deposited.Comment: 4 pages, 3 figures, Phys. Rev. B 55 (1997), in pres

New Perspective on Formation Energies and Energy Levels of Point Defects in Nonmetals

We propose a powerful scheme to accurately determine the formation energy and thermodynamic charge transition levels of point defects in nonmetals. Previously unknown correlations between defect properties and the valence-band width of the defect-free host material are identified allowing for a determination of the former via an accurate knowledge of the latter. These correlations are identified through a series of hybrid density-functional theory computations and an unbiased exploration of the parameter space that defines the Hyde-Scuseria-Ernzerhof family of hybrid functionals. The applicability of this paradigm is demonstrated for point defects in Si, Ge, ZnO, and ZrO2

First-principles modeling of localized d states with the GW@LDA+U approach

First-principles modeling of systems with localized d states is currently a great challenge in condensed-matter physics. Density-functional theory in the standard local-density approximation (LDA) proves to be problematic. This can be partly overcome by including local Hubbard U corrections (LDA+U) but itinerant states are still treated on the LDA level. Many-body perturbation theory in the GW approach offers both a quasiparticle perspective (appropriate for itinerant states) and an exact treatment of exchange (appropriate for localized states), and is therefore promising for these systems. LDA+U has previously been viewed as an approximate GW scheme. We present here a derivation that is simpler and more general, starting from the static Coulomb-hole and screened exchange approximation to the GW self-energy. Following our previous work for f-electron systems [H. Jiang, R.I. Gomez-Abal, P. Rinke, and M. Scheffler, Phys. Rev. Lett. 102, 126403 (2009)] we conduct a systematic investigation of the GW method based on LDA+U(GW@LDA+U), as implemented in our recently developed all-electron GW code FHI-gap (Green’s function with augmented plane waves) for a series of prototypical d-electron systems: (1) ScN with empty d states, (2) ZnS with semicore d states, and (3) late transition-metal oxides (MnO, FeO, CoO, and NiO) with partially occupied d states. We show that for ZnS and ScN, the GW band gaps only weakly depend on U but for the other transition-metal oxides the dependence on U is as strong as in LDA+U. These different trends can be understood in terms of changes in the hybridization and screening. Our work demonstrates that GW@LDA+U with "physical" values of U provides a balanced and accurate description of both localized and itinerant states

Electronic band structure of zirconia and hafnia polymorphs from the GW perspective

The electronic structure of crystalline ZrO2 and HfO2 in the cubic, tetragonal, and monoclinic phase has been investigated using many-body perturbation theory in the GW approach based on density-functional theory calculations in the local-density approximation (LDA). ZrO2 and HfO2 are found to have very similar quasiparticle band structures. Small differences between them are already well described at the LDA level indicating that the filled f shell in HfO2 has no significant effect on the GW corrections. A comparison with direct and inverse photoemission data shows that the GW density of states agrees very well with experiment. A systematic investigation into the structural and morphological dependence of the electronic structure reveals that the internal displacement of the oxygen atoms in the tetragonal phase has a significant effect on the band gap

Jahn-Teller stabilization of a "polar" metal oxide surface: Fe3O4(001)

Using ab initio thermodynamics we compile a phase diagram for the surface of Fe3O4(001) as a function of temperature and oxygen pressures. A hitherto ignored polar termination with octahedral iron and oxygen forming a wave-like structure along the [110]-direction is identified as the lowest energy configuration over a broad range of oxygen gas-phase conditions. This novel geometry is confirmed in a x-ray diffraction analysis. The stabilization of the Fe3O4(001)-surface goes together with dramatic changes in the electronic and magnetic properties, e.g., a halfmetal-to-metal transition.Comment: 4 pages, 4 figure